A conducting sphere of radius R1 is given a free charge Q. The sphere is surrounded by an uncharged concentric spherical dielectric shell having an inner radius R1, an outer radius R2, and a dielectric constant κ. The system is far removed from other objects.

(a) Find the electric field everywhere in space.

(b) What is the potential of the conducting sphere relative to V = 0 at infinity?

(c) Find the total electrostatic potential energy of the system.