Force on charges inside/out of a hollow conductor

[wizang]

Homework Statement

Two charges, q and q', are located respectively, inside and outside a hollow conductor. Charge q' experiences a force due to q, but not vice versa. Prove this statement and explain the apparently violation of Newton's third law. There is no net charge on the conductor.

Homework Equations

None really, conceptual problem.

The Attempt at a Solution

I always have a hard time with E+M conceptual problems in particular for some reason. I'll muddle my way through an explanation, feel free to correct/ridicule or whatever. For example, let's say the charge inside the conductor is negative, and the charge outside is positive. The inner charge with induce a positive charge on the inner surface of the conductor, and a positive charge on the outside. The outer charge will feel a force due to the negative charge on the conductor due to the inner charge. Here's where I feel less confident. I think of the inner charge being sort of "shielded" against the outer charge since there is a positive charge on the inside of the conductor. The outer charge is exerting a force on the conductor then rather than the inner charge. I can't really explain how this is okay under the third law, any hints? Thank you very much.

 

[rude man]

I was waiting for someone else to help, but as there don't seem to be any other volunteers ...

OK, it's obvious why there should be an electeric field at q'. Just invoke the Gauss theorem.

The E field inside the sphere (where q is located) is zero, because charge on the (outer)surface moves towards q' and away from the opposite direction, away from q'. This sets up a neutralizing field within the sphere such that the net field is zero.

Of course, the force is on the sphere in lieu of being on q, so ole' Isaac is not violated.

I have tried to prove this rigorously but can't think of a way to do that. There must be some conservation law that can prove it.