Question

Figure shows a neutral conductor (spherical shape) having a random shaped cavity. A charge $Q$ is placed in the cavity. Choose the correct statement(s).

• A. The induced charges appearing on ${\text{S}}_1$ are uniformly distributed.
• B. The charges appearing on ${\text{S}}_2$ are uniformly distributed.
• C. Electric field due to induced charges on ${\text{S}}_1$ and $Q$ is Non-zero at point $\text{P}$.
• D. The induced charges appearing on ${\text{S}}_1$ are non-uniformly distributed.

Answer 1

Answer: (B), (C), (D)

The induced charges appearing on ${\text{S}}_1$ are non-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 surface of the conductor. Hence, any cavity of any shape and size is always shielded from outer electrical influence.

So, the electric field due to induced charges on ${\text{S}}_1$ is directed towards $S_1$ and electric field due to charge $Q$ at point $\text{P}$ is also directed towards $S_1$. Therefore, Net electric field at point $P$ is Non-zero, and influence of charges $S_2$ at point $P$ will be zero due to electrostatic shielding.

Due to the induction process, the $+Q$ charge placed in the cavity induces $-Q$ charge on the surface ${\text{S}}_1$. Since the surface ${\text{S}}_1$ is non-uniform and charge is also not placed symmetrically, so the induced charge will be non-uniformly distributed.

Since the conductor is electrically neutral, $+Q$ charge appears on $S_2$. The surface is uniform, so the induced charge on it will be uniformly distributed.

Hence, option (a), (c) and (d) are correct statements.