Physics Book - User contributions [en]

Superposition principle

2015-12-06T01:48:02Z

Rtolentino3:

This topic covers the Superposition Principle. This was the first and original article on this topic and also the best.
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]
*[[Electric Force]]
*[[Magnetic Force]]
*[[Magnetic Field]]

===Further reading===
*[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/coulomb-s-law-135/superposition-of-forces-483-853/ Additional Textbook Explanation]

*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

*[http://www.physicsbook.gatech.edu/Superposition_Principle This guy who made a Superposition principle on this wiki even though I already made one]

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

Superposition principle

2015-12-06T01:47:26Z

Rtolentino3: /* Further reading */

This topic covers the Superposition Principle
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]
*[[Electric Force]]
*[[Magnetic Force]]
*[[Magnetic Field]]

===Further reading===
*[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/coulomb-s-law-135/superposition-of-forces-483-853/ Additional Textbook Explanation]

*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

*[http://www.physicsbook.gatech.edu/Superposition_Principle This guy who made a Superposition principle on this wiki even though I already made one]

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

Superposition principle

2015-12-06T01:47:13Z

Rtolentino3: /* See also */

This topic covers the Superposition Principle
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]
*[[Electric Force]]
*[[Magnetic Force]]
*[[Magnetic Field]]

===Further reading===
[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/coulomb-s-law-135/superposition-of-forces-483-853/ Additional Textbook Explanation]

[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

[http://www.physicsbook.gatech.edu/Superposition_Principle This guy who made a Superposition principle on this wiki even though I already made one]

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

Superposition principle

2015-12-06T01:45:59Z

Rtolentino3: /* See also */

This topic covers the Superposition Principle
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]

===Further reading===
[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/coulomb-s-law-135/superposition-of-forces-483-853/ Additional Textbook Explanation]

[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

[http://www.physicsbook.gatech.edu/Superposition_Principle This guy who made a Superposition principle on this wiki even though I already made one]

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

Superposition principle

2015-12-06T01:45:15Z

Rtolentino3: /* See also */

This topic covers the Superposition Principle
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]

===Further reading===
[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/coulomb-s-law-135/superposition-of-forces-483-853/ Additional Textbook Explanation]
[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

Superposition principle

2015-12-06T01:42:56Z

Rtolentino3: /* Examples */

This topic covers the Superposition Principle
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]

===Further reading===

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

Superposition principle

2015-12-06T01:42:41Z

Rtolentino3: /* Examples */

This topic covers the Superposition Principle
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
File:1111.PNG|
</gallery> Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]

===Further reading===

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

File:1111.PNG

2015-12-06T01:41:24Z

Rtolentino3:

Superposition principle

2015-12-06T01:26:00Z

Rtolentino3: /* A Computational Model */

This topic covers the Superposition Principle
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
===Simple===
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
</gallery>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]

===Further reading===

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

Superposition principle

2015-12-06T01:24:18Z

Rtolentino3:

This topic covers the Superposition Principle
==The Main Idea==
The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===
[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Using these in the equation for an electric field from a point charge, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Then, simply add the two electric fields together:

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Examples==
===Simple===
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field
</gallery>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the invidiual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However these two guys who were probably your bane of existence in Calc II, were proved wrong by Joseph Fourier, and is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]

===Further reading===

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

[[Fields]]

Superposition principle

2015-12-06T01:08:43Z

Rtolentino3:

Superposition principle

2015-12-06T01:06:51Z

Rtolentino3: /* Examples */

Superposition principle

2015-12-06T01:06:42Z

Rtolentino3: /* A Computational Model */

Superposition principle

2015-12-06T01:06:17Z

Rtolentino3:

File:1234556.JPG

2015-12-06T01:05:34Z

Rtolentino3:

Superposition principle

2015-11-16T02:16:38Z

Rtolentino3: /* History */

Superposition principle

2015-11-16T02:14:18Z

Rtolentino3: /* Further reading */

Superposition principle

2015-11-16T02:09:38Z

Rtolentino3: /* Connectedness */

Superposition principle

2015-11-16T02:09:22Z

Rtolentino3: /* Connectedness */

Superposition principle

2015-11-16T01:57:48Z

Rtolentino3: /* The Main Idea */

Superposition principle

2015-11-16T01:57:14Z

Rtolentino3: /* External links */

Superposition principle

2015-11-16T01:54:46Z

Rtolentino3: /* See also */

Superposition principle

2015-11-16T01:54:15Z

Rtolentino3: /* References */

Superposition principle

2015-11-16T01:53:34Z

Rtolentino3: /* See also */

Superposition principle

2015-11-16T01:53:07Z

Rtolentino3: /* See also */

Superposition principle

2015-11-16T01:52:13Z

Rtolentino3: /* See also */

Superposition principle

2015-11-16T01:50:27Z

Rtolentino3: /* Examples */

Superposition principle

2015-11-16T01:48:30Z

Rtolentino3:

Superposition principle

2015-11-16T01:47:52Z

Rtolentino3: /* Simple */

Superposition principle

2015-11-16T01:47:36Z

Rtolentino3: /* Simple */

Superposition principle

2015-11-16T01:47:10Z

Rtolentino3: /* Simple */

File:Superposition Principle.JPG

2015-11-16T01:45:34Z

Rtolentino3:

Superposition principle

2015-11-16T01:42:27Z

Rtolentino3: /* The Main Idea */

Superposition principle

2015-11-16T01:41:49Z

Rtolentino3:

Superposition principle

2015-11-16T01:31:46Z

Rtolentino3: Created page with "This topic covers Gravitational Potential Energy. ==The Main Idea== State, in your own words, the main idea for this topic Electric Field of Capacitor ===A Mathematical Mod..."

This topic covers Gravitational Potential Energy.

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===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==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== 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==

This section contains the the references you used while writing this page

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