Question

Figure shows a neutral conductor (random shape) having spherical cavity. A charge $Q$ is placed symmertrically at the center of cavity choose the correct statement(s)

• A. $\overrightarrow{E}$ due to ${\text{S}}_1$ and $Q$ is zero at point $\text{P}$.
• B. The induced charges appearing on ${\text{S}}_1$ are uniformly distributed.
• C. The induced charges appearing on ${\text{S}}_1$ are non-uniformly distributed.
• D. No charges appear on surface ${\text{S}}_2$.

Answer 1

Answer: (A), (B)

The induced charges appearing on ${\text{S}}_1$ are uniformly distributed.


Electric field inside a cavity in a conductor is always zero. Even if the conductor is charged or charges are induced on a neutral conductor by an external field, all charges reside only on the outer surface of the conductor. Hence, any cavity of any shape and size is always shielded from outer electric influence.

So, the electric field due to ${\text{S}}_1$ and $Q$ at point $\text{P}$ is zero, due to electrostatic shielding.

Due to the induction process, the $+Q$ charge placed at centre induces $-Q$ charge on the surface ${\text{S}}_1$. Since the surface area of ${\text{S}}_1$ is uniform and the charge is placed at the centre of the cavity, so the induced charge will be uniformly distributed.

Since the conductor is electrically neutral, $+Q$ charge appears on $S_2$. The surface is non-uniform so, the induced charge on it will be non-uniformly distributed (charge density inversely proportional to radius of curvature).

Hence, option (a) and (b) are correct statements.