AP Physics C Electricity : Calculating Electric Potential

Study concepts, example questions & explanations for AP Physics C Electricity

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Example Questions

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Example Question #171 : Ap Physics C

Ap physics c e m potential problems  2 6 16  1  2

Three equal point charges  are placed at the vertices of an equilateral triangle of side length . Calculate the potential at the center of the triangle, labeled P.

Possible Answers:

Correct answer:

Explanation:

Draw a line from the center perpendicular to any side of the triangle. This line divides the side into two equal pieces of length . From the center, draw another line to one of the vertices at the end of this side. This produces a 30-60-90 triangle with longer leg , so the hypotenuse (the distance from the vertex to the center) is . The potential at the center is due to three of these charges, so it must be

Example Question #21 : Electricity

Ap physics c e m potential problems  2 6 16  1  1

A uniformly charged hollow disk has inner radius  and outer radius , and carries a total charge . Calculate the potential a distance  from the center, on the axis of the disk.

Possible Answers:

Correct answer:

Explanation:

Use a polar coordinate system with surface charge density  and area element . The distance from the point of interest to a point a distance  from the center is , so the potential is

Example Question #171 : Ap Physics C

Ap physics c e m potential problems  2 6 16  1

Two point charges  and  are separated by a distance . Calculate the potential at point P, a distance  from charge  in the direction perpendicular to the line connecting the two charges.

Possible Answers:

Correct answer:

Explanation:

By the Pythagorean theorem, the distance from point P to charge  is . Because point P is also  from charge , it follows that the potential is

Example Question #21 : Electricity And Magnetism Exam

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A nonuniformly charged ring of radius  carries a linear charge density of . Calculate the potential at the center of the ring.

Possible Answers:

Correct answer:

Explanation:

Use a polar coordinate system, the given linear charge density , and length element . Since every point on the ring is the same distance  from the center, we calculate the potential as

 

Example Question #22 : Electricity And Magnetism Exam

Ap physics c e m potential problems  2 6 16   6

In this model of a dipole, two charges  and  are separated by a distance  as shown in the figure, where the charges lie on the x-axis at  and  respectively. Calculate the exact potential a distance  from the origin at angle  from the axis of the dipole.

Possible Answers:

Correct answer:

Explanation:

By the law of cosines, the distance from the point to charge  is

 .

The distance to charge  can be found by using the law of cosines using the supplementary angle , for which . Therefore the distance to  is

 .

Lastly, the exact potential is given by

.

Remark: Far from the dipole (approximating ) gives the much simpler equation for the potential of an ideal electric dipole .

Example Question #181 : Ap Physics C

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A uniformly charged hollow spherical shell of radius  carries a total charge . Calculate the potential a distance  (where ) from the center of the sphere.

Possible Answers:

Correct answer:

Explanation:

Use a spherical coordinate system and place the point of interest a distance  from the center on the z-axis. By the law of cosines, the distance from this point to any point on the sphere is . Using surface charge density  and area element , we evaluate the potential as:

.

 Remarkably, this is the same potential that would exist a distance  from a point charge.

Example Question #11 : Calculating Electric Potential

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A thin bar of length L lies in the xy plane and carries linear charge density , where  ranges from 0 to . Calculate the potential at the point  on the y-axis.

Possible Answers:

Correct answer:

Explanation:

Use the linear charge density  and length element , where each point is  from the point . The potential is therefore

Example Question #181 : Ap Physics C

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A uniformly charged ring of radius  carries a total charge . Calculate the potential a distance  from the center, on the axis of the ring.

Possible Answers:

Correct answer:

Explanation:

Use the linear charge density  and length element . The distance from each point on the ring to the point on the axis is . Lastly, integrate over  from  to  to obtain

Example Question #181 : Ap Physics C

Ap physics c e m potential problems  2 6 16

A uniformly charged square frame of side length  carries a total charge . Calculate the potential at the center of the square.

You may wish to use the integral:

Possible Answers:

Correct answer:

Explanation:

Calculate the potential due to one side of the bar, and then multiply this by  to get the total potential from all four sides. Orient the bar along the x-axis such that its endpoints are at , and use the linear charge density . The potential is therefore

 

 

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