Answer to Question #27406 in Electricity and Magnetism for Shourya Saraswat

Question

A charge q is distributed uniformly throughout a spherical volume of radius R . Setting V=0 at infinity , show that the potential at a distance r from the center , where r<R , is given by

V = q [3(R)^2-(r)^2] / 8(pi)(epsilon)(R)^3