Question

A conductor with an inner cavity, like that shown in Fig.22.23c from the textbook, carries a total charge of +5.40 nC. The charge within the cavity, insulated from the conductor is -7.80 nC. How much charge is on How much charge is on the inner surface of the conductor? How much charge is on the outer surface of the conductor?

Answer 1

Charge residing on the inside of the conductor is -7.80nC. This will induce an equal and opposite charge of +7.80nC uniformly over the inner surface of the conductor. This can be shown to be true if you create a Gaussian Surface of radius bigger than the inner radius of the conductor but smaller than the outer radius. Then by Gauss' Law the charge enclosed should be zero since the Electric Field inside a conductor must be zero.

So the charge on the inner surface of the conductor is q_inner = +7.80 nC

Now this +7.80nC induces an equal and opposite charge of -7.80nC uniformly over the outer surface of the conductor.

But we know that there is already a charge of +5.40nC residing on the outer surface of the conductor therefore the net charge on the outer surface now will be: q_outer = -( 7.80 + 5.40) nC = -2.40nC