Question

A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge is placed at the centre of the spherical cavity, the surface charge density on the outer surface is

• A. $\frac{-q}{4\pi R^{2}_{1}}$
• B. $\frac{q}{4\pi R^{2}_{2}}$
• C. $\frac{q^2}{4\pi R^{2}_{1}}$
• D. $\frac{2q}{4\pi R^{2}_{2}}$

Answer 1

Answer: (B)

Surface charge density on the outer surface $=\frac{+q}{4\pi R^{2}_{2}}$ When a charge $+q$ is placed at the centre of spherical cavity as shown in figure.

Charge induced on the inner surface of shell $= - q \,... (i)$
Charge induced on the outer surface of shell $= + q\, ... (ii)$
$\therefore $ Surface charge density on the inner surface $=\frac{-q}{4\pi R^{2}_{1}}$