Question

In the figure shown, a spherical conductor has a spherical cavity. A charge $Q$ is placed as shown in figure. Then, choose the correct statement(s):

• A. Charge distribution on ${\text{S}}_1$ is uniform and on ${\text{S}}_2$ is non-uniform.
• B. Charge distribution on ${\text{S}}_2$ is uniform and on ${\text{S}}_1$ is non-uniform.
• C. Charge distributions on both ${\text{S}}_1$ and ${\text{S}}_2$ are uniform.
• D. Charge distributions on ${\text{S}}_1$ and ${\text{S}}_2$ are non-uniform.

Answer 1

The correct option is B Charge distribution on ${\text{S}}_2$ is uniform and on ${\text{S}}_1$ is non-uniform.

Due to the induction process, the $+Q$ charge placed inside the cavity induces $-Q$ charge on the surface ${\text{S}}_1$. Since the charge is not placed at the geometrical centre of the cavity, so the charge distribution on ${\text{S}}_1$ is non-uniform. [in order to make the electric field at every point in the cavity equal to zero.

However, since the electric field doesn't pass through the conductor, charge distribution on the outer surface is not influenced by $Q$. Hence, charge distribution on $S_2$ will be uniform, independent of the location of $Q$.
Option (b) is correct.

Why this question? Charge distribution on the inner surface is uniform only if the cavity is spherical and the charge is placed at the geometric center.