### All AP Physics C Electricity Resources

## Example Questions

### Example Question #171 : Ap Physics C

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:**

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

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:**

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

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:**

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

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:**

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

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:**

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

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:**

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

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:**

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

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:**

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

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:**

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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