First slide

Gauss's Law

Question

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

Moderate

A

+Q
B

-Q
C

+Q/2
D

Zero

Solution

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 $ε_{0}$ be the permittivity of free space. Now, according to Gauss's law, we have the electric flux
$ϕ = \vec{E} \cdot d \vec{s} = \frac{q}{ε_{0}}$
where E=0 ; thus q=0. Therefore, the charge inside the conductor is zero. That is, the charges appears on the outer surface of the conductor.

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