An isolated conductor has net charge 8.0 C and a cavity with a particle of charg

Question

An isolated conductor has net charge 8.0 C and a cavity with a particle of charge q = + 12 C .

(a) Determine the charge on the cavity wall.

(b) Determine the charge on the outer surface.

These are my teachers requirements if you could please follow them I would really appreciate it thank you :)

In addition to being neat and clear, and actually answering the question, you must:

1) show the original principle (often in equation form)

2) substitute variables as needed

3) solve it first (before substituting numbers)

4) show every substitution (with units and correct sig figs)

5) present a boxed answer (with units and correct sig figs)

In a Force problem in more than one dimension, you MUST start with a Free Body Diagram.

Explanation / Answer

Use Gauss' Law, the electric flux through a closed surface is proportional to the charge enclosed:

= q

a) Choose you Gaussian Surface with the thickness of the conductor. You know that electric field in the material of a conductor is zero at equilibrium (because if it wasn't, there'd be a force on the conduction electrons, which would accelerate, which would violate the conditions of equilibrium). So, the flux through your Gaussian Surface is zero, as

= E dA

and we just noted that E was zero.

That means that the charge within the Gaussian Surface must also be zero. But you know there's a +12C point charge in the cavity. The only way the charge within the Gaussian Surface can be zero, then, is if there is a charge of -12C on the cavity wall.

b) Then, note that charge must be conserved. The conductor has a net charge of -8C, but there's -12C on the cavity wall. Therefore, the outer surface must have

-8C - (-12C) = +4C

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