Question

A number of spherical conductors of different radii are changed to same potential. The surface charge density of each conductor is related with its radius as

• A. $\sigma \propto \frac{1}{R^2}$
• B. $\sigma \propto \frac{1}{R}$
• C. $\sigma \propto R$
• D. None of these

Answer 1

The correct option is B $\sigma \propto \frac{1}{R}$

$\sigma =\frac{q}{A}\sigma =\frac{q}{4\pi r^2}$(as sphere).

$v=\frac{q}{4\pi {ϵ}_{0}r}=\frac{\sigma r}{{ϵ}_0}$

$\therefore \sigma =\frac{v{ϵ}_0}{r}$(As $v$ is constant).

$\therefore \sigma \propto \frac{1}{r}$