Assume the earth to be a spherical conductor of radius 6400 km. Calculate the capacitance of earth.

711 μF

The correct answer is Option (4) → 711 μF

$\text{Given: Radius of Earth } R = 6400~\text{km} = 6.4 \times 10^6~\text{m}$

$\text{Capacitance of a isolated spherical conductor: } C = 4 \pi \epsilon_0 R$

$\epsilon_0 = 8.854 \times 10^{-12}~\text{F/m}$

$C = 4 \pi (8.854 \times 10^{-12}) (6.4 \times 10^6)$

$C \approx 7.12 \times 10^{-4}~\text{F}$

$\text{Answer: } C \approx 7.12 \times 10^{-4}~\text{F}$