A metal sphere of radius r1 carries a positive charge of amount Q. A concentric spherical metal shell with inner radius r2 and outer radius r3 surrounds the inner sphere and carries a total positive...

A metal sphere of radius r1 carries a positive charge of amount Q. A concentric spherical metal shell with inner radius r2

and outer radius r3 surrounds the inner sphere and carries a total positive charge of amount 4Q, with some of this charge on

the outer surface (at r3) and some on the inner surface (at r2).

(a) How is the charge of 4Q distributed on the two surfaces of the outer shell? Prove this!

(b) What is the potential (relative to infinity) just outside r3, halfway between r2 and r3, just inside r2, just outside r1,

and at the center?