1.75 Energy of concentric shells *

(a) Concentric spherical shells of radius a and b, with a b, carry charge Q and -Q, respectively, each charge uniformly distributed. Find the energy stored in the electric field of this system.

(b) Calculate the stored energy in a second way: start with two neutral shells, and then gradually transfer positive charge from the outer shell to the inner shell in a spherically symmetric manner. At an intermediate stage when there is charge q on the inner shell, find the work required to transfer an additional charge dq. And then integrate over q.