Magnetic Field of a Loop

2016-04-18T01:02:17Z

Lakshitha: /* Direction of Magnetic Field */

Claimed by Jeffrey Mullavey; CLAIMED BY LAKSHITHA ANBAZHAKAN TO EDIT SPRING 2016

== Creation of a Magnetic Loop==

Like other magnetic field patterns, A magnetic field can be created through motion of charge through a loop. The system is not considered to be in equilibrium, therefore there is a movement of a mobile sea of electrons, which causes an electric current in the wire. Ideal loops are considered to be circular, so for the sake of calculations, a perfectly circular loop will be used. Thus, the conventional current is directed clockwise or counterclockwise through the loop. Formulas have been derived to assist in the calculation of these magnetic fields.

==Calculation of Magnetic Field==

The magnetic field created by a loop is easiest to calculate on axis. This means drawing a line though the center of the loop perpendicular to the circumference. This axis is commonly referred to as the "z-axis." The magnetic field is calculated by integrating across the bounds of the loop (0 to 2 pi), but can also be approximated with great accuracy using a derived formula. Calculation of magnetic field off of this axis is much more difficult, and usually requires the assistance of computer software. For this reason, only the calculation on axis will be addressed.

===Magnitude of Magnetic Field===

When calculating the magnetic field at a point on the z-axis, one can use the following formula:

<math>\vec B=\frac{\mu_0}{4 \pi} \frac{2I \pi R^2}{(z^2 + R^2)^{3/2}} \text{ ,where R is the radius of the circular loop, and z is the distance from the center of the loop} </math>

This allows for the calculation of the magnitude in units of Teslas.

If the distance from the center of the loop is much greater than the radius of the loop, an approximation can be made. The formula can be simplified to

<math>\vec B=\frac{\mu_0}{4 \pi} \frac{2I \pi R^2}{z^3} \text{ ,where z is much greater than R} </math>

===Direction of Magnetic Field===

[[File: Mag Field in Loop.PNG]]

The right hand rule can be used to find the direction of the magnetic field at a given point. Putting your right fingers in the direction of the conventional current, and curling them over the vector r will allow your thumb to point in the direction of the magnetic field. For example, a conventional current, I, running counterclockwise would produce a field pointing out of the page on the z-axis. This rule holds regardless of where the observational location is on the center axis.

[[File: RHR7.PNG]]

The magnetic field pattern for locations outside the ring points in the opposite direction, in accordance with the right hand rule. The right fingers still point in the direction of the current, however the observational vector perpendicular to the perimeter of the loop is now in the opposite direction. Thus, the magnetic field is in the opposite direction.

===Multiple Loops===

In many scenarios, electric current will run through a formation of a number of loops, N. In this case, the magnitude of the induced magnetic field can be found by calculating the field produced by one loop and multiplying it by the number of loops.

==Connectedness==
Magnetic fields from electric loops are observed often in science. For example, a solenoid is often modeled as a bunch of loops contributing to a collective magnetic field. It is important to be able to model the field, since many scientific applications of magnetism involve circular loops. The calculations can be compared to experiments done in the lab.
In all concentrations of engineering, electric and magnetic properties are important. For example, these concepts can be applied to the synthesis and manufacturing of conductors and carbon nanotubes. In many electrical experiments, it is important to understand how objects will be impacted by the creation of an induced magnetic field.

==References==

Matter and Interactions Vol. II

[[Category:Fields]]

2015-12-04T02:13:41Z

Lakshitha: /* The Main Idea */

Claimed by lakshitha

The energy principle is a broad equation that can be used to describe the changes in the different types of energy and any work that acts on a system or the transfer of heat into a system. There are many different types of energy, some of which include Kinetic Energy, Potential Energy, Chemical Energy, Rest Energy, Thermal Energy, etc.

==The Main Idea==

There are many ways to use the energy principle; most of the problems you will encounter will have no work acting on the system and no transfer of heat, thus E<sub>sys,initial</sub> = E<sub>sys,final</sub>. Other problems will involve only work acting on the system and no heat. It's important to identify what your system is before making any assumptions about its energy and whether there is any transfer of heat or any work acting on it. It's also useful to note that all objects have rest energy and a object has kinetic energy if it is moving; but, since rest energy is only changed when there is a change in mass of the object, it can usually be disregarded in any calculations. There are also different types of potential energy: Spring Potential Energy, Gravitational Potential Energy, Electric Potential Energy, and Gravitational Potential Energy near the surface of the Earth. Potentially Energy is only included if there is more than one object in your choice of system. For example, a system consisting of one proton and one electron would have Electric Potential Energy. But, a system of an asteroid and Earth would have Gravitational Potential Energy.

[[File:hydrogen atom.jpg|middle]] [[File:asteroidEarth.png|middle]]

For any multi-particle system, you have to take into account the potential energy between each of the objects. It's also key to note that potential energy is zero at very large distances.

==Mathematical Models==

<b> NOTE: These are a lot of equations, but don't get overwhelmed. You simply have to pick and choose which ones are necessary for the problem given; examples are shown below. For in-depth explanations on each type of energy, look at the associated pages on the Main Page or click on the links in the 'See also' section below. </b>

<b> The Energy Principle </b><br>
EQ 1: <math>{∆E} = {Q + W}</math> where <math>{Q}</math> is heat and <math>{W}</math> is the amount of work acting on the system.

EQ 2: <math>{∆E} = {∆K + ∆E_{Rest} + ∆U + ∆E_{Thermal}}</math> - the different types of energy that can be associated with a given particle in a system. Not all have to be present.

EQ 3: <math> E_{Rest}=mc^2 </math> - Rest Energy, where <b>m</b> is the mass and <b>c</b> is the speed of light.

EQ 4: <math>K=\frac{1}{2}mv²</math> - Kinetic Energy, where <b>m</b> is the mass and <b>v</b> is the velocity (for speeds less than the speed of light).

EQ 5: <math>∆E_{Thermal} = mC∆T </math> - Thermal energy, were <b>m</b> is the mass, <b>C</b> is the specific heat of water (4.2 J/g/K), and <b>T</b> is temperature.

<i>Potential Energy Equations:</i>

EQ 6: [[File:Ugrav.jpg|middle]].

EQ 7: [[File:Ugrav,earth.jpg|middle]].

EQ 8: [[File:Uelec.jpg|middle]].

EQ 9: [[File:Uspring.jpg|middle]].

====A Computational Model====

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===

A 1.3 kg book is pushed off a ledge and falls 4.22 m to the ground. What is its kinetic energy the instant that it hits the ground?

[[File:1solpic.jpg|middle]] [[File:1sol.jpg|middle]]

===Middling===

A 45 kg box moves along with a speed of 3.2 m/s. Someone comes up from behind and pushes it for 2.7 m while exerting a force of 185 N. What is the final speed of the box?

[[File:2solpic.jpg|middle]] [[File:Second Solution.jpg|middle]]

===Difficult===

The radius of Mars (from the center to just above the atmosphere) is 3220 km, and its mass is 2 ✕ 10^32 kg. An object is launched straight up from just above the atmosphere of Mars. What initial speed is needed so that when the object is far from Mars its final speed is 1000 m/s?

[[File:3solpic.jpg|middle]] [[File:3sol.jpg|middle]]

==Connectedness==
The Energy Principle can be used for a variety of situations; the fact that it can tell us something about the work acting on a system with only knowing about what energies are present (and vice versa) is what makes this such a fundamental principle. The energy principle is also used to describe the conservation of energy, which is something I find pretty interesting. Energy doesn't just disappear, it's simply converted into a different form. This topic has a huge connection to my major, Biology, because chemical energy (obtained from food) is necessary for a healthy and active body.

==History==

Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'. Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat. The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot. He is often known as "the father of thermodynamics". It all began with the development of the steam engine during the Industrial Revolution. He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

[[Category:Which Category did you place this in?]]

File:3solpic.jpg

2015-12-04T02:12:09Z

Lakshitha:

File:2solpic.jpg

2015-12-04T02:11:51Z

Lakshitha:

File:1solpic.jpg

2015-12-04T02:09:12Z

Lakshitha:

The Energy Principle

2015-12-04T01:27:33Z

Lakshitha: /* Examples */

Claimed by lakshitha

The energy principle is a broad equation that can be used to describe the changes in the different types of energy and any work that acts on a system or the transfer of heat into a system. There are many different types of energy, some of which include Kinetic Energy, Potential Energy, Chemical Energy, Rest Energy, Thermal Energy, etc.

==The Main Idea==

There are many ways to use the energy principle; most of the problems you will encounter will have no work acting on the system and no transfer of heat, thus E<sub>sys,initial</sub> = E<sub>sys,final</sub>. Other problems will involve only work acting on the system and no heat. It's important to identify what your system is before making any assumptions about its energy and whether there is any transfer of heat or any work acting on it. It's also useful to note that all objects have rest energy and a object has kinetic energy if it is moving; but, since rest energy is only changed when there is a change in mass of the object, it can usually be disregarded in any calculations. There are also different types of potential energy: Spring Potential Energy, Gravitational Potential Energy, Electric Potential Energy, and Gravitational Potential Energy near the surface of the Earth. Potentially Energy is only included if there is more than one object in your choice of system. For example, a system consisting of one proton and one electron would have Electric Potential Energy. But, a system of an asteroid and Earth would have Gravitational Potential Energy.

[[File:hydrogen atom.jpg|middle]] [[File:asteroidEarth.png|middle]]

For any multi-particle system, you have to take into account the potential energy between each of the objects.

==Mathematical Models==

<b> NOTE: These are a lot of equations, but don't get overwhelmed. You simply have to pick and choose which ones are necessary for the problem given; examples are shown below. For in-depth explanations on each type of energy, look at the associated pages on the Main Page or click on the links in the 'See also' section below. </b>

<b> The Energy Principle </b><br>
EQ 1: <math>{∆E} = {Q + W}</math> where <math>{Q}</math> is heat and <math>{W}</math> is the amount of work acting on the system.

EQ 2: <math>{∆E} = {∆K + ∆E_{Rest} + ∆U + ∆E_{Thermal}}</math> - the different types of energy that can be associated with a given particle in a system. Not all have to be present.

EQ 3: <math> E_{Rest}=mc^2 </math> - Rest Energy, where <b>m</b> is the mass and <b>c</b> is the speed of light.

EQ 4: <math>K=\frac{1}{2}mv²</math> - Kinetic Energy, where <b>m</b> is the mass and <b>v</b> is the velocity (for speeds less than the speed of light).

EQ 5: <math>∆E_{Thermal} = mC∆T </math> - Thermal energy, were <b>m</b> is the mass, <b>C</b> is the specific heat of water (4.2 J/g/K), and <b>T</b> is temperature.

<i>Potential Energy Equations:</i>

EQ 6: [[File:Ugrav.jpg|middle]].

EQ 7: [[File:Ugrav,earth.jpg|middle]].

EQ 8: [[File:Uelec.jpg|middle]].

EQ 9: [[File:Uspring.jpg|middle]].

====A Computational Model====

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===

A 1.3 kg book is pushed off a ledge and falls 4.22 m to the ground. What is its kinetic energy the instant that it hits the ground?

[[File:1solpic.jpg|middle]] [[File:1sol.jpg|middle]]

===Middling===

A 45 kg box moves along with a speed of 3.2 m/s. Someone comes up from behind and pushes it for 2.7 m while exerting a force of 185 N. What is the final speed of the box?

[[File:2solpic.jpg|middle]] [[File:Second Solution.jpg|middle]]

===Difficult===

The radius of Mars (from the center to just above the atmosphere) is 3220 km, and its mass is 2 ✕ 10^32 kg. An object is launched straight up from just above the atmosphere of Mars. What initial speed is needed so that when the object is far from Mars its final speed is 1000 m/s?

[[File:3solpic.jpg|middle]] [[File:3sol.jpg|middle]]

==Connectedness==
The Energy Principle can be used for a variety of situations; the fact that it can tell us something about the work acting on a system with only knowing about what energies are present (and vice versa) is what makes this such a fundamental principle. The energy principle is also used to describe the conservation of energy, which is something I find pretty interesting. Energy doesn't just disappear, it's simply converted into a different form. This topic has a huge connection to my major, Biology, because chemical energy (obtained from food) is necessary for a healthy and active body.

==History==

Thermodynamics was brought up as a science in the 18th and 19th centuries. However, it was first brought up by Galilei, who introduced the concept of temperature and invented the first thermometer. G. Black first introduced the word 'thermodynamics'. Later, G. Wilke introduced another unit of measurement known as the calorie that measures heat. The idea of thermodynamics was brought up by Nicolas Leonard Sadi Carnot. He is often known as "the father of thermodynamics". It all began with the development of the steam engine during the Industrial Revolution. He devised an ideal cycle of operation. During his observations and experimentations, he had the incorrect notion that heat is conserved, however he was able to lay down theorems that led to the development of thermodynamics. In the 20th century, the science of thermodynamics became a conventional term and a basic division of physics. Thermodynamics dealt with the study of general properties of physical systems under equilibrium and the conditions necessary to obtain equilibrium.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html
https://www.grc.nasa.gov/www/k-12/airplane/thermo2.html
http://www.phys.nthu.edu.tw/~thschang/notes/GP21.pdf
http://www.eoearth.org/view/article/153532/

[[Category:Which Category did you place this in?]]