Electrostatic potential energy of a nonconducting sphere

[Edasaur]

Homework Statement

Determine the total electrostatic potential energy of a nonconducting sphere of radius r0 carrying a total charge Q distributed uniformly throughout its volume.
Express your answer in terms of the variables Q, r0, and appropriate constants.

Homework Equations

V = kQ/r

U = qV

The Attempt at a Solution

Since the total amount of charge within the sphere is Q and the sphere has a radius of r0, we can make V = kQ/r0. Since U = qV, then U = kqQ/r0. However, I'm not sure how to express q in terms of Q.

 

[Andrew Mason]

Homework Statement

Determine the total electrostatic potential energy of a nonconducting sphere of radius r0 carrying a total charge Q distributed uniformly throughout its volume.
Express your answer in terms of the variables Q, r0, and appropriate constants.

Homework Equations

V = kQ/r

U = qV

The Attempt at a Solution

Since the total amount of charge within the sphere is Q and the sphere has a radius of r0, we can make V = kQ/r0. Since U = qV, then U = kqQ/r0. However, I'm not sure how to express q in terms of Q.

If the charge Q is uniformly distributed over the entire volume of the sphere, v, the charge density is σ = Q/v. So the charge in a volume dv is dq = σdv

Using this charge density, work out the potential energy of a hollow sphere of inside radius r and outside radius r+dr formed around the outside of a solid charged sphere of radius r. Integrate that from r=0 to r=r0.

AM