Calculating Net Charge on a Spherical Conducting Shell

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Homework Statement

10C of charge are placed on a spherical conducting shell. A -3C point charge is placed at the center of the cavity. The net charge in coulombs on the inner surface of the shell is...

A. -7
B. -3
C. 0
D. +3
E. +7

Homework Equations

$$\oint \vec{E}\cdot d\vec{a} =\frac{Q_{enc}}{\epsilon_0}$$

The Attempt at a Solution

Well, I believe the E field in conducting shell is 0 and inside the cavity the field will also be zero. So, the charges must be on the inner and outer surfaces of the spherical conducting shell. It looks like I should be solving for Q(enclosed) in Gauss's law since that is the net charge but I'm not totally sure about that. I'm stuck now with what to do.

 

[LowlyPion]

Well, I believe the E field in conducting shell is 0 and inside the cavity the field will also be zero. So, the charges must be on the inner and outer surfaces of the spherical conducting shell. I'm stuck now with what to do.

I think you almost have it.

Inside the sphere there is an e-field about the point charge though. But you are right there is no field in the conductor. (If there was, the electrons would rearrange themselves wouldn't they?)

So if there is no field in the conductor ... and you draw a Gaussian surface inside the conductor around whatever charge there may be on the inner surface, and Gauss Law is the net of the charge contained inside and ... oh did I mention already that the conductor had no field? ... so doesn't that mean then ...

 

[roflcopter]

But you are right there is no field in the conductor. (If there was, the electrons would rearrange themselves wouldn't they?)

Yes they would rearrange themselves since E would be not be 0 and so there would be a force F=qE.

Now, since E=0 in the conductor then when solving for q in Gauss's law q is equal to zero. So, there should be an equal magnitude charge on the inner surface with an opposite sign (compared to the enclosed charge from the cavity) in order to balance things out.

So the answer looks like +3.

 

[LowlyPion]

So the answer looks like +3.

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