Physics - Capacitor Question with Solution | TestHub

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, $R=\frac{3V}{A}$ The capacitance of earth is, $C_E=4\pi {ϵ}_{0}R=4\pi {ϵ}_0\left(\frac{3V}{A}\right)=\frac{12\pi {ϵ}_{0}V}{A}$