# Electric Potential of grounded hollow metal sphere

1. Feb 26, 2012

### ti-84minus

1. The problem statement, all variables and given/known data
There is a solid metal ball of radius 'a' (with charge Q) that is placed inside a hollow metal sphere (inner radius = 'b', outer radius = 'c'). The metal sphere is grounded (so V = 0 at r = c).
a) Find the electric potential V everywhere.
b) Find the charge on the metal shell at r = c and r = b.

2. Relevant equations
V = U/q0.
V = $\frac{1}{4\pi\epsilon_{0}}\int\frac{dq}{r}$

3. The attempt at a solution
I considered the problem case by case:
r<a : V = $\frac{Q}{4\pi r\epsilon_{0}}$

a<r<b
b<r<c
r>c

Would the other three cases have the same result, since electric field is zero when b<r<c and r>c? (actually, when r>c, IS the electric field zero, since the sphere is grounded?)

Thanks for your help!