1. Three spherical conductors of equal size have charges 1, 1/2, and -1/2 deposited on them, respectively.

c) A spherical conductor of radius R has a charge Q deposited somewhere inside of it and is subsequently allowed to reach equilibrium. The radius of the conductor is then shrunk to half its original size. What is the new charge density on the surface of the sphere as a function of Q and R? What is the new charge density inside of the volume (excluding the outer surface).

d) An insulator of radius R has a charge Q deposited evenly somewhere inside of it. The radius of the insulator is the shrunk to half its original size. What is the new charge density inside of the volume of the sphere?