# AP Physics C Electricity : Understanding Electrostatics

## Example Questions

### Example Question #1 : Understanding Electrostatics

A hollow metal sphere with a diameter of 10cm has a net charge of  distributed uniformly across its surface. What is the magnitude of the field a distance 2.0m from the center of the sphere?

Explanation:

Relevant equations:

(electric field of point charge)

Anywhere outside the metal sphere, the electric field is the same as it would be for a point charge of the same magnitude, located at the center of the sphere. So, calculate the electric field of a point charge given:

Plugging in gives:

### Example Question #1 : Electricity

Two infinite parallel conducting sheets each have positive charge density . What is the magnitude and direction of the electric field to the right of the right sheet?

, to the left

, to the right

, to the right

, to the right

, to the right

Explanation:

Relevant equations:

(field due to single infinite plane)

Electric field is additive; in other words, the total electric field from the two planes is the sum of their individual fields:

The direction of the electric field is away from positive source charges. Thus, to the right of these positively charged planes, the field points away to the right.

### Example Question #1 : Electricity

Consider a spherical capacitor made of two nested spheres. The smaller sphere has a radius of  and a charge of , and lies within a larger sphere with radius  and a charge of

Which of the following equations accurately describes the capacitance of this spherical capacitor?

Due to symmetry, this scenario would not produce capacitance

Explanation:

To solve this problem, we will need to derive an equation.

We know that:

We can use Gauss's law to derive the electric field between the two circles yielding:

Doing our integration with respect to  from  to , we get:

We can plug this back into our equation for capacitance to get: