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Charges on Conductors

An isolated c...

Question

An isolated conductor of any shape has a net charge of $+ 15 μ C$ . Inside the conductor is a cavity within which is a point-charge of $+ 3.0 μ C$ . What is the charge on the cavity wall and on the outer surface of the conductor?

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Solution

Within a conductor, the total charge must be zero. Thus,
$\begin{matrix} q_{p} + q_{i} = 0 q_{i} = - q_{p} = - 3 μ C \end{matrix}$
The total charge has a net charge of $- 15 μ C$ , hence
$\begin{matrix} q_{i} + q_{o} = - 15 μ C q_{o} = - 15 μ C - q_{i} = - 12 μ C \end{matrix}$

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