A solid, conducting sphere of radius "a" and charge -Q is concentric with a spherical conducting shell of inner radius "b" and outer radius "c". The net charge on the shell is +3Q. Take the zero of electric potential to be at some point at infinity.
a.) Use Gauss's law to find the charge on the inner and outer surface of the shell.
b.) Use the superposition principle for potential to find the potential at all points in space.
c.) Use the results of part b) to find the electric field at all points in space.
The Attempt at a Solution
For part a) I took a gaussian surface between the radius b and c, so the E field is zero. Therefore Qinner-Q=0, so Qinner=Q. So outer charge must be 2Q then.
I am completely stuck on part b). What I think I am supposed to do is get the net charge, 2Q, and multiply that by Ke, and divide it by the radius. So basically the answer will be 2QK/r, where r is the radius of the point in space I am trying to find, but that seems really wrong, especially when I am trying to find the E fields from that, as taking the negative derivative will just give me the same result. How should I do this?