Question

Charge Q=+ 3.00 μC is distributed uniformly over the volume of an insulating sphere that has radius R = 6.00 cm .What is the potential difference between the center of the sphere and the surface of the sphere?

Answer 1

For an insulating sphere distributed by charge, the potential function at an outside point and at an inside point are different.

The potential at an outside point is given as(x>R)

x is the distance of the point from the center. The above function is for x > R or x = R

The potential at an inside point is given as (x<R)

Therefore, from the question,

So,

Potential at surface is:

The potential at the center is given by:

Therefore, potential difference is: