# Gauss' Law conductors

• PhysicsInNJ
In summary, the 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. The charge on the outer surface of the middle conductor is -Q, as the total charge on the second conductor is -2Q and the inner surface is -Q, making the outer surface -Q as well. This is because the electric field within a conductor is zero, and the charge on the outer surface does not affect it.

## 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.

PhysicsInNJ said:
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!

PhysicsInNJ said:
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?

PhysicsInNJ said:
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.
PhysicsInNJ said:
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.
PhysicsInNJ said:
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!