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)

$R$

Answer 2

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