# AP Physics C Electricity : Electricity

## Example Questions

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### Example Question #31 : Electricity And Magnetism Exam

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.

Explanation:

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

### Example Question #11 : Calculating Electric Potential

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

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

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:

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

### Example Question #1 : Understanding Charge Distributions On Objects

Consider a spherical shell with radius  and charge . What is the magnitude of the electric field at the center of this spherical shell?

Zero

Zero

Explanation:

According to the shell theorem, the total electric field at the center point of a charged spherical shell is always zero. At this point, any electric field lines will result in symmetry, canceling each other out and creating a net field of zero at that point.

### Example Question #1 : Interpreting Electric Charge Diagrams

A charge of unknown value is held in place far from other charges. Its electric field lines and some lines of electric equipotential (V1 and V2) are shown in the diagram.

A second point charge, known to be negative, is placed at point A in the diagram. In which direction will the second, negative charge freely move?

Toward the original charge Q

It will remain stationary

Toward point A

Toward point C