# Electric Potential with Non-conducting sphere and conducting shell

Tags:
1. Nov 17, 2014

### electronvolt

1. The problem statement, all variables and given/known data
A spherical nonconductor of radius a carries charge +Q uniformly spread through its volume. 2 hemispherical conducting shells of inner radius b and outer radius c are placed concentrically with the nonconducting sphere to form a single conducting sphere.

The conducting shell is momentarily connected by a wire to 0 potential (grounded) and then the wire is removed.
Determine the electric potential at r=b just outside the conducting shell
a) Before the conducting shell is introduced
b) After the conductor is introduced but before it is grounded
c) After the conductor is grounded.

2. Relevant equations
Potential difference =
V= ${\frac{Q}{4πε_0r}}$.

3. The attempt at a solution
For a) The nonconducting sphere can be modeled as a point charge, so the potential at b is simply ${\frac{Q}{4πε_0b}}$.

For b) The electric field is the same at all points except that when b<r<c, where the electric field is 0. So the potential at b should be the same as the potential at c, so V = ${\frac{Q}{4πε_0c}}$.

For c) While the conducting shell is grounded it will gain negative charge -Q due to the positive charge on the nonconducting sphere. Once the wire is removed the net charge of both the nonconducting sphere and shell will be 0, and so the electric field for r>c will be 0. The electric field inside of the conducting will also be 0. Since the field is zero from infinitely far away to b, the electric potential is 0. I'm not at all confident about this answer, though.

Any assistance would be greatly appreciated.

2. Nov 17, 2014

### Simon Bridge

(b) check your reasoning ... the conducting sphere is electrically neutral, so what happens to the charges when it is brought close to the charged sphere?
(c) think of it as charge conducted away.