A conducting spherical shell has inner radius a, outer radius b, and has a +Q point charge at the center. A charge of -Q is put on the conductor.
a) What is the charge on the inner and outer surface of the shell?
b) What is the electric field everywhere?
c) What is the electric potential everywhere?
V = -∫E[itex]\bullet[/itex]dl
The Attempt at a Solution
a) From conservation of charge and the fact that it's a conductor, the charge on the inner surface of the shell is -Q and the charge on the outer surface is 0. In addition, there is no charge inside the shell.
b) For 0 < r < a, Gauss's Law gives E = kQ/(r^2)
For a < r < b, E = 0
For r > b, E = 0
c) This is where I'm stuck. E = 0 for r > b, so the potential difference is 0. But the question asks for the actual potential function. Normally, I would use V = kQ/r. But Q = 0 in this case, so V = 0. So that would mean V = 0 for a < r < b Lastly, for 0 < r < a,
V(r) = V(a) - kQ((1/a)-(1/r)) = 0 - kQ((1/a)-(1/r)) = kQ((1/r)-(1/a)).
I believe this is what the answer should be. Please, can anyone tell me if they agree?