A ball of charge of radius R has a uniform charge density and a total charge

Question:

A ball of charge of radius R has a uniform charge density ρ and a total charge Q = 4/3 πR3ρ.

(a) Find the electrostatic energy density at a distance r from the center of the ball for r < R and for r > R.

(b) Find the energy in a spherical shell of volume 4πr2 dr for both r < R and r > R.

(c) Compute the total electrostatic energy by integrating your expressions from part (b), and show that your result can be written U = 3/5 kQ2/R. Explain why this result is greater than that for a spherical conductor of radius R carrying a total charge Q.