A conductor A with a cavity as shown in the figure is given a charge Q. Find the net charge which appears on the inner surface of the cavity.

Assume a Gaussian surface that is lying wholly within a conductor and enclosing the cavity. The electric field intensity (E) acting inside the charged conductor is zero.
Let q be the charge inside the conductor and ${\mathrm{\epsilon }}_0$ be the permittivity of free space. Now, according to Gauss's law, we have the electric flux
$\mathrm{\varphi }=\overrightarrow{\mathrm{E}}\cdot \mathrm{d}\overrightarrow{\mathrm{s}}=\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$
where E=0 ; thus q=0. Therefore, the charge inside the conductor is zero. That is, the charges appear on the outer surface of the conductor.