Question

The capacity of an isolated conducting sphere of radius $R$ is proportional to

• A. $R^2$
• B. $\frac{1}{R^2}$
• C. $\frac{1}{R}$
• D. $R$

Answer 1

Answer: (D)

The capacitance of the conductor is
$C=\frac{q}{V}$
Potential on sphere of radius $R$ is
$V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{R}$
$\therefore C=\frac{q\times 4\pi {\epsilon }_{0}R}{q}=4\pi {\epsilon }_{0}R$
$\Rightarrow C\propto R$