# Gauss' Law conductors

## Homework Statement

Three concentric hollow spherical conductors are charged as follows: the inner conductor carries charge Q, the middle conductor carries charge -2Q, and the outer conductor carries charge -Q. What is the charge on the outer surface of the middle conductor?

Flux= Qenc / ε0

## The Attempt at a Solution

Because the flux inside a conductor has to be zero, I drew a gaussian surface in the second conductor, since the first conductor is carrying Q, the inner surface of the 2nd conductor should carry -Q, and the outer surface, to neutralize that should carry Q.

This is incorrect, and the correct answer is apparently -Q.

## Answers and Replies

Doc Al
Mentor
drew a gaussian surface in the second conductor, since the first conductor is carrying Q, the inner surface of the 2nd conductor should carry -Q,
Good!

and the outer surface, to neutralize that should carry Q.
The outer surface doesn't have to 'neutralize' anything. Hint: What's the total charge on the second conductor?

Doen't the inside of the conductor itself have to have no electric field? and if you have uneven charges there would be a field? And if the total charge of the second conductor is -2Q, and the inner surface is -Q, then they just are additive and the outer surface becomes -Q?

Doc Al
Mentor
Doen't the inside of the conductor itself have to have no electric field?
That's correct: within the conducting material, the electric field is zero.
and if you have uneven charges there would be a field?
Not sure what you mean by "uneven". Realize that the charge on the outer surface of the conductor has no effect on the field within it.
And if the total charge of the second conductor is -2Q, and the inner surface is -Q, then they just are additive and the outer surface becomes -Q?
Correct. That's all there is to it.

PhysicsInNJ
That was what I was getting caught up in, that the charge on the outside does not effect the field inside. Thank you!!