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		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32104</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32104"/>
		<updated>2018-04-19T03:08:26Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|600px]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg|600px]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32097</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32097"/>
		<updated>2018-04-19T03:06:38Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|600px]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32095</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32095"/>
		<updated>2018-04-19T03:06:11Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|400px]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32085</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32085"/>
		<updated>2018-04-19T03:02:58Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|300px]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|300px]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|300px]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|300px]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32075</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32075"/>
		<updated>2018-04-19T03:01:29Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|150px]]&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32069</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32069"/>
		<updated>2018-04-19T02:59:38Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|50px]]&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32067</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32067"/>
		<updated>2018-04-19T02:59:09Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|10px]]&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32064</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32064"/>
		<updated>2018-04-19T02:57:08Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|frame|50px]]&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32062</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=32062"/>
		<updated>2018-04-19T02:55:52Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is found throughout science, technology, engineering, and mathematics. In fact, it is a defining principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
To understand this law more fully, one can look at the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area. This is the basis for the equation ф=∮E da. When you integrate the change of A, you get the flux. &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg]]&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 4: In this example, the Qenc is equal to zero. This was determined by adding up all of the fluxes through every surface. This can also be determined by seeing that the same fluxes travel through the same areas of the tent. The equation Ф=∮B da=0 helps explain this when considering that Ф is the same in both equations.   &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss&#039;s_Law1234.jpeg]]&lt;br /&gt;
&lt;br /&gt;
== Headline text ==&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law can be found in many areas of science, technology, engineering, and mathematics. In fact, Gauss&#039;s Law and  other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. This distribution is found throughout statistics and probability and is used everyday by people in STEM fields. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29. &lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
Additional to many engineering majors. Gauss&#039;s Law has applications in many different STEM job fields. Engineering majors learn about the different Gaussian laws in college and apply them in there jobs. Millions of people are applying his laws to the world and will continue to do so. Gauss has had a huge impact on the world and will continue to have a big impact on the future. Gauss has done great work with his work.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31836</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31836"/>
		<updated>2018-04-19T00:47:41Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Intermediate Examples:&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31835</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31835"/>
		<updated>2018-04-19T00:47:06Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31834</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31834"/>
		<updated>2018-04-19T00:46:10Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: /* Examples */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31829</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31829"/>
		<updated>2018-04-19T00:41:30Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|500px|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
Example 3: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31825</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31825"/>
		<updated>2018-04-19T00:40:18Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018; Claimed by Patricia Estrada Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|500px|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Example 3: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31820</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31820"/>
		<updated>2018-04-19T00:37:34Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|500px|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Example 3: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31817</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31817"/>
		<updated>2018-04-19T00:36:46Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|500px|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_Example_1.jpeg]]&lt;br /&gt;
&lt;br /&gt;
Example 1: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Example 3: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=File:IMG_1031.jpg&amp;diff=31808</id>
		<title>File:IMG 1031.jpg</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=File:IMG_1031.jpg&amp;diff=31808"/>
		<updated>2018-04-19T00:33:58Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31784</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31784"/>
		<updated>2018-04-19T00:24:30Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
&lt;br /&gt;
Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|500px|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Example 3: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist. He contributed to a wide variety of fields especially in mathematical and scientific study. In fact his contributions are so great that he is referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  These names highlight his illustriousness in those fields as he is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31762</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31762"/>
		<updated>2018-04-19T00:15:50Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
 1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|500px|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Example 3: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist who contributed notably to a wide variety of fields regarding mathematical and scientific study. He has been referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  He is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31761</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31761"/>
		<updated>2018-04-19T00:15:16Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
 1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|Gauss for]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|500px|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Example 3: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist who contributed notably to a wide variety of fields regarding mathematical and scientific study. He has been referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  He is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31760</id>
		<title>Gauss&#039;s Law</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Gauss%27s_Law&amp;diff=31760"/>
		<updated>2018-04-19T00:13:24Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Charu Thomas (SPRING 2017)&#039;&#039;&#039; Claimed by Lin Htet Kyaw FALL 2017; Claimed by Ishita Mathur Spring 2018; Claimed by Eric Salisbury Spring 2018&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is physical principal in electromagnetism. It was first discovered by Joseph-Louis Lagrange in 1773 and furthered by Carl Friedrich Gauss in 1813. At it&#039;s core, it describes the relationship between charges and electric flux. The Law presents that the  net electric flux outside a surface is equal to the charge inside the surface over the constant permittivity of space. In equation form it looks like, Φ=Q/εₒ. In addition, this law also relates the integral over Electric field enclosed multiplied by the change in area to net electric flux outside a surface. In equation form this looks like Φ=∮E*dA. This monumental discovery has been the foundation for current physics for over 200 years. &lt;br /&gt;
&lt;br /&gt;
Additionally, Coulomb&#039;s Law and Gauss&#039;s Law are innately connected. Coulomb&#039;s Law relates charge to electric field. Gauss&#039;s Law relates charge to electric flux. Both laws, relate charge to an electrical property. For clarification, the electric flux is a quantity that is equal to the product of the perpendicular component of E-field and the area of the closed surface. Not only do these two laws look similar at the surface, but using one law it is quite easy to derive the other law. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
&lt;br /&gt;
We know from the previous introduction of flux that there is a relationship between the electric flux on a closed surface and the charges inside the surface. However, we would like to figure out what that particular factor is. &lt;br /&gt;
&lt;br /&gt;
We start by considering a point charge of +Q enclosed by an imaginary spherical shell.&lt;br /&gt;
&lt;br /&gt;
[[File:gaussv2212.jpg]]&lt;br /&gt;
&lt;br /&gt;
Everywhere on the imaginary shell, the electric field produced is parallel to the normal unit vector. Cos(0) = 1, so the dot product evaluates to the magnitude of the electric field. Recall that the surface area of the imaginary sphere is 4*pi*r^2. With Coulomb&#039;s Law and the surface area of a sphere, we get that electric flux is equal to +Q/ε0. This implies that the factor is 1/ε0.&lt;br /&gt;
&lt;br /&gt;
Note that if the point charge was negative, the electric field would still be parallel, just opposite direction. Cos(180) = -1 so the dot product would be -1 times the magnitude of the electric field.&lt;br /&gt;
&lt;br /&gt;
To summarize, the idea of Gauss&#039;s Law is that the electric flux out of a closed surface is equivalent to the charge enclosed, divided by the permittivity.  &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
&lt;br /&gt;
A very helpful and clear summary of this Law can be found in the diagram below.  As can be seen on the left side of this diagram, change in flux equals electric field multiplied by change in area.  &lt;br /&gt;
&lt;br /&gt;
Image Taken from Hyperphysics &lt;br /&gt;
&lt;br /&gt;
[[File:Gaulaw.gif]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To more clearly state it, in integral form, the formula for this Law is the electric flux equals the total charge contained by a closed surface, divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1). &lt;br /&gt;
&lt;br /&gt;
[[File:Adc2dff3156800a39ef0a9df76a7d868.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Additionally, Gauss&#039;s law can be written in differential form. &lt;br /&gt;
&lt;br /&gt;
[[File:Screen Shot 2018-04-18 at 5.31.54 PM.png]]&lt;br /&gt;
&lt;br /&gt;
In this equation, ρ is electric charge density, ∇*E is divergence of electric field, and ε0 = 8.854187817...×10−12 F⋅m−1. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The picture below illustrates Gauss&#039;s Law with a detailed explanation.&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_14.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Easy Example&#039;&#039;&#039;&lt;br /&gt;
[[File:IMG_1031.jpg]]&lt;br /&gt;
&lt;br /&gt;
Looking at the images on the right hand side of the screen, we find an easy example in which we will find the electric field in a uniformly charged plate (+Q). &lt;br /&gt;
 1. Recall Gauss&#039;s Formula:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss for.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
2. Now look carefully at the diagram below and go through each of the surfaces one by one. Ask yourself, in what direction does the normal vector point?&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ex.jpg|400px|thumb|Gauss ex]]&lt;br /&gt;
&lt;br /&gt;
3. Therefore, in the sides where there is 90 degree angle made with E, the flux will just be zero!&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss fl.jpg|thumb|Gauss formula]]&lt;br /&gt;
&lt;br /&gt;
4. In the only case where the flux is not zero is in the sides A and B of the box (which are the same in magnitude). We compute the flux as follows:&lt;br /&gt;
&lt;br /&gt;
[[File:Gauss ans.jpg|500px|thumb|Gauss ans]]&lt;br /&gt;
&lt;br /&gt;
Remember, when doing Gauss&#039;s problems, always think about you n vector before diving into the formula. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intermediate Examples:&lt;br /&gt;
&lt;br /&gt;
Example 1: In order to apply Gauss&#039;s Law, it is important to be certain you are working with a closed surface, then set electric flux equal to the internal field divided by the permittivity (epsilon naught: ε0 = 8.854187817...×10−12 F⋅m−1).  An example of this Law being applied can be found below. &lt;br /&gt;
&lt;br /&gt;
[[File:Gauss_law3.png]]&lt;br /&gt;
&lt;br /&gt;
Example 2: The example below shows how to calculate the net charge enclosed by a box.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource2.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Example 3: The example below shows how to determine the net charge located inside a box and is fundamental to understanding Gauss&#039;s Law. It demonstrates the idea that to calculate the net charge inside a box, we have to start off by calculating the fluxes acting on all surfaces on the box by using the Gauss&#039;s Law.&lt;br /&gt;
&lt;br /&gt;
[[File:Wiki resource.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Connectedness==&lt;br /&gt;
Gauss&#039;s Law, as well as the other Maxwell Equations form a basis for electrodynamics. They are the fundamental core of this field of study. Gauss&#039;s Law is also connected to the Gaussian/Normal distribution, which is a continuous probability distribution that is characterized by a bell-shaped curve. &lt;br /&gt;
&lt;br /&gt;
As Industrial and Systems Engineering majors, we deal with many statistical distributions. A very important fundamental distribution is the Gaussian distribution or the Normal Distribution. With inference, the Gaussian Distribution comes up in confidence intervals for single statistics. With comparison inference, like finding the pairwise difference between statistics, generally we use other distributions such as the T-Distribution. However, the T-Distribution approximates the Gaussian distribution with degrees of freedom greater than 29.&lt;br /&gt;
&lt;br /&gt;
As civil and environmental engineering majors, we also deal with the Gaussian/Normal Distribution in our fields. As an example, the speed data of traffic on a highway is said to follow the normal distribution.&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
&lt;br /&gt;
[[File:220px-Carl_Friedrich_Gauss_(C._A._Jensen).jpg]]&lt;br /&gt;
&lt;br /&gt;
Carl Friedrich Gauss was a German Mathematician and Physicist who contributed notably to a wide variety of fields regarding mathematical and scientific study. He has been referred to as the &amp;quot;greatest mathematician since antiquity&amp;quot; and the &amp;quot;foremost of mathematicians&amp;quot;.  He is considered one of the most impactful and influential contributors to the fields of Mathematics and Physics in history.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law is tied in closely with the other of Maxwell&#039;s equations that can be found here in the Physics Book.&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Gauss%27s_Flux_Theorem&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Faraday%27s_Law&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Magnetic_Flux&lt;br /&gt;
&lt;br /&gt;
http://physicsbook.gatech.edu/Ampere%27s_Law&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://physics.info/law-gauss/&lt;br /&gt;
&lt;br /&gt;
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter24/Chapter24.html&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Gauss%27s_law&lt;br /&gt;
&lt;br /&gt;
https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss&lt;br /&gt;
&lt;br /&gt;
http://physicscatalyst.com/elec/guass_0.php&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html&lt;br /&gt;
&lt;br /&gt;
http://www.pas.rochester.edu/~stte/phy114S09/lectures/lect04.pdf&lt;br /&gt;
&lt;br /&gt;
https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Gauss_Law.pdf&lt;br /&gt;
&lt;br /&gt;
http://www.sciencedirect.com/science/article/pii/S2090447911000165&lt;br /&gt;
&lt;br /&gt;
spiff.rit.edu&lt;br /&gt;
&lt;br /&gt;
study.com&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Which Category did you place this in?]]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Magnetic_Flux&amp;diff=31733</id>
		<title>Magnetic Flux</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Magnetic_Flux&amp;diff=31733"/>
		<updated>2018-04-18T23:07:46Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Rahul Singi (Spring 2017)&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Claimed by Vansh Kareer (Fall 2017)&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
Recall that according to Gauss&#039;s law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic &#039;monopoles&#039;, we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don&#039;t exist. It follows that the equivalent of Gauss&#039;s law for magnetic fields reduces to:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA = 0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Realistically, the magnetic flux though any CLOSED surface is zero. The magnetic flux through an area will be its own individual value. This rule is useful when solving for a an unknown magnetic field that&#039;s coming from a side of a surface when the other fields from the other sides are known. Magnetic flux is measured in SI units of Weber (Wb), named after German physicist and co-inventor of the telegraph Wilhelm Weber. &lt;br /&gt;
&lt;br /&gt;
This is the Gauss&#039;s law general form for finding magnetic flux through an area (not closed surface).&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
To fully understand the meaning of this equation, an understanding of normal vectors and dot products is required. Relative to a surface, a normal vector runs perpendicular to the surface at a certain point. For currved surfaces, such as the one shown below, there are many different normal vectors for each plane of the surface.&lt;br /&gt;
&lt;br /&gt;
[[File:normalvectors.png]]&lt;br /&gt;
&lt;br /&gt;
Thus Gauss&#039;s law for magnetic flux can be expanded via the dot product definition, where theta is the angle between the plane of the surface area and the vector of magnetic field at that location.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA =\oint B * dA * cos(\theta)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
As seen on the formula described on the section above, the magnetic flux of an object depends on the size and shape of the object. Therefore, it is hard to show one specific computational model that can correctly illustrate magnetic flux. However, below are some images that show the magnetic flux of three common types of surfaces: closed, open, and solenoid. &lt;br /&gt;
&lt;br /&gt;
A closed surface: [[File:closedsingi.gif]]&lt;br /&gt;
&lt;br /&gt;
An open surface: [[File:opensingi.gif]]&lt;br /&gt;
&lt;br /&gt;
Solenoid: [[File:solenoidsingi.gif]]&lt;br /&gt;
&lt;br /&gt;
==Further Description==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law for magnetism tells us that magnetic monopoles do not exist. If magnetic monopoles existed, they would be sources and sinks of the magnetic field, and therefore the right-hand side could differ from zero. Gauss&#039;s Law for magnetism is one of the four Maxwell&#039;s equations, which form the foundation for the entire theory of classical electrodynamics.&lt;br /&gt;
&lt;br /&gt;
The magnitude of the magnetic flux depends on the strength of the magnetic field, the size of the surface area, and the angle between the direction in which the surface area points and the direction of the magnetic field (the definition of a dot-product; only the component of the magnetic field nromal to the surface is considered).&lt;br /&gt;
&lt;br /&gt;
[[File:MagFlux.gif]]&lt;br /&gt;
&lt;br /&gt;
As stated before, another of Maxwell&#039;s equations, Gauss&#039;s Law for electric fields, concerns electric field flux.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_E = \iint_S E \cdot dS = \dfrac{Q}{\epsilon_0}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Here, &amp;lt;math&amp;gt;\Phi_E &amp;lt;/math&amp;gt; represents electric field flux, E represent the electric field present, S represents the closed surface area being considered, Q is the total electric charge encompassed by the surface area, and &amp;lt;math&amp;gt;\epsilon_0&amp;lt;/math&amp;gt; is the electric constant (known as the permittivity of free space). Thus, the electric field through a closed surface area is not always zero, unlike the magnetic flux through a closed surface, which is zero due to the lack of existence of magnetic monopoles. This electric field flux equation is the opposite of Gauss&#039;s law for magnetic flux, indicating the importance of electric monopoles (free positive and negative charges) to electric field flux.&lt;br /&gt;
&lt;br /&gt;
==Applications==&lt;br /&gt;
Magnetic flux is very closely related to electric flux using Gauss&#039;s law for electric fields (one of the four Maxwell equations). &lt;br /&gt;
&lt;br /&gt;
There are a few important real-world applications of magnetic flux. As described by Faraday&#039;s Law, when a coiled wire moves through a magnetic field, a voltage is produced. This voltage is dependent on the magnetic flux (due to the surrounding magnetic field) through the area of the coiled wire, as seen below. &lt;br /&gt;
&lt;br /&gt;
[[File:FluxinMagField.jpg]]&lt;br /&gt;
&lt;br /&gt;
Via the Faraday-Lenz law, engineers can easily calculate the voltage generated by a coiled wire in a magnetic field. The relationship is electro-motive force equals the negative rate of change of magnetic flux over time.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = -\dfrac{d\Phi}{dt} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Practice Problems==&lt;br /&gt;
===Walkthroughs===&lt;br /&gt;
&lt;br /&gt;
Simple Walthrough:[https://www.youtube.com/watch?v=xKEEOEvYVB4]&lt;br /&gt;
&lt;br /&gt;
Middling Walkthrough: [https://www.youtube.com/watch?v=M0SRan7UW6k]&lt;br /&gt;
&lt;br /&gt;
Advanced Walkthrough: [https://www.youtube.com/watch?v=ba8ADUeGd9w]&lt;br /&gt;
&lt;br /&gt;
Once you get the hang of the process of solving magnetic flux problems using the walkthroughs, try some of the basic questions, then move on to the more advanced questions below. &lt;br /&gt;
===Basic===&lt;br /&gt;
&lt;br /&gt;
1) As shown below, there a current-carrying wire alongside a coil of wire. Using Gauss&#039;s Law, calculate the magnitude of magnetic flux through the coil of wire. [Question from Khan Academy; solution through link below]&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx1.jpg]]&lt;br /&gt;
&lt;br /&gt;
2) Calculate the magnetic flux through the coiled wire given the magnetic field present.&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx2.png]]&lt;br /&gt;
&lt;br /&gt;
3) Calculate the magnetic flux through the coiled wire given the magnetic fields present.&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx3.png]]&lt;br /&gt;
&lt;br /&gt;
4) A wire of resistance 7 ohms and length 3.8 m is bent into a circle and is concentric with a solenoid in which the magnetic flux changes from 5 T·m2 to 3 T·m2 in 0.2 seconds. What is the emf in the wire?&lt;br /&gt;
&lt;br /&gt;
===Advanced===&lt;br /&gt;
&lt;br /&gt;
1) There is a small bar magnet with a magnetic dipole D located at the origin (0,0,0). It&#039;s aligned with the y-axis. There is a circular disk with a radius of R facing perpendicular to the yz plane and its center is 4 meters away on the +x axis from the bar magnet. What is the magnetic flux going through the disk in terms of the given variable? (Consult with your professor for the solution).&lt;br /&gt;
&lt;br /&gt;
2) Referring back to the previous problem, the disk is now tilted so that the angle between the yz plane and the surface is 30 degrees. Find the new magnetic flux in terms of the given variables.&lt;br /&gt;
&lt;br /&gt;
3) A square with side length T is directly facing the xy plane 3 meters away from a current carrying 1 meter wire (from a portion of a nearby circuit powered by a battery with an emf of U). The wire is aligned with the y axis. The magnetic flux going through the square is G. Find the resistance of the wire.&lt;br /&gt;
&lt;br /&gt;
==Solutions==&lt;br /&gt;
===Basic===&lt;br /&gt;
1) Khan Academy: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
2) Use the base form of Gauss&#039;s Law of magnetic flux.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dA=0.02 m *0.04 m= 0.0008 m^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA=0.2 T * 0.0008 m^2= 0.00016 T*m^2=0.00016 Wb&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
3) Here, employ the same method as the last problem, but remember that the two magnetic fields run in opposite directions.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dA=0.1 m *0.15 m= 0.015 m^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA=(0.2-0.1) T * 0.015 m^2= 0.0015 T*m^2=0.0015 Wb&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
4) Recall that magnitude of electro-motive force equals the change in magnetic flux over time.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = \dfrac{d\Phi}{dt} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = \dfrac{(5 T*m^2-3 T*m^2)}{(0.2 s)} = 10 V &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
A major part of the history of magnetic flux is tied to Carl Freidrich Gauss. Gauss was a 19th century German physicist and mathematician that had notable contributions in not only the world of physics but across the fields of algebra, astronomy, and geometry. However, in this course, he is mainly known for the introduction of one of the four Maxwell&#039;s Laws(partial differential equations), titled Gauss&#039;s Law which describes the equation used to calculate magnetic flux. &lt;br /&gt;
&lt;br /&gt;
Prior to Gauss&#039;s study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.  &lt;br /&gt;
&lt;br /&gt;
Lagrange: [[File:lgsingi.jpg]]&lt;br /&gt;
&lt;br /&gt;
Gauss: [[File:gsingi.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Further Reading==&lt;br /&gt;
What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
Overview: [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/fluxmg.html]&lt;br /&gt;
&lt;br /&gt;
In-Depth Tutorial: [http://www.electronics-tutorials.ws/electromagnetism/magnetism.html]&lt;br /&gt;
&lt;br /&gt;
==Helpful Links/Videos==&lt;br /&gt;
Khan Academy: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/v/flux-and-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
Quick Explanation: [https://www.youtube.com/watch?v=3NYg34_vy7k]&lt;br /&gt;
&lt;br /&gt;
In-Depth Explanation: [https://www.youtube.com/watch?v=1RcpSUr8GtA]&lt;br /&gt;
&lt;br /&gt;
Another Problem: [http://physicstasks.eu/552/magnetic-flux-through-a-square]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/fluxmg.html]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://wiki.kidzsearch.com/wiki/Magnetic_flux]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://physics.stackexchange.com/questions/188503/how-do-magnetic-field-lines-cancel-outside-of-a-solenoid]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://tempuss.it/2016/01/25/la-matematica-di-lagrange/g-l-lagrange/]&lt;br /&gt;
&lt;br /&gt;
Pictures: [https://www.rare-earth-magnets.com/johann-carl-friedrich-gauss]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://ka-perseus-images.s3.amazonaws.com/b5a3d44ae79a1f1a298d8e9c4952f47c940e0567.svg]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://ka-perseus-images.s3.amazonaws.com/bfc3a0cdf4a86d74832e68cdd9a2eeb6a320da15.svg]&lt;br /&gt;
&lt;br /&gt;
Picture: [http://www.solvephysics.com/magnetism_prob23a.png]&lt;br /&gt;
&lt;br /&gt;
Picture: [http://www.solvephysics.com/magnetism_prob24a.png]&lt;br /&gt;
&lt;br /&gt;
WebAssign Instructional Application for PHYS 2212, Georgia Institute of Technology.&lt;br /&gt;
&lt;br /&gt;
Resource : [http://www.solvephysics.com/topic_magnetic_flux_induction.shtml]&lt;br /&gt;
&lt;br /&gt;
Resource: [https://en.wikipedia.org/wiki/Magnetic_flux]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Surface_normals.svg/300px-Surface_normals.svg.png]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Magnetic_Flux&amp;diff=31710</id>
		<title>Magnetic Flux</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Magnetic_Flux&amp;diff=31710"/>
		<updated>2018-04-18T22:42:49Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Rahul Singi (Spring 2017)&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Claimed by Vansh Kareer (Fall 2017)&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Claimed by Patricia Estrada (Spring 2018)&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
Recall that according to Gauss&#039;s law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic &#039;monopoles&#039;, we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don&#039;t exist. It follows that the equivalent of Gauss&#039;s law for magnetic fields reduces to:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA = 0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Realistically, the magnetic flux though any CLOSED surface is zero. The magnetic flux through an area will be its own individual value. This rule is useful when solving for a an unknown magnetic field that&#039;s coming from a side of a surface when the other fields from the other sides are known. Magnetic flux is measured in SI units of Weber (Wb), named after German physicist and co-inventor of the telegraph Wilhelm Weber. &lt;br /&gt;
&lt;br /&gt;
This is the Gauss&#039;s law general form for finding magnetic flux through an area (not closed surface).&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
To fully understand the meaning of this equation, an understanding of normal vectors and dot products is required. Relative to a surface, a normal vector runs perpendicular to the surface at a certain point. For currved surfaces, such as the one shown below, there are many different normal vectors for each plane of the surface.&lt;br /&gt;
&lt;br /&gt;
[[File:normalvectors.png]]&lt;br /&gt;
&lt;br /&gt;
Thus Gauss&#039;s law for magnetic flux can be expanded via the dot product definition, where theta is the angle between the plane of the surface area and the vector of magnetic field at that location.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA =\oint B * dA * cos(\theta)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
As seen on the formula described on the section above, the magnetic flux of an object depends on the size and shape of the object. Therefore, it is hard to show one specific computational model that can correctly illustrate magnetic flux. However, below are some images that show the magnetic flux of three common types of surfaces: closed, open, and solenoid. &lt;br /&gt;
&lt;br /&gt;
A closed surface: [[File:closedsingi.gif]]&lt;br /&gt;
&lt;br /&gt;
An open surface: [[File:opensingi.gif]]&lt;br /&gt;
&lt;br /&gt;
Solenoid: [[File:solenoidsingi.gif]]&lt;br /&gt;
 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Further Description==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law for magnetism tells us that magnetic monopoles do not exist. If magnetic monopoles existed, they would be sources and sinks of the magnetic field, and therefore the right-hand side could differ from zero. Gauss&#039;s Law for magnetism is one of the four Maxwell&#039;s equations, which form the foundation for the entire theory of classical electrodynamics.&lt;br /&gt;
&lt;br /&gt;
The magnitude of the magnetic flux depends on the strength of the magnetic field, the size of the surface area, and the angle between the direction in which the surface area points and the direction of the magnetic field (the definition of a dot-product; only the component of the magnetic field nromal to the surface is considered).&lt;br /&gt;
&lt;br /&gt;
[[File:MagFlux.gif]]&lt;br /&gt;
&lt;br /&gt;
As stated before, another of Maxwell&#039;s equations, Gauss&#039;s Law for electric fields, concerns electric field flux.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_E = \iint_S E \cdot dS = \dfrac{Q}{\epsilon_0}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Here, &amp;lt;math&amp;gt;\Phi_E &amp;lt;/math&amp;gt; represents electric field flux, E represent the electric field present, S represents the closed surface area being considered, Q is the total electric charge encompassed by the surface area, and &amp;lt;math&amp;gt;\epsilon_0&amp;lt;/math&amp;gt; is the electric constant (known as the permittivity of free space). Thus, the electric field through a closed surface area is not always zero, unlike the magnetic flux through a closed surface, which is zero due to the lack of existence of magnetic monopoles. This electric field flux equation is the opposite of Gauss&#039;s law for magnetic flux, indicating the importance of electric monopoles (free positive and negative charges) to electric field flux.&lt;br /&gt;
&lt;br /&gt;
==Applications==&lt;br /&gt;
Magnetic flux is very closely related to electric flux using Gauss&#039;s law for electric fields (one of the four Maxwell equations). &lt;br /&gt;
&lt;br /&gt;
There are a few important real-world applications of magnetic flux. As described by Faraday&#039;s Law, when a coiled wire moves through a magnetic field, a voltage is produced. This voltage is dependent on the magnetic flux (due to the surrounding magnetic field) through the area of the coiled wire, as seen below. &lt;br /&gt;
&lt;br /&gt;
[[File:FluxinMagField.jpg]]&lt;br /&gt;
&lt;br /&gt;
Via the Faraday-Lenz law, engineers can easily calculate the voltage generated by a coiled wire in a magnetic field. The relationship is electro-motive force equals the negative rate of change of magnetic flux over time.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = -\dfrac{d\Phi}{dt} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Practice Problems==&lt;br /&gt;
===Walkthroughs===&lt;br /&gt;
&lt;br /&gt;
Simple Walthrough:[https://www.youtube.com/watch?v=xKEEOEvYVB4]&lt;br /&gt;
&lt;br /&gt;
Middling Walkthrough: [https://www.youtube.com/watch?v=M0SRan7UW6k]&lt;br /&gt;
&lt;br /&gt;
Advanced Walkthrough: [https://www.youtube.com/watch?v=ba8ADUeGd9w]&lt;br /&gt;
&lt;br /&gt;
Once you get the hang of the process of solving magnetic flux problems using the walkthroughs, try some of the basic questions, then move on to the more advanced questions below. &lt;br /&gt;
===Basic===&lt;br /&gt;
&lt;br /&gt;
1) As shown below, there a current-carrying wire alongside a coil of wire. Using Gauss&#039;s Law, calculate the magnitude of magnetic flux through the coil of wire. [Question from Khan Academy; solution through link below]&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx1.jpg]]&lt;br /&gt;
&lt;br /&gt;
2) Calculate the magnetic flux through the coiled wire given the magnetic field present.&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx2.png]]&lt;br /&gt;
&lt;br /&gt;
3) Calculate the magnetic flux through the coiled wire given the magnetic fields present.&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx3.png]]&lt;br /&gt;
&lt;br /&gt;
4) A wire of resistance 7 ohms and length 3.8 m is bent into a circle and is concentric with a solenoid in which the magnetic flux changes from 5 T·m2 to 3 T·m2 in 0.2 seconds. What is the emf in the wire?&lt;br /&gt;
&lt;br /&gt;
===Advanced===&lt;br /&gt;
&lt;br /&gt;
1) There is a small bar magnet with a magnetic dipole D located at the origin (0,0,0). It&#039;s aligned with the y-axis. There is a circular disk with a radius of R facing perpendicular to the yz plane and its center is 4 meters away on the +x axis from the bar magnet. What is the magnetic flux going through the disk in terms of the given variable? (Consult with your professor for the solution).&lt;br /&gt;
&lt;br /&gt;
2) Referring back to the previous problem, the disk is now tilted so that the angle between the yz plane and the surface is 30 degrees. Find the new magnetic flux in terms of the given variables.&lt;br /&gt;
&lt;br /&gt;
3) A square with side length T is directly facing the xy plane 3 meters away from a current carrying 1 meter wire (from a portion of a nearby circuit powered by a battery with an emf of U). The wire is aligned with the y axis. The magnetic flux going through the square is G. Find the resistance of the wire.&lt;br /&gt;
&lt;br /&gt;
==Solutions==&lt;br /&gt;
===Basic===&lt;br /&gt;
1) Khan Academy: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
2) Use the base form of Gauss&#039;s Law of magnetic flux.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dA=0.02 m *0.04 m= 0.0008 m^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA=0.2 T * 0.0008 m^2= 0.00016 T*m^2=0.00016 Wb&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
3) Here, employ the same method as the last problem, but remember that the two magnetic fields run in opposite directions.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dA=0.1 m *0.15 m= 0.015 m^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA=(0.2-0.1) T * 0.015 m^2= 0.0015 T*m^2=0.0015 Wb&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
4) Recall that magnitude of electro-motive force equals the change in magnetic flux over time.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = \dfrac{d\Phi}{dt} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = \dfrac{(5 T*m^2-3 T*m^2)}{(0.2 s)} = 10 V &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
A major part of the history of magnetic flux is tied to Carl Freidrich Gauss. Gauss was a 19th century German physicist and mathematician that had notable contributions in not only the world of physics but across the fields of algebra, astronomy, and geometry. However, in this course, he is mainly known for the introduction of one of the four Maxwell&#039;s Laws(partial differential equations), titled Gauss&#039;s Law which describes the equation used to calculate magnetic flux. &lt;br /&gt;
&lt;br /&gt;
Prior to Gauss&#039;s study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.  &lt;br /&gt;
&lt;br /&gt;
Lagrange: [[File:lgsingi.jpg]]&lt;br /&gt;
&lt;br /&gt;
Gauss: [[File:gsingi.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Further Reading==&lt;br /&gt;
What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
Overview: [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/fluxmg.html]&lt;br /&gt;
&lt;br /&gt;
In-Depth Tutorial: [http://www.electronics-tutorials.ws/electromagnetism/magnetism.html]&lt;br /&gt;
&lt;br /&gt;
==Helpful Links/Videos==&lt;br /&gt;
Khan Academy: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/v/flux-and-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
Quick Explanation: [https://www.youtube.com/watch?v=3NYg34_vy7k]&lt;br /&gt;
&lt;br /&gt;
In-Depth Explanation: [https://www.youtube.com/watch?v=1RcpSUr8GtA]&lt;br /&gt;
&lt;br /&gt;
Another Problem: [http://physicstasks.eu/552/magnetic-flux-through-a-square]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/fluxmg.html]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://wiki.kidzsearch.com/wiki/Magnetic_flux]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://physics.stackexchange.com/questions/188503/how-do-magnetic-field-lines-cancel-outside-of-a-solenoid]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://tempuss.it/2016/01/25/la-matematica-di-lagrange/g-l-lagrange/]&lt;br /&gt;
&lt;br /&gt;
Pictures: [https://www.rare-earth-magnets.com/johann-carl-friedrich-gauss]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://ka-perseus-images.s3.amazonaws.com/b5a3d44ae79a1f1a298d8e9c4952f47c940e0567.svg]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://ka-perseus-images.s3.amazonaws.com/bfc3a0cdf4a86d74832e68cdd9a2eeb6a320da15.svg]&lt;br /&gt;
&lt;br /&gt;
Picture: [http://www.solvephysics.com/magnetism_prob23a.png]&lt;br /&gt;
&lt;br /&gt;
Picture: [http://www.solvephysics.com/magnetism_prob24a.png]&lt;br /&gt;
&lt;br /&gt;
WebAssign Instructional Application for PHYS 2212, Georgia Institute of Technology.&lt;br /&gt;
&lt;br /&gt;
Resource : [http://www.solvephysics.com/topic_magnetic_flux_induction.shtml]&lt;br /&gt;
&lt;br /&gt;
Resource: [https://en.wikipedia.org/wiki/Magnetic_flux]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Surface_normals.svg/300px-Surface_normals.svg.png]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Magnetic_Flux&amp;diff=31709</id>
		<title>Magnetic Flux</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Magnetic_Flux&amp;diff=31709"/>
		<updated>2018-04-18T22:42:37Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Claimed by Rahul Singi (Spring 2017)&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Claimed by Vansh Kareer (Fall 2017)&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;quot;&amp;quot;Claimed by Patricia Estrada (Spring 2018)&amp;quot;&amp;quot;&lt;br /&gt;
&lt;br /&gt;
==The Main Idea==&lt;br /&gt;
===A Mathematical Model===&lt;br /&gt;
Recall that according to Gauss&#039;s law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic &#039;monopoles&#039;, we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don&#039;t exist. It follows that the equivalent of Gauss&#039;s law for magnetic fields reduces to:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA = 0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Realistically, the magnetic flux though any CLOSED surface is zero. The magnetic flux through an area will be its own individual value. This rule is useful when solving for a an unknown magnetic field that&#039;s coming from a side of a surface when the other fields from the other sides are known. Magnetic flux is measured in SI units of Weber (Wb), named after German physicist and co-inventor of the telegraph Wilhelm Weber. &lt;br /&gt;
&lt;br /&gt;
This is the Gauss&#039;s law general form for finding magnetic flux through an area (not closed surface).&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
To fully understand the meaning of this equation, an understanding of normal vectors and dot products is required. Relative to a surface, a normal vector runs perpendicular to the surface at a certain point. For currved surfaces, such as the one shown below, there are many different normal vectors for each plane of the surface.&lt;br /&gt;
&lt;br /&gt;
[[File:normalvectors.png]]&lt;br /&gt;
&lt;br /&gt;
Thus Gauss&#039;s law for magnetic flux can be expanded via the dot product definition, where theta is the angle between the plane of the surface area and the vector of magnetic field at that location.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA =\oint B * dA * cos(\theta)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===A Computational Model===&lt;br /&gt;
As seen on the formula described on the section above, the magnetic flux of an object depends on the size and shape of the object. Therefore, it is hard to show one specific computational model that can correctly illustrate magnetic flux. However, below are some images that show the magnetic flux of three common types of surfaces: closed, open, and solenoid. &lt;br /&gt;
&lt;br /&gt;
A closed surface: [[File:closedsingi.gif]]&lt;br /&gt;
&lt;br /&gt;
An open surface: [[File:opensingi.gif]]&lt;br /&gt;
&lt;br /&gt;
Solenoid: [[File:solenoidsingi.gif]]&lt;br /&gt;
 &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Further Description==&lt;br /&gt;
&lt;br /&gt;
Gauss&#039;s Law for magnetism tells us that magnetic monopoles do not exist. If magnetic monopoles existed, they would be sources and sinks of the magnetic field, and therefore the right-hand side could differ from zero. Gauss&#039;s Law for magnetism is one of the four Maxwell&#039;s equations, which form the foundation for the entire theory of classical electrodynamics.&lt;br /&gt;
&lt;br /&gt;
The magnitude of the magnetic flux depends on the strength of the magnetic field, the size of the surface area, and the angle between the direction in which the surface area points and the direction of the magnetic field (the definition of a dot-product; only the component of the magnetic field nromal to the surface is considered).&lt;br /&gt;
&lt;br /&gt;
[[File:MagFlux.gif]]&lt;br /&gt;
&lt;br /&gt;
As stated before, another of Maxwell&#039;s equations, Gauss&#039;s Law for electric fields, concerns electric field flux.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_E = \iint_S E \cdot dS = \dfrac{Q}{\epsilon_0}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Here, &amp;lt;math&amp;gt;\Phi_E &amp;lt;/math&amp;gt; represents electric field flux, E represent the electric field present, S represents the closed surface area being considered, Q is the total electric charge encompassed by the surface area, and &amp;lt;math&amp;gt;\epsilon_0&amp;lt;/math&amp;gt; is the electric constant (known as the permittivity of free space). Thus, the electric field through a closed surface area is not always zero, unlike the magnetic flux through a closed surface, which is zero due to the lack of existence of magnetic monopoles. This electric field flux equation is the opposite of Gauss&#039;s law for magnetic flux, indicating the importance of electric monopoles (free positive and negative charges) to electric field flux.&lt;br /&gt;
&lt;br /&gt;
==Applications==&lt;br /&gt;
Magnetic flux is very closely related to electric flux using Gauss&#039;s law for electric fields (one of the four Maxwell equations). &lt;br /&gt;
&lt;br /&gt;
There are a few important real-world applications of magnetic flux. As described by Faraday&#039;s Law, when a coiled wire moves through a magnetic field, a voltage is produced. This voltage is dependent on the magnetic flux (due to the surrounding magnetic field) through the area of the coiled wire, as seen below. &lt;br /&gt;
&lt;br /&gt;
[[File:FluxinMagField.jpg]]&lt;br /&gt;
&lt;br /&gt;
Via the Faraday-Lenz law, engineers can easily calculate the voltage generated by a coiled wire in a magnetic field. The relationship is electro-motive force equals the negative rate of change of magnetic flux over time.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = -\dfrac{d\Phi}{dt} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Practice Problems==&lt;br /&gt;
===Walkthroughs===&lt;br /&gt;
&lt;br /&gt;
Simple Walthrough:[https://www.youtube.com/watch?v=xKEEOEvYVB4]&lt;br /&gt;
&lt;br /&gt;
Middling Walkthrough: [https://www.youtube.com/watch?v=M0SRan7UW6k]&lt;br /&gt;
&lt;br /&gt;
Advanced Walkthrough: [https://www.youtube.com/watch?v=ba8ADUeGd9w]&lt;br /&gt;
&lt;br /&gt;
Once you get the hang of the process of solving magnetic flux problems using the walkthroughs, try some of the basic questions, then move on to the more advanced questions below. &lt;br /&gt;
===Basic===&lt;br /&gt;
&lt;br /&gt;
1) As shown below, there a current-carrying wire alongside a coil of wire. Using Gauss&#039;s Law, calculate the magnitude of magnetic flux through the coil of wire. [Question from Khan Academy; solution through link below]&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx1.jpg]]&lt;br /&gt;
&lt;br /&gt;
2) Calculate the magnetic flux through the coiled wire given the magnetic field present.&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx2.png]]&lt;br /&gt;
&lt;br /&gt;
3) Calculate the magnetic flux through the coiled wire given the magnetic fields present.&lt;br /&gt;
&lt;br /&gt;
[[File:FluxEx3.png]]&lt;br /&gt;
&lt;br /&gt;
4) A wire of resistance 7 ohms and length 3.8 m is bent into a circle and is concentric with a solenoid in which the magnetic flux changes from 5 T·m2 to 3 T·m2 in 0.2 seconds. What is the emf in the wire?&lt;br /&gt;
&lt;br /&gt;
===Advanced===&lt;br /&gt;
&lt;br /&gt;
1) There is a small bar magnet with a magnetic dipole D located at the origin (0,0,0). It&#039;s aligned with the y-axis. There is a circular disk with a radius of R facing perpendicular to the yz plane and its center is 4 meters away on the +x axis from the bar magnet. What is the magnetic flux going through the disk in terms of the given variable? (Consult with your professor for the solution).&lt;br /&gt;
&lt;br /&gt;
2) Referring back to the previous problem, the disk is now tilted so that the angle between the yz plane and the surface is 30 degrees. Find the new magnetic flux in terms of the given variables.&lt;br /&gt;
&lt;br /&gt;
3) A square with side length T is directly facing the xy plane 3 meters away from a current carrying 1 meter wire (from a portion of a nearby circuit powered by a battery with an emf of U). The wire is aligned with the y axis. The magnetic flux going through the square is G. Find the resistance of the wire.&lt;br /&gt;
&lt;br /&gt;
==Solutions==&lt;br /&gt;
===Basic===&lt;br /&gt;
1) Khan Academy: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
2) Use the base form of Gauss&#039;s Law of magnetic flux.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dA=0.02 m *0.04 m= 0.0008 m^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA=0.2 T * 0.0008 m^2= 0.00016 T*m^2=0.00016 Wb&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
3) Here, employ the same method as the last problem, but remember that the two magnetic fields run in opposite directions.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;dA=0.1 m *0.15 m= 0.015 m^2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\Phi_B = \oint B \cdot dA=(0.2-0.1) T * 0.015 m^2= 0.0015 T*m^2=0.0015 Wb&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
4) Recall that magnitude of electro-motive force equals the change in magnetic flux over time.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = \dfrac{d\Phi}{dt} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\epsilon = \dfrac{(5 T*m^2-3 T*m^2)}{(0.2 s)} = 10 V &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
A major part of the history of magnetic flux is tied to Carl Freidrich Gauss. Gauss was a 19th century German physicist and mathematician that had notable contributions in not only the world of physics but across the fields of algebra, astronomy, and geometry. However, in this course, he is mainly known for the introduction of one of the four Maxwell&#039;s Laws(partial differential equations), titled Gauss&#039;s Law which describes the equation used to calculate magnetic flux. &lt;br /&gt;
&lt;br /&gt;
Prior to Gauss&#039;s study on the subject however, Joseph-Louis Lagrange (famous Italian mathematician) had studied the subject. However, Gauss completed the formulation of the theory and published it in 1813.  &lt;br /&gt;
&lt;br /&gt;
Lagrange: [[File:lgsingi.jpg]]&lt;br /&gt;
&lt;br /&gt;
Gauss: [[File:gsingi.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Further Reading==&lt;br /&gt;
What is Magnetic Flux?: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
Overview: [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/fluxmg.html]&lt;br /&gt;
&lt;br /&gt;
In-Depth Tutorial: [http://www.electronics-tutorials.ws/electromagnetism/magnetism.html]&lt;br /&gt;
&lt;br /&gt;
==Helpful Links/Videos==&lt;br /&gt;
Khan Academy: [https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/v/flux-and-magnetic-flux]&lt;br /&gt;
&lt;br /&gt;
Quick Explanation: [https://www.youtube.com/watch?v=3NYg34_vy7k]&lt;br /&gt;
&lt;br /&gt;
In-Depth Explanation: [https://www.youtube.com/watch?v=1RcpSUr8GtA]&lt;br /&gt;
&lt;br /&gt;
Another Problem: [http://physicstasks.eu/552/magnetic-flux-through-a-square]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/fluxmg.html]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://wiki.kidzsearch.com/wiki/Magnetic_flux]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://physics.stackexchange.com/questions/188503/how-do-magnetic-field-lines-cancel-outside-of-a-solenoid]&lt;br /&gt;
&lt;br /&gt;
Pictures: [http://tempuss.it/2016/01/25/la-matematica-di-lagrange/g-l-lagrange/]&lt;br /&gt;
&lt;br /&gt;
Pictures: [https://www.rare-earth-magnets.com/johann-carl-friedrich-gauss]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://ka-perseus-images.s3.amazonaws.com/b5a3d44ae79a1f1a298d8e9c4952f47c940e0567.svg]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://ka-perseus-images.s3.amazonaws.com/bfc3a0cdf4a86d74832e68cdd9a2eeb6a320da15.svg]&lt;br /&gt;
&lt;br /&gt;
Picture: [http://www.solvephysics.com/magnetism_prob23a.png]&lt;br /&gt;
&lt;br /&gt;
Picture: [http://www.solvephysics.com/magnetism_prob24a.png]&lt;br /&gt;
&lt;br /&gt;
WebAssign Instructional Application for PHYS 2212, Georgia Institute of Technology.&lt;br /&gt;
&lt;br /&gt;
Resource : [http://www.solvephysics.com/topic_magnetic_flux_induction.shtml]&lt;br /&gt;
&lt;br /&gt;
Resource: [https://en.wikipedia.org/wiki/Magnetic_flux]&lt;br /&gt;
&lt;br /&gt;
Picture: [https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Surface_normals.svg/300px-Surface_normals.svg.png]&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7923</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7923"/>
		<updated>2015-12-02T06:35:19Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
[[Click on the following link to enjoy a Rutherford Scattering simulation!]]&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Famous Quotes ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.”&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7921</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7921"/>
		<updated>2015-12-02T06:35:03Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
[[Click on the following link to enjoy a Rutherford Scattering simulation!]]&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=== Famous Quotes ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.”&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7920</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7920"/>
		<updated>2015-12-02T06:34:41Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
[[Click on the following link to enjoy a Rutherford Scattering simulation!]]&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
=== Famous Quotes ===&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.”&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7919</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7919"/>
		<updated>2015-12-02T06:34:11Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
[[Click on the following link to enjoy a Rutherford Scattering simulation!]]&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.”&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Further reading==&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Talk:Rutherford_Experiment_and_Atomic_Collisions&amp;diff=7857</id>
		<title>Talk:Rutherford Experiment and Atomic Collisions</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Talk:Rutherford_Experiment_and_Atomic_Collisions&amp;diff=7857"/>
		<updated>2015-12-02T05:35:21Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: Blanked the page&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Talk:Rutherford_Experiment_and_Atomic_Collisions&amp;diff=7854</id>
		<title>Talk:Rutherford Experiment and Atomic Collisions</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Talk:Rutherford_Experiment_and_Atomic_Collisions&amp;diff=7854"/>
		<updated>2015-12-02T05:34:15Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: Created page with &amp;quot;Hi! I claimed this topic on Nov 9th, so more than 2 weeks before you did.. You can check on the History tab.. I guess you didn&amp;#039;t realize someone elses was already working on t...&amp;quot;&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Hi! I claimed this topic on Nov 9th, so more than 2 weeks before you did.. You can check on the History tab.. I guess you didn&#039;t realize someone elses was already working on this topic. I&#039;m letting you know so that you have enough time to do your entry on another topic. I&#039;m sorry about that!&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7843</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7843"/>
		<updated>2015-12-02T05:31:26Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
[[Click on the following link to enjoy a Rutherford Scattering simulation!]]&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.”&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7840</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7840"/>
		<updated>2015-12-02T05:31:01Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
[[Click on the following link to enjoy a Rutherford Scattering simulation!]]&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.”&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7837</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7837"/>
		<updated>2015-12-02T05:30:01Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7833</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7833"/>
		<updated>2015-12-02T05:29:06Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;&#039;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&lt;br /&gt;
&lt;br /&gt;
The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&#039;&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7831</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7831"/>
		<updated>2015-12-02T05:28:20Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&amp;quot;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&lt;br /&gt;
&lt;br /&gt;
The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&amp;quot;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7821</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7821"/>
		<updated>2015-12-02T05:26:35Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.png]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=File:Gold_foil.png&amp;diff=7816</id>
		<title>File:Gold foil.png</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=File:Gold_foil.png&amp;diff=7816"/>
		<updated>2015-12-02T05:26:03Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: Pestrada8 uploaded a new version of &amp;amp;quot;File:Gold foil.png&amp;amp;quot;&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&lt;br /&gt;
&lt;br /&gt;
The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7813</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7813"/>
		<updated>2015-12-02T05:24:01Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: ERNEST RUTHERFORD&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7812</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7812"/>
		<updated>2015-12-02T05:23:34Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th&lt;br /&gt;
&#039;&#039;&#039;Ernest Rutherford&#039;&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7811</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7811"/>
		<updated>2015-12-02T05:23:05Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Ernest Rutherford&#039;&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
 &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7807</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7807"/>
		<updated>2015-12-02T05:21:43Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Ernest Rutherford&#039;&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism. &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated.&lt;br /&gt;
 &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.htm&lt;br /&gt;
&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7801</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7801"/>
		<updated>2015-12-02T05:19:04Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Ernest Rutherford&#039;&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism. &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated. &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R.jpg]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.html&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=File:Gold_foil.png&amp;diff=7800</id>
		<title>File:Gold foil.png</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=File:Gold_foil.png&amp;diff=7800"/>
		<updated>2015-12-02T05:18:28Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: Pestrada8 uploaded a new version of &amp;amp;quot;File:Gold foil.png&amp;amp;quot;&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;J. J. Thomson had modeled the atom as a sphere in which positive charge and mass were evenly spread. Electrons orbited within the positive sphere. This was called the plum pudding model.&lt;br /&gt;
&lt;br /&gt;
The results of the gold foil experiment allowed Rutherford to build a more accurate model of the atom, in which nearly all of the mass was concentrated in a tiny, dense nucleus. Most of the atom’s volume was empty space. The nucleus was like a fly floating in a football stadium – remembering of course that the fly was much heavier than the stadium! Electrons orbited at some distance from the nucleus. This was called the Rutherford model. It resembles planets orbiting a star.&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=File:Experiment_R.jpg&amp;diff=7795</id>
		<title>File:Experiment R.jpg</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=File:Experiment_R.jpg&amp;diff=7795"/>
		<updated>2015-12-02T05:17:21Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7794</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7794"/>
		<updated>2015-12-02T05:16:36Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Ernest Rutherford&#039;&#039;&#039; &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism. &lt;br /&gt;
[[File:Ernest_Rutherford_1905.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Experiment_R.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated. &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R.jpg]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.html&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=File:Ernest_Rutherford_1905.jpg&amp;diff=7793</id>
		<title>File:Ernest Rutherford 1905.jpg</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=File:Ernest_Rutherford_1905.jpg&amp;diff=7793"/>
		<updated>2015-12-02T05:15:45Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7784</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7784"/>
		<updated>2015-12-02T05:07:24Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Ernest Rutherford&#039;&#039;&#039; &lt;br /&gt;
[[File:Ernest_Rutherford_LOC.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism. &lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Experiment_R.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated. &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R.jpg]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.html&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=File:Ernest_Rutherford_LOC.jpg&amp;diff=7779</id>
		<title>File:Ernest Rutherford LOC.jpg</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=File:Ernest_Rutherford_LOC.jpg&amp;diff=7779"/>
		<updated>2015-12-02T05:05:48Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7777</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7777"/>
		<updated>2015-12-02T05:04:55Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Ernest Rutherford&#039;&#039;&#039;&lt;br /&gt;
[[File:Ernest_Rutherford.jpg]]&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism. &lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Experiment_.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated. &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R.jpg]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.html&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
	<entry>
		<id>http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7776</id>
		<title>Ernest Rutherford</title>
		<link rel="alternate" type="text/html" href="http://www.physicsbook.gatech.edu/index.php?title=Ernest_Rutherford&amp;diff=7776"/>
		<updated>2015-12-02T05:04:26Z</updated>

		<summary type="html">&lt;p&gt;Pestrada8: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Claimed by pestrada8 on November 9th&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Ernest Rutherford&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
==Personal Life and Education==&lt;br /&gt;
&lt;br /&gt;
[[File:Ernest_Rutherford.jpg]]&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford was born in New Zealand, specifically at Spring Grove in rural Nelson, on August 30th 1871. He was the fourth child out of twelve, and was born in a country that by the time had had only fifty years of European settlement away from the British Colonies. His mother a teacher, and his father, a wheelwright, engineer and later on a flax-miller, provided him a good education. When he was ten years old he received his first science book, which led him to carry out one of his first experiments, a miniature firing cannon, which exploded without injuring anyone. In 1887, he won a Scholarship to attend secondary school and two years later he won one of the ten scholarships available on a national level to attend the University of New Zealand. A few years later he graduated with a BA in Pure Mathematics and Latin (which were both mandatory), Applied Mathematics, French, English and Physics. He won the only Senior Scholarship in Mathematics available in New Zealand, which led him to return to School to pursue a Masters in Mathematics and Physics. As an undergraduate he conducted an experiment inspired by Tesla, to determine if iron was magnetic when exposed to high frequencies of magnetizing currents. In 1893 he obtained his Master of Arts degree in Mathematics and Mathematical Physics and Physical science, which he earned with double First Class Honors. He tried being a permanent School teacher and considered the field of Medicine, but finally returned to College to take a BS degree in geology and chemistry, where he continued exploring and experimenting with magnetism. &lt;br /&gt;
&lt;br /&gt;
==Scientific Contributions==&lt;br /&gt;
===Alpha and Beta Particles===&lt;br /&gt;
Among the most important scientific contributions of Ernest Rutherford are the discovery of the alpha and beta radiation. In 1898, Rutherford started carrying out experiments in which he allowed radiation from uranium to pass through an increasing number of metal foil layers, and he observed that beta particles had a bigger penetrating power than the alpha rays. He paid close attention to the movement of these particles in a magnetic field, from which he concluded that alpha particles were positively charged. Moreover, by measuring the mass to charge ratio he hypothesize that the alpha particles were helium ions that had a positive 2 charge. With the help of his co-worker, Frederick Soddy, who would later win a Nobel Prize, Rutherford concluded that the alpha particles were atomic in nature, that were produced when larger atoms disintegrated- becoming slightly smaller atoms- and that alpha particles were indestructible. &lt;br /&gt;
We will now explore his main scientific contribution, the discovery of the atom’s nucleus and proton.&lt;br /&gt;
&lt;br /&gt;
===Gold foil experiment===&lt;br /&gt;
&lt;br /&gt;
[[File:Gold_foil.jpg]]&lt;br /&gt;
&lt;br /&gt;
What Ernest Rutherford is most well-known is for his conclusions of the Gold-foil experiment. This experiment consisted in throwing alpha particles through a gold foil to observe the behavior of the particles. What Ernest discovered was that almost all alpha particles passed straight through the foil, but some of them were deflected back as if they had hit something that made them rebound. Ernest concluded that the reason why this happened was that the atom, despite the widely accepted plum pudding model, in fact was almost all empty space and that had a positively charged nucleus at the center, which was the one repelling the alpha particles. This gave birth to a new nuclear model, which is still today the most widely accepted model. The nucleus of the atom he claimed to have a diameter of around 10e-14 meters. Later, the negative lumps that at the beginning led to plum pudding model were discovered to be electrons, which are negatively charged, that orbited the nucleus with a radius of around 10e-10. This confirmed Rutherford’s conclusion that almost all of the atom was empty space.&lt;br /&gt;
After this discovery, he carried out further experiments to discover what the nucleus was made of. In 1919, he claimed that the nucleus was made of protons. The experiment he carried out to make this conclusion consisted in placing a source of alpha radiation inside a cylinder of nitrogen gas that had one open end covered with a sheet of aluminium foil. Outside the opening, he placed a screen, were flashes of light were observed. These flashes were caused when particles hit the screen, but since the aluminium foil didn’t allow the alpha particles to pass through, there had to be another, smaller particle hitting the screen. With the help of two of his research students, Rutherford took measurements of the deflection angles of the particles and calculated that the proton was smaller than most nuclei, and had a positive charge equal in magnitude to that of electrons. Analyzing the distribution of the deflected alpha particles, which was different for different forces (i.e: magnetic, hard sphere, etc) he was able to assure that the nucleus was positively charged. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Click on the following link to enjoy a Rutherford Scattering simulation!&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
[[File:Experiment_.jpg]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Nuclear Physics Applications==&lt;br /&gt;
&lt;br /&gt;
Ernest Rutherford’s discovery of the nuclear structure of an atom established the ground for nuclear processes using radioactive decay, and thus he is known as “The Father of Nuclear Physics”. He influenced many scientists, in particular Leó Szilárd, who was inspired by Rutherford to think about the possibility of controlling nuclear chain reactions to produce energy. &lt;br /&gt;
Since his discoveries, nuclear physics took off and opened the door to a myriad applications. Not only nuclear physics is used to provide the US with 22% of its electricity, but it is also used in the medical field (diagnostics, therapy, radiobiology and biomedical tracers), it is used in material analysis (nanotechnology, geology and climate, ion implantation, material structure), in computation and nuclear defense (weapon analysis, long-term storage, functionality, homeland security). Ultimately, his contributions have understand the nuclear processes of fission and fusion and left behind the believed theories of up until the 19th century of atoms being the smallest building blocks of matter.&lt;br /&gt;
A current example of an investigation following Rutherford’s steps was published in Science News, where the hypothesis that the radius of the proton could be about 4% smaller than thought is being debated. &lt;br /&gt;
If you are interested in the topic visit: https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Famous Quotes ==&lt;br /&gt;
&lt;br /&gt;
“I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race. The best sprinters in this road of investigation are Becquerel and the Curies.” &lt;br /&gt;
&lt;br /&gt;
“Lord Kelvin had limited the age of the Earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium!”&lt;br /&gt;
&lt;br /&gt;
&amp;quot;We haven&#039;t the money, so we&#039;ve got to think&amp;quot;&lt;br /&gt;
&lt;br /&gt;
[[File:Ern_R.jpg]]&lt;br /&gt;
&lt;br /&gt;
===Further reading===&lt;br /&gt;
&lt;br /&gt;
https://www.sciencenews.org/article/incredible-shrinking-proton&lt;br /&gt;
&lt;br /&gt;
===External links===&lt;br /&gt;
&lt;br /&gt;
http://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2007-spring-2008/&lt;br /&gt;
https://phet.colorado.edu/sims/rutherford-scattering/rutherford-scattering_en.jar&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&lt;br /&gt;
http://www.famousscientists.org/ernest-rutherford/&lt;br /&gt;
http://www.chemheritage.org/discover/online-resources/chemistry-in-history/themes/atomic-and-nuclear-structure/rutherford.aspx&lt;br /&gt;
http://www.rutherford.org.nz/&lt;br /&gt;
https://www.aip.org/history/exhibits/rutherford/sections/alpha-particles-atom.html&lt;br /&gt;
https://en.wikibooks.org/wiki/A-level_Physics/Forces,_Fields_and_Energy/The_nuclear_atom&lt;br /&gt;
http://www.biography.com/people/ernest-rutherford-39099&lt;/div&gt;</summary>
		<author><name>Pestrada8</name></author>
	</entry>
</feed>