The earth is assumed to be charged conducting sphere having volume $V$ and surface area $A$. The capacitance…
The earth is assumed to be charged conducting sphere having volume $V$ and surface area $A$. The capacitance of the earth in free space is
$\frac{2 \pi \epsilon_0 V}{A}$
$\frac{12 \pi \epsilon_0 V}{A}$
$\frac{8 \pi \epsilon_0 V}{A}$
$\frac{4 \pi \epsilon_0 V}{A}$
Solution
If we assume shape of earth be solid sphere of radius $R$.
The ratio of earth volume to surface area: $\frac{V}{A}=\frac{\left(\frac{4}{3} \pi R^3\right)}{4 \pi R^2}=\frac{R}{3}$ or, $R=\frac{3 V}{A}$
The capacitance of earth is,
$C_E=4 \pi \epsilon_0 R=4 \pi \epsilon_0\left(\frac{3 V}{A}\right)=\frac{12 \pi \epsilon_0 V}{A}$