Physics Book - User contributions [en]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-18T03:13:08Z

Amohile3:

''Claimed by Aditya Mohile''

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

==Examples==

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

===Simple===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==Connectedness==
#How is this topic connected to something that you are interested in?
::I am very interested in electronics and circuitry so knowing that potential difference is path independent definitely helps in determining the voltage between 2 points in a complicated circuit with many paths.
#How is it connected to your major?
::I am an electrical engineering major so this knowledge is very applicable to determining the voltage between 2 points in a circuit that contains many loops or is very complex.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
Luigi Galvani, an Italian physicist, discovered something he called "animal electricity" which was two different metals connected in series with a frog leg and each other. However, Alessandro Volta, another Italian physicist, realized that the frog leg was acting as a conductor and a detector of electricity, or an electrolyte. He later replaced the frog leg with brine soaked paper and noticed the same results. Through this, Volta discovered electromotive force relating to a galvanic cell, realizing that the difference between the two electrode potentials caused electricity to flow.

== See also ==

https://en.wikipedia.org/wiki/Voltage

===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html#c2

===External links===

http://mathwiki.ucdavis.edu/Core/Calculus/Vector_Calculus/Integration_in_Vector_Fields/Path_Independence,_Conservative_Fields,_and_Potential_Functions

==References==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-18T03:12:56Z

Amohile3:

''Claimed by Aditya Mohile''
Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

==Examples==

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

===Simple===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==Connectedness==
#How is this topic connected to something that you are interested in?
::I am very interested in electronics and circuitry so knowing that potential difference is path independent definitely helps in determining the voltage between 2 points in a complicated circuit with many paths.
#How is it connected to your major?
::I am an electrical engineering major so this knowledge is very applicable to determining the voltage between 2 points in a circuit that contains many loops or is very complex.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
Luigi Galvani, an Italian physicist, discovered something he called "animal electricity" which was two different metals connected in series with a frog leg and each other. However, Alessandro Volta, another Italian physicist, realized that the frog leg was acting as a conductor and a detector of electricity, or an electrolyte. He later replaced the frog leg with brine soaked paper and noticed the same results. Through this, Volta discovered electromotive force relating to a galvanic cell, realizing that the difference between the two electrode potentials caused electricity to flow.

== See also ==

https://en.wikipedia.org/wiki/Voltage

===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html#c2

===External links===

http://mathwiki.ucdavis.edu/Core/Calculus/Vector_Calculus/Integration_in_Vector_Fields/Path_Independence,_Conservative_Fields,_and_Potential_Functions

==References==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-18T03:10:49Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

==Examples==

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

===Simple===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==Connectedness==
#How is this topic connected to something that you are interested in?
::I am very interested in electronics and circuitry so knowing that potential difference is path independent definitely helps in determining the voltage between 2 points in a complicated circuit with many paths.
#How is it connected to your major?
::I am an electrical engineering major so this knowledge is very applicable to determining the voltage between 2 points in a circuit that contains many loops or is very complex.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
Luigi Galvani, an Italian physicist, discovered something he called "animal electricity" which was two different metals connected in series with a frog leg and each other. However, Alessandro Volta, another Italian physicist, realized that the frog leg was acting as a conductor and a detector of electricity, or an electrolyte. He later replaced the frog leg with brine soaked paper and noticed the same results. Through this, Volta discovered electromotive force relating to a galvanic cell, realizing that the difference between the two electrode potentials caused electricity to flow.

== See also ==

https://en.wikipedia.org/wiki/Voltage

===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html#c2

===External links===

http://mathwiki.ucdavis.edu/Core/Calculus/Vector_Calculus/Integration_in_Vector_Fields/Path_Independence,_Conservative_Fields,_and_Potential_Functions

==References==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-18T03:10:01Z

Amohile3:

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

==Examples==

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

===Simple===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==Connectedness==
#How is this topic connected to something that you are interested in?
::I am very interested in electronics and circuitry so knowing that potential difference is path independent definitely helps in determining the voltage between 2 points in a complicated circuit with many paths.
#How is it connected to your major?
::I am an electrical engineering major so this knowledge is very applicable to determining the voltage between 2 points in a circuit that contains many loops or is very complex.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
Luigi Galvani, an Italian physicist, discovered something he called "animal electricity" which was two different metals connected in series with a frog leg and each other. However, Alessandro Volta, another Italian physicist, realized that the frog leg was acting as a conductor and a detector of electricity, or an electrolyte. He later replaced the frog leg with brine soaked paper and noticed the same results. Through this, Volta discovered electromotive force relating to a galvanic cell, realizing that the difference between the two electrode potentials caused electricity to flow.

== See also ==

https://en.wikipedia.org/wiki/Voltage

===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html#c2

===External links===

http://mathwiki.ucdavis.edu/Core/Calculus/Vector_Calculus/Integration_in_Vector_Fields/Path_Independence,_Conservative_Fields,_and_Potential_Functions

==References==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-18T02:44:28Z

Amohile3: /* History */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==Connectedness==
#How is this topic connected to something that you are interested in?
::I am very interested in electronics and circuitry so knowing that potential difference is path independent definitely helps in determining the voltage between 2 points in a complicated circuit with many paths.
#How is it connected to your major?
::I am an electrical engineering major so this knowledge is very applicable to determining the voltage between 2 points in a circuit that contains many loops or is very complex.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
Luigi Galvani, an Italian physicist, discovered something he called "animal electricity" which was two different metals connected in series with a frog leg and each other. However, Alessandro Volta, another Italian physicist, realized that the frog leg was acting as a conductor and a detector of electricity, or an electrolyte. He later replaced the frog leg with brine soaked paper and noticed the same results. Through this, Volta discovered electromotive force relating to a galvanic cell, realizing that the difference between the two electrode potentials caused electricity to flow.

== 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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-18T02:21:47Z

Amohile3: /* Connectedness */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==Connectedness==
#How is this topic connected to something that you are interested in?
::I am very interested in electronics and circuitry so knowing that potential difference is path independent definitely helps in determining the voltage between 2 points in a complicated circuit with many paths.
#How is it connected to your major?
::I am an electrical engineering major so this knowledge is very applicable to determining the voltage between 2 points in a circuit that contains many loops or is very complex.

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-18T02:20:40Z

Amohile3: /* Connectedness */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==Connectedness==
#How is this topic connected to something that you are interested in?
:I am very interested in electronics and circuitry so knowing that potential difference is path independent definitely helps in determining the voltage between 2 points in a complicated circuit with many paths.
#How is it connected to your major?
:I am an electrical engineering major so this knowledge is very applicable to determining the voltage between 2 points in a circuit that contains many loops or is very complex.

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-18T02:19:48Z

Amohile3: /* Connectedness */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==Connectedness==
#How is this topic connected to something that you are interested in?
I am very interested in electronics and circuitry, so knowing that path independent definitely helps in determining the voltage between 2 points in a complicated circuit with many paths.
#How is it connected to your major?
I am an electrical engineering major so this knowledge is very applicable to determining the voltage between 2 points in a circuits that contains many loops or is very complex.

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:56:29Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:53:21Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:51:36Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{r} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{r} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:48:57Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>
'''Step 2'''
:Calculate the potential difference from A to C following the path A → D → C.
:First calculate the potential difference from A to D.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l}</math>
:Use the same electric field of the sphere calculated in step 1, shown below.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AD} = \int_{A}^{D} \vec{E} \cdot d\vec{l} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V</math>
:Now calculate the potential difference from D to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{DC} = \int_{D}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{DC} = \int_{r_{1}}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now add <math>\Delta V_{AD}</math> to <math>\Delta V_{DC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AD} + \Delta V_{DC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{r_{1}^{2}}) = 0V </math>
:Notice that either path taken from A to C results in the same potential difference of 0V.

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:30:43Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}</math>
:Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
:Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
:<math>\Delta V_{BC} = \int_{R}^{r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{r_{1}^{2}} - \frac{Q}{R_{2}})</math>
:Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AB} = \Delta V_{BC} + \Delta V_{AC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{-Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:25:08Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}}</math>
Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
::<math>\Delta V_{AB} = \int_{R}^{-r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{-Q}{r_{1}^{2}} - \frac{Q}{R_{2}})</math>
Now add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
<math>\Delta V_{AB} = \Delta V_{BC} + \Delta V_{AC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{-Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:24:26Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}}</math>
Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
::<math>\Delta V_{AB} = \int_{R}^{-r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{-Q}{r_{1}^{2}} - \frac{Q}{R_{2}})</math>
Now add <math>\Delta V{AB}</math> to <math>\Delta V{BC}</math> to get <math>\Delta V{AC}</math>
<math>\Delta V{AB} = \Delta V{BC} + \Delta V{AC} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}}) + \frac{1}{4\pi\epsilon_{0}}(\frac{-Q}{r_{1}^{2}} - \frac{Q}{R_{2}}) = 0V </math>

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:20:52Z

Amohile3: /* Difficult */

Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{AB}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.

===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===
[[File:Wiki_simple.jpg|center]]
'''Problem''': Locations A, B, and C are in a region of uniform electric field, as shown in the diagram above. Location A is at < -0.6, 0, 0> m. Location B is at < 0.4, 0, 0>. Location C is at < 0.4, -0.3, 0>m. In the region the electric field = < -750, 400, 0> N/C. Calculate the potential difference between A and C traveling from A to B then to C. Calculate the potential difference traveling from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to B.
:<math>\Delta l = < 0.4, 0, 0> - < -0.6, 0, 0> = < 1, 0, 0></math>
'''Step 2'''
:Calculate the potential difference between A and B.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*0 + 0*0) = 750V</math>
'''Step 3'''
:Calculate the displacement vector from B to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < 0.4, 0, 0> = < 0, -0.3, 0></math>
'''Step 4'''
:Calculate the potential difference between B and C.
:<math>\Delta V_{BC} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BC} = -(-750*0 + 400*-0.3 + 0*0) = 120V</math>
'''Step 5'''
:Add <math>\Delta V_{AB}</math> to <math>\Delta V_{BC}</math> to get <math>\Delta V_{AC}</math>
:<math>\Delta V_{AC} = \Delta V_{AB} + \Delta V_{BC} = 750 + 120 = 870V</math>
Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from A to C.
:<math>\Delta l = < 0.4, -0.3, 0> - < -0.6, 0, 0> = < 1, -0.3, 0></math>
'''Step 2'''
:Calculate the potential difference between A and C.
:<math>\Delta V_{AB} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AB} = -(-750*1 + 400*-0.3 + 0*0) = 750 + 120 = 870V</math>
As you can see, potential difference from A to C directly is the same as the potential difference from A to B then to C.

===Middling===
[[File:Wiki_middling.jpg|350px|center]]
'''Problem''': A capacitor consists of two charged disks of radius 4.7 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 56 µC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.5 mm, and the distance s2 = 0.6 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Find the potential difference between B and D, traveling through A. Find the potential difference from B to D directly.
'''Step 1'''
:Calculate the electric field inside the capacitor.
:<math>\vec E_{cap} = \frac{Q/A}{\epsilon_{0}}</math>
:<math>\vec E_{cap} = \frac{(56*10^{-6})/(\pi*4.7^{2})}{8.85*10^{-12}} = < 91179.912, 0, 0></math>
The electric field only has an x-component because the field travels from the positively charged plate to the negatively charged plate, traveling in the +x direction.

'''Step 2'''
:Calculate the displacement vector from B to A.
:Set the origin at B.
:<math>\Delta l = < s_{1}, 0, 0> - < 0, 0, 0> = < s_{1}, 0, 0> = < 0.0015, 0, 0></math>
'''Step 3'''
:Calculate the potential difference between B and A.
:<math>\Delta V_{BA} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{BA} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
'''Step 4'''
:Calculate the displacement vector from A to D
:<math>\Delta l = < s_{1}, s_{2}, 0> - < s_{1}, 0, 0> = < 0, s_{2}, 0> = < 0, s_{2}, 0> = < 0, 0.006, 0></math>
'''Step 5'''
:Calculate the potential difference between A and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0 + 0*0 + 0*0) = 0V</math>
'''Step 6'''
:Add <math>\Delta V_{BA}</math> to <math>\Delta V_{AD}</math> to get <math>\Delta V_{BD}</math>
:<math>\Delta V_{BD} = \Delta V_{BA} + \Delta V_{AD} = -136.770 + 0 = -136.770V</math>
Notice that the voltage is negative since we are going from the positively charged plate (high potential) to the negatively charged plate (low potential) losing potential energy in the process.

Now you have to calculate the potential difference from A to C directly.

'''Step 1'''
:Calculate the displacement vector from B to D.
:<math>\Delta l = < s_{1}, s_{2}, 0> - < 0, 0, 0> = < s_{1}, s_{2}, 0> = < s_{1}, s_{2}, 0> = < 0.0015, 0.006, 0></math>
'''Step 2'''
:Calculate the potential difference between B and D.
:<math>\Delta V_{AD} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>
:<math>\Delta V_{AD} = -(91179.912*0.0015 + 0*0 + 0*0) = -136.770V</math>
Notice that potential difference traveling from B to A then D is the same as the potential difference traveling from B to D directly. This exemplifies that the potential difference does not depend on the path taken to get from one point to another.

===Difficult===
[[File:Wiki_difficult.png|center]]
'''Problem''': A uniform spherical shell of charge +Q is centered at point B, as shown in the figure below. Show that ΔV = VC − VA is independent of path by calculating ΔV for each of these two paths (actually do the integrals). (Use the following as necessary: Q, R for the radius of the spherical shell, r1 for the radius of the circular arc A → D → C with B at its center, and ε0.)

'''Step 1'''
:Calculate the potential difference from A to C following the path A → B → C.
:First, calculate the potential difference from A to B.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
:In order to calculate the potential difference from A to B, calculate the electric field of the sphere.
:<math>\vec{E}_{sphere} = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}}</math>
Now plug the electric field calculated above into the integral and solve.
:<math>\Delta V_{AB} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = \int_{r_{1}}^{R} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>
Now calculate the potential difference from B to C.
:Use the electric field of the sphere calculated above to solve the below integral.
:<math>\Delta V_{BC} = \int_{B}^{C} \vec{E} \cdot d\vec{l}</math>
::<math>\Delta V_{AB} = \int_{R}^{-r_{1}} \frac{1}{4\pi\epsilon_{0}}\frac{Q}{R^{2}} \cdot d\vec{l} = \frac{1}{4\pi\epsilon_{0}}(\frac{-Q}{R^{2}} - \frac{Q}{r_{1}^{2}})</math>

==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==

Matter & Interactions volume II by Ruth W. Chabay and Bruce A. Sherwood.

[[Category:Energy]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T19:03:45Z

Amohile3:

File:Wiki difficult.png

2016-04-17T18:50:28Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T18:49:37Z

Amohile3: /* Middling */

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T18:41:14Z

Amohile3: /* Middling */

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T18:40:12Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T17:24:03Z

Amohile3: /* Middling */

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T17:23:41Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T17:21:49Z

Amohile3: /* Examples */

File:Wiki middling.jpg

2016-04-17T17:05:14Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T17:01:09Z

Amohile3: /* Simple */

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T16:59:11Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T16:54:18Z

Amohile3: /* A Mathematical Model */

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T16:52:31Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T16:51:35Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T16:41:21Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T16:36:45Z

Amohile3: /* Examples */

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T16:35:22Z

Amohile3:

File:Wiki simple.jpg

2016-04-17T16:25:11Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-17T16:24:36Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-16T22:31:34Z

Amohile3:

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-16T22:12:20Z

Amohile3:

'''CLAIMED BY ADITYA MOHILE'''
Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{BA} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

The potential difference, <math>\Delta V_{BA}</math>, is the integral of the electrical field from point A to point B. This integral, however, is the dot product of <math>\vec{E}</math> and <math>d\vec{l}</math> which is equal to the sum of the negative electric field multiplied by the difference of the x,y and z components of the 2 points, as see from the equation above. This proves that the path taken from point A to point B does not matter, only the difference in the positions of points A and B are important in calculating the potential difference.
===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?]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-16T21:52:33Z

Amohile3:

'''CLAIMED BY ADITYA MOHILE'''
Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another because the difference between the locations of the two points remain the same regardless of the path taken to get from one to another.

===A Mathematical Model===
:<math>\Delta V_{BA} = \int_{A}^{B} \vec{E} \cdot d\vec{l} = -(E_{x}\Delta x + E_{y}\Delta y + E_{z}\Delta z)</math>

===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?]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-16T21:43:42Z

Amohile3:

'''CLAIMED BY ADITYA MOHILE'''
Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another.

===A Mathematical Model===
:<math>\Delta V_{BA} = \int_{A}^{B} \vec{E} \cdot d\vec{l}</math>
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?]]

Potential Difference Path Independence, claimed by Aditya Mohile

2016-04-16T21:38:08Z

Amohile3: Created page with "'''CLAIMED BY ADITYA MOHILE''' Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to..."

'''CLAIMED BY ADITYA MOHILE'''
Potential difference is a scalar quantity that measures the difference of electric potential between 2 points. The path taken from one point to another does not affect the potential difference therefore potential difference is said to be path independent.
==The Main Idea==

The potential difference between two points does not depend on the path taken to get from one point to another.

===A Mathematical Model===
:<math>\Delta V_{BA} = V(x_B) - V(x_A) = - \int_{r_0}^{x_B} \vec{E} \cdot d\vec{l} - \left( - \int_{r_0}^{x_A} \vec{E} \cdot d\vec{l} \right) </math>
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?]]

Main Page

2016-04-15T00:25:27Z

Amohile3: /* Path independence and round trip potential */

__NOTOC__
Welcome to the Georgia Tech Wiki for Introductory Physics. This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in three semester of introductory physics. You can add subcategories as needed but a single topic should direct readers to a page in one of these categories.

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===

====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Help with VPython=====
<div class=“mw-collapsible-content”>
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Vectors and Units=====
<div class=“mw-collapsible-content”>
*[[Vectors]]
*[[SI units]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Interactions=====
<div class=“mw-collapsible-content”>
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Velocity and Momentum=====
<div class=“mw-collapsible-content”>
*[[Newton’s First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:vpython_resources Software for Projects]

</div>

===Week 2===
====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Momentum and the Momentum Principle=====
<div class=“mw-collapsible-content”>
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Constant Force=====
<div class=“mw-collapsible-content”>
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:scalars_and_vectors Scalars and Vectors]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:displacement_and_velocity Displacement and Velocity]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:modeling_with_vpython Modeling Motion with VPython]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:relative_motion Relative Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:graphing_motion Graphing Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum_principle The Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:acceleration Acceleration & The Change in Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:motionPredict Applying the Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:constantF Constant Force Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:iterativePredict Iterative Prediction of Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>

===Week 3===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Analytic Prediction with a Constant Force=====
<div \
class=“mw-collapsible-content”>
*[[Analytical Prediction]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Varying Force=====
<div \
class=“mw-collapsible-content”>
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke’s Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:drag Drag]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:impulseGraphs Impulse Graphs]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:springMotion Non-constant Force: Springs & Spring-like Interactions]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:friction Contact Interactions: The Normal Force & Friction]

</div>

===Week 4===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Fundamental Interactions=====
<div class=“mw-collapsible-content”>
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]

</div>

===Week 5===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Conservation of Momentum=====
<div class=“mw-collapsible-content”>
*[[Conservation of Momentum]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Properties of Matter=====
<div class=“mw-collapsible-content”>
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young’s Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:model_of_a_wire Modeling a Solid Wire: springs in series and parallel]

</div>

===Week 6===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Identifying Forces=====
<div class=“mw-collapsible-content”>
*[[Free Body Diagram]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Curving Motion=====
<div class=“mw-collapsible-content”>
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_accel Gravitational Acceleration]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:freebodydiagrams Free Body Diagrams]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:curving_motion Curved Motion]

</div>

===Week 7===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Energy Principle=====
<div class=“mw-collapsible-content”>
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy What is Energy?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:point_particle The Simplest System: A Single Particle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work Work: Mechanical Energy Transfer]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_cons Conservation of Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]

</div>

===Week 8===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Work by Non-Constant Forces=====
<div \
class=“mw-collapsible-content”>
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Potential Energy=====
<div class=“mw-collapsible-content”>
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work_by_nc_forces Work Done by Non-Constant Forces]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:power Power: The Rate of Energy Change]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 9===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Multiparticle Systems=====
<div class=“mw-collapsible-content”>
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_sep Separating Energy in Multi-Particle Systems]

</div>

===Week 10===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Choice of System=====
<div class=“mw-collapsible-content”>
*[[System & Surroundings]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Thermal Energy, Dissipation and Transfer of Energy=====
<div \
class=“mw-collapsible-content”>
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Rotational and Vibrational Energy=====
<div \
class=“mw-collapsible-content”>
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:escape_speed Escape Speed]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:internal_energy Internal Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 11===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Different Models of a System=====
<div \
class=“mw-collapsible-content”>
*[[Real Systems]]
*[[Point Particle Systems]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Models of Friction=====
<div class=“mw-collapsible-content”>
*[[Friction]]
*[[Static Friction]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 12===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Collisions=====
<div class=“mw-collapsible-content”>
*[[Newton’s Third Law of Motion]]
*[[Collisions]]
*[[Collisions 2]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:collisions Colliding Objects]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real Point Particle and Real Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:colliding_systems Collisions]

</div>

===Week 13===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Rotations=====
<div class=“mw-collapsible-content”>
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Angular Momentum=====
<div class=“mw-collapsible-content”>
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>
===Week 14===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Analyzing Motion with and without Torque=====
<div \
class=“mw-collapsible-content”>
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:torque Torques Cause Changes in Rotation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]

</div>

===Week 15===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Introduction to Quantum Concepts=====
<div \class=“mw-collapsible-content”>
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]

</div>

<div style=“float:left; width:30%; padding:1%;”>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Page claimed by Laura Winalski]]*
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric force====
<div class="mw-collapsible-content">

*[[Electric Force]] Claimed by Amarachi Eze
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====

<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''Bold text'''====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of Potential Difference, claimed by Tyler Quill]]
</div>

== Claimed by Tyler Quill ==

</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
*[[Conventional Current]]*
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
The Hall effect is a phenomenon that describes why charged particles collect to one side of a conductor in the presence of a magnetic field. It is used to determine the charge of a mobile particle inside a conductor.

== Main Idea ==

The Hall Effect is a phenomenon that is created when charged particles moving through a conductor are submitted to a magnetic field. The magnetic field pushes the charged particles to one side of the conductor. This causes a buildup of charges on one side of the conductor which creates a polarization of the conductor perpendicular to the current flow. Eventually this charge will stabilize as the mobile charges will resist the magnetic field.

===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?]]

<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
[[File:Example.jpg]]

====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[RL Circuits]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>

Main Page

2016-04-15T00:24:51Z

Amohile3: /* Electric potential */

__NOTOC__
Welcome to the Georgia Tech Wiki for Introductory Physics. This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in three semester of introductory physics. You can add subcategories as needed but a single topic should direct readers to a page in one of these categories.

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===

====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Help with VPython=====
<div class=“mw-collapsible-content”>
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Vectors and Units=====
<div class=“mw-collapsible-content”>
*[[Vectors]]
*[[SI units]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Interactions=====
<div class=“mw-collapsible-content”>
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Velocity and Momentum=====
<div class=“mw-collapsible-content”>
*[[Newton’s First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:vpython_resources Software for Projects]

</div>

===Week 2===
====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Momentum and the Momentum Principle=====
<div class=“mw-collapsible-content”>
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Constant Force=====
<div class=“mw-collapsible-content”>
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:scalars_and_vectors Scalars and Vectors]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:displacement_and_velocity Displacement and Velocity]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:modeling_with_vpython Modeling Motion with VPython]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:relative_motion Relative Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:graphing_motion Graphing Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum_principle The Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:acceleration Acceleration & The Change in Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:motionPredict Applying the Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:constantF Constant Force Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:iterativePredict Iterative Prediction of Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>

===Week 3===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Analytic Prediction with a Constant Force=====
<div \
class=“mw-collapsible-content”>
*[[Analytical Prediction]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Varying Force=====
<div \
class=“mw-collapsible-content”>
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke’s Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:drag Drag]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:impulseGraphs Impulse Graphs]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:springMotion Non-constant Force: Springs & Spring-like Interactions]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:friction Contact Interactions: The Normal Force & Friction]

</div>

===Week 4===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Fundamental Interactions=====
<div class=“mw-collapsible-content”>
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]

</div>

===Week 5===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Conservation of Momentum=====
<div class=“mw-collapsible-content”>
*[[Conservation of Momentum]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Properties of Matter=====
<div class=“mw-collapsible-content”>
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young’s Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:model_of_a_wire Modeling a Solid Wire: springs in series and parallel]

</div>

===Week 6===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Identifying Forces=====
<div class=“mw-collapsible-content”>
*[[Free Body Diagram]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Curving Motion=====
<div class=“mw-collapsible-content”>
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_accel Gravitational Acceleration]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:freebodydiagrams Free Body Diagrams]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:curving_motion Curved Motion]

</div>

===Week 7===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Energy Principle=====
<div class=“mw-collapsible-content”>
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy What is Energy?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:point_particle The Simplest System: A Single Particle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work Work: Mechanical Energy Transfer]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_cons Conservation of Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]

</div>

===Week 8===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Work by Non-Constant Forces=====
<div \
class=“mw-collapsible-content”>
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Potential Energy=====
<div class=“mw-collapsible-content”>
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work_by_nc_forces Work Done by Non-Constant Forces]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:power Power: The Rate of Energy Change]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 9===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Multiparticle Systems=====
<div class=“mw-collapsible-content”>
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_sep Separating Energy in Multi-Particle Systems]

</div>

===Week 10===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Choice of System=====
<div class=“mw-collapsible-content”>
*[[System & Surroundings]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Thermal Energy, Dissipation and Transfer of Energy=====
<div \
class=“mw-collapsible-content”>
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Rotational and Vibrational Energy=====
<div \
class=“mw-collapsible-content”>
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:escape_speed Escape Speed]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:internal_energy Internal Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 11===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Different Models of a System=====
<div \
class=“mw-collapsible-content”>
*[[Real Systems]]
*[[Point Particle Systems]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Models of Friction=====
<div class=“mw-collapsible-content”>
*[[Friction]]
*[[Static Friction]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 12===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Collisions=====
<div class=“mw-collapsible-content”>
*[[Newton’s Third Law of Motion]]
*[[Collisions]]
*[[Collisions 2]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:collisions Colliding Objects]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real Point Particle and Real Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:colliding_systems Collisions]

</div>

===Week 13===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Rotations=====
<div class=“mw-collapsible-content”>
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Angular Momentum=====
<div class=“mw-collapsible-content”>
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>
===Week 14===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Analyzing Motion with and without Torque=====
<div \
class=“mw-collapsible-content”>
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:torque Torques Cause Changes in Rotation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]

</div>

===Week 15===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Introduction to Quantum Concepts=====
<div \class=“mw-collapsible-content”>
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]

</div>

<div style=“float:left; width:30%; padding:1%;”>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Page claimed by Laura Winalski]]*
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric force====
<div class="mw-collapsible-content">

*[[Electric Force]] Claimed by Amarachi Eze
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====

<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''Bold text'''====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of Potential Difference, claimed by Tyler Quill]]
</div>

== Claimed by Tyler Quill ==

</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
*[[Conventional Current]]*
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
The Hall effect is a phenomenon that describes why charged particles collect to one side of a conductor in the presence of a magnetic field. It is used to determine the charge of a mobile particle inside a conductor.

== Main Idea ==

The Hall Effect is a phenomenon that is created when charged particles moving through a conductor are submitted to a magnetic field. The magnetic field pushes the charged particles to one side of the conductor. This causes a buildup of charges on one side of the conductor which creates a polarization of the conductor perpendicular to the current flow. Eventually this charge will stabilize as the mobile charges will resist the magnetic field.

===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?]]

<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
[[File:Example.jpg]]

====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[RL Circuits]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>

Main Page

2016-04-14T04:51:41Z

Amohile3: /* Path independence and round trip potential */

__NOTOC__
Welcome to the Georgia Tech Wiki for Introductory Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in three semester of introductory physics. You can add subcategories as needed but a single topic should direct readers to a page in one of these categories.

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===

====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Help with VPython=====
<div class=“mw-collapsible-content”>
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Vectors and Units=====
<div class=“mw-collapsible-content”>
*[[Vectors]]
*[[SI units]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Interactions=====
<div class=“mw-collapsible-content”>
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Velocity and Momentum=====
<div class=“mw-collapsible-content”>
*[[Newton’s First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:vpython_resources Software for Projects]

</div>

===Week 2===
====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Momentum and the Momentum Principle=====
<div class=“mw-collapsible-content”>
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Constant Force=====
<div class=“mw-collapsible-content”>
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:scalars_and_vectors Scalars and Vectors]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:displacement_and_velocity Displacement and Velocity]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:modeling_with_vpython Modeling Motion with VPython]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:relative_motion Relative Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:graphing_motion Graphing Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum_principle The Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:acceleration Acceleration & The Change in Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:motionPredict Applying the Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:constantF Constant Force Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:iterativePredict Iterative Prediction of Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>

===Week 3===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Analytic Prediction with a Constant Force=====
<div \
class=“mw-collapsible-content”>
*[[Analytical Prediction]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Varying Force=====
<div \
class=“mw-collapsible-content”>
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke’s Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:drag Drag]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:impulseGraphs Impulse Graphs]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:springMotion Non-constant Force: Springs & Spring-like Interactions]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:friction Contact Interactions: The Normal Force & Friction]

</div>

===Week 4===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Fundamental Interactions=====
<div class=“mw-collapsible-content”>
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]

</div>

===Week 5===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Conservation of Momentum=====
<div class=“mw-collapsible-content”>
*[[Conservation of Momentum]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Properties of Matter=====
<div class=“mw-collapsible-content”>
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young’s Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:model_of_a_wire Modeling a Solid Wire: springs in series and parallel]

</div>

===Week 6===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Identifying Forces=====
<div class=“mw-collapsible-content”>
*[[Free Body Diagram]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Curving Motion=====
<div class=“mw-collapsible-content”>
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_accel Gravitational Acceleration]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:freebodydiagrams Free Body Diagrams]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:curving_motion Curved Motion]

</div>

===Week 7===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Energy Principle=====
<div class=“mw-collapsible-content”>
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy What is Energy?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:point_particle The Simplest System: A Single Particle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work Work: Mechanical Energy Transfer]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_cons Conservation of Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]

</div>

===Week 8===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Work by Non-Constant Forces=====
<div \
class=“mw-collapsible-content”>
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Potential Energy=====
<div class=“mw-collapsible-content”>
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work_by_nc_forces Work Done by Non-Constant Forces]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:power Power: The Rate of Energy Change]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 9===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Multiparticle Systems=====
<div class=“mw-collapsible-content”>
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_sep Separating Energy in Multi-Particle Systems]

</div>

===Week 10===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Choice of System=====
<div class=“mw-collapsible-content”>
*[[System & Surroundings]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Thermal Energy, Dissipation and Transfer of Energy=====
<div \
class=“mw-collapsible-content”>
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Rotational and Vibrational Energy=====
<div \
class=“mw-collapsible-content”>
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:escape_speed Escape Speed]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:internal_energy Internal Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 11===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Different Models of a System=====
<div \
class=“mw-collapsible-content”>
*[[Real Systems]]
*[[Point Particle Systems]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Models of Friction=====
<div class=“mw-collapsible-content”>
*[[Friction]]
*[[Static Friction]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 12===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Collisions=====
<div class=“mw-collapsible-content”>
*[[Newton’s Third Law of Motion]]
*[[Collisions]]
*[[Collisions 2]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:collisions Colliding Objects]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real Point Particle and Real Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:colliding_systems Collisions]

</div>

===Week 13===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Rotations=====
<div class=“mw-collapsible-content”>
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Angular Momentum=====
<div class=“mw-collapsible-content”>
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>
===Week 14===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Analyzing Motion with and without Torque=====
<div \
class=“mw-collapsible-content”>
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:torque Torques Cause Changes in Rotation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]

</div>

===Week 15===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Introduction to Quantum Concepts=====
<div \class=“mw-collapsible-content”>
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]

</div>

<div style=“float:left; width:30%; padding:1%;”>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Page claimed by Laura Winalski]]*
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric force====
<div class="mw-collapsible-content">

*[[Electric Force]] Claimed by Amarachi Eze
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====

<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''Bold text'''====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of Potential Difference, claimed by Tyler Quill]]
</div>

== Claimed by Tyler Quill ==

</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
*[[Conventional Current]]*
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hall effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[RL Circuits]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>

Main Page

2016-04-14T04:47:07Z

Amohile3: /* Electric potential */

__NOTOC__
Welcome to the Georgia Tech Wiki for Introductory Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in three semester of introductory physics. You can add subcategories as needed but a single topic should direct readers to a page in one of these categories.

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===

====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Help with VPython=====
<div class=“mw-collapsible-content”>
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Vectors and Units=====
<div class=“mw-collapsible-content”>
*[[Vectors]]
*[[SI units]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Interactions=====
<div class=“mw-collapsible-content”>
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Velocity and Momentum=====
<div class=“mw-collapsible-content”>
*[[Newton’s First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:vpython_resources Software for Projects]

</div>

===Week 2===
====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Momentum and the Momentum Principle=====
<div class=“mw-collapsible-content”>
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Constant Force=====
<div class=“mw-collapsible-content”>
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:scalars_and_vectors Scalars and Vectors]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:displacement_and_velocity Displacement and Velocity]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:modeling_with_vpython Modeling Motion with VPython]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:relative_motion Relative Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:graphing_motion Graphing Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum_principle The Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:acceleration Acceleration & The Change in Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:motionPredict Applying the Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:constantF Constant Force Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:iterativePredict Iterative Prediction of Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>

===Week 3===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Analytic Prediction with a Constant Force=====
<div \
class=“mw-collapsible-content”>
*[[Analytical Prediction]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Varying Force=====
<div \
class=“mw-collapsible-content”>
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke’s Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:drag Drag]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:impulseGraphs Impulse Graphs]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:springMotion Non-constant Force: Springs & Spring-like Interactions]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:friction Contact Interactions: The Normal Force & Friction]

</div>

===Week 4===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Fundamental Interactions=====
<div class=“mw-collapsible-content”>
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]

</div>

===Week 5===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Conservation of Momentum=====
<div class=“mw-collapsible-content”>
*[[Conservation of Momentum]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Properties of Matter=====
<div class=“mw-collapsible-content”>
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young’s Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:model_of_a_wire Modeling a Solid Wire: springs in series and parallel]

</div>

===Week 6===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Identifying Forces=====
<div class=“mw-collapsible-content”>
*[[Free Body Diagram]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Curving Motion=====
<div class=“mw-collapsible-content”>
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_accel Gravitational Acceleration]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:freebodydiagrams Free Body Diagrams]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:curving_motion Curved Motion]

</div>

===Week 7===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Energy Principle=====
<div class=“mw-collapsible-content”>
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy What is Energy?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:point_particle The Simplest System: A Single Particle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work Work: Mechanical Energy Transfer]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_cons Conservation of Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]

</div>

===Week 8===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Work by Non-Constant Forces=====
<div \
class=“mw-collapsible-content”>
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Potential Energy=====
<div class=“mw-collapsible-content”>
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work_by_nc_forces Work Done by Non-Constant Forces]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:power Power: The Rate of Energy Change]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 9===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Multiparticle Systems=====
<div class=“mw-collapsible-content”>
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_sep Separating Energy in Multi-Particle Systems]

</div>

===Week 10===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Choice of System=====
<div class=“mw-collapsible-content”>
*[[System & Surroundings]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Thermal Energy, Dissipation and Transfer of Energy=====
<div \
class=“mw-collapsible-content”>
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Rotational and Vibrational Energy=====
<div \
class=“mw-collapsible-content”>
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:escape_speed Escape Speed]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:internal_energy Internal Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 11===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Different Models of a System=====
<div \
class=“mw-collapsible-content”>
*[[Real Systems]]
*[[Point Particle Systems]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Models of Friction=====
<div class=“mw-collapsible-content”>
*[[Friction]]
*[[Static Friction]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 12===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Collisions=====
<div class=“mw-collapsible-content”>
*[[Newton’s Third Law of Motion]]
*[[Collisions]]
*[[Collisions 2]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:collisions Colliding Objects]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real Point Particle and Real Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:colliding_systems Collisions]

</div>

===Week 13===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Rotations=====
<div class=“mw-collapsible-content”>
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Angular Momentum=====
<div class=“mw-collapsible-content”>
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>
===Week 14===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Analyzing Motion with and without Torque=====
<div \
class=“mw-collapsible-content”>
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:torque Torques Cause Changes in Rotation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]

</div>

===Week 15===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Introduction to Quantum Concepts=====
<div \class=“mw-collapsible-content”>
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]

</div>

<div style=“float:left; width:30%; padding:1%;”>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Page claimed by Laura Winalski]]*
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric force====
<div class="mw-collapsible-content">

*[[Electric Force]] Claimed by Amarachi Eze
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====

<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''Bold text'''====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of Potential Difference, claimed by Tyler Quill]]
</div>

== Claimed by Tyler Quill ==

</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
*[[Conventional Current]]*
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hall effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[RL Circuits]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>

Main Page

2016-04-14T04:46:25Z

Amohile3: /* Electric potential */

__NOTOC__
Welcome to the Georgia Tech Wiki for Introductory Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in three semester of introductory physics. You can add subcategories as needed but a single topic should direct readers to a page in one of these categories.

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===

====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Help with VPython=====
<div class=“mw-collapsible-content”>
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Vectors and Units=====
<div class=“mw-collapsible-content”>
*[[Vectors]]
*[[SI units]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Interactions=====
<div class=“mw-collapsible-content”>
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Velocity and Momentum=====
<div class=“mw-collapsible-content”>
*[[Newton’s First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:vpython_resources Software for Projects]

</div>

===Week 2===
====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Momentum and the Momentum Principle=====
<div class=“mw-collapsible-content”>
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Constant Force=====
<div class=“mw-collapsible-content”>
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:scalars_and_vectors Scalars and Vectors]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:displacement_and_velocity Displacement and Velocity]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:modeling_with_vpython Modeling Motion with VPython]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:relative_motion Relative Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:graphing_motion Graphing Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum_principle The Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:acceleration Acceleration & The Change in Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:motionPredict Applying the Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:constantF Constant Force Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:iterativePredict Iterative Prediction of Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>

===Week 3===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Analytic Prediction with a Constant Force=====
<div \
class=“mw-collapsible-content”>
*[[Analytical Prediction]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Varying Force=====
<div \
class=“mw-collapsible-content”>
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke’s Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:drag Drag]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:impulseGraphs Impulse Graphs]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:springMotion Non-constant Force: Springs & Spring-like Interactions]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:friction Contact Interactions: The Normal Force & Friction]

</div>

===Week 4===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Fundamental Interactions=====
<div class=“mw-collapsible-content”>
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]

</div>

===Week 5===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Conservation of Momentum=====
<div class=“mw-collapsible-content”>
*[[Conservation of Momentum]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Properties of Matter=====
<div class=“mw-collapsible-content”>
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young’s Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:model_of_a_wire Modeling a Solid Wire: springs in series and parallel]

</div>

===Week 6===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Identifying Forces=====
<div class=“mw-collapsible-content”>
*[[Free Body Diagram]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Curving Motion=====
<div class=“mw-collapsible-content”>
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_accel Gravitational Acceleration]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:freebodydiagrams Free Body Diagrams]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:curving_motion Curved Motion]

</div>

===Week 7===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Energy Principle=====
<div class=“mw-collapsible-content”>
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy What is Energy?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:point_particle The Simplest System: A Single Particle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work Work: Mechanical Energy Transfer]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_cons Conservation of Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]

</div>

===Week 8===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Work by Non-Constant Forces=====
<div \
class=“mw-collapsible-content”>
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Potential Energy=====
<div class=“mw-collapsible-content”>
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work_by_nc_forces Work Done by Non-Constant Forces]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:power Power: The Rate of Energy Change]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 9===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Multiparticle Systems=====
<div class=“mw-collapsible-content”>
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_sep Separating Energy in Multi-Particle Systems]

</div>

===Week 10===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Choice of System=====
<div class=“mw-collapsible-content”>
*[[System & Surroundings]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Thermal Energy, Dissipation and Transfer of Energy=====
<div \
class=“mw-collapsible-content”>
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Rotational and Vibrational Energy=====
<div \
class=“mw-collapsible-content”>
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:escape_speed Escape Speed]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:internal_energy Internal Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 11===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Different Models of a System=====
<div \
class=“mw-collapsible-content”>
*[[Real Systems]]
*[[Point Particle Systems]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Models of Friction=====
<div class=“mw-collapsible-content”>
*[[Friction]]
*[[Static Friction]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 12===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Collisions=====
<div class=“mw-collapsible-content”>
*[[Newton’s Third Law of Motion]]
*[[Collisions]]
*[[Collisions 2]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:collisions Colliding Objects]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real Point Particle and Real Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:colliding_systems Collisions]

</div>

===Week 13===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Rotations=====
<div class=“mw-collapsible-content”>
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Angular Momentum=====
<div class=“mw-collapsible-content”>
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>
===Week 14===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Analyzing Motion with and without Torque=====
<div \
class=“mw-collapsible-content”>
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:torque Torques Cause Changes in Rotation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]

</div>

===Week 15===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Introduction to Quantum Concepts=====
<div \class=“mw-collapsible-content”>
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]

</div>

<div style=“float:left; width:30%; padding:1%;”>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Page claimed by Laura Winalski]]*
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric force====
<div class="mw-collapsible-content">

*[[Electric Force]] Claimed by Amarachi Eze
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====

<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''Bold text'''====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence]] claimed by Aditya Mohile
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of Potential Difference, claimed by Tyler Quill]]
</div>

== Claimed by Tyler Quill ==

</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
*[[Conventional Current]]*
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hall effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

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====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

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====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
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====Semiconductors====
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*[[Semiconductor Devices]]
</div>
</div>

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====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[RL Circuits]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>