Electrical capacity of earth is approximately :

The correct answer is Option (3) → 711 μF

The Earth can be treated as an isolated conducting sphere of radius \( R \). A charge \( Q \) on it gives the surface potential \( V = Q/(4\pi\varepsilon_0 R) \), so its capacitance is

    \( \displaystyle C = \frac{Q}{V} = 4\pi\varepsilon_0 R = \frac{R}{9\times10^{9}} \)

    \( R = 6.4\times10^{6}\,\mathrm{m} \)

    \( \displaystyle C = \frac{6.4\times10^{6}}{9\times10^{9}}\,\mathrm{F} = 7.11\times10^{-4}\,\mathrm{F} \approx 711\,\mu\mathrm{F} \)

Even a body as large as the Earth has a capacitance of well under a millifarad, which shows how large a unit the farad is.