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

Rajasthan PMTRajasthan PMT 2007Electrostatic Potential and Capacitance

Solution:

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