Assume the earth to be a spherical conductor of radius 6400 km. Calculate the capacitance of earth.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 711\,\mu\mathrm{F} \)
An isolated spherical conductor has potential \( V = Q/(4\pi\varepsilon_0 R) \) at its surface, so its capacitance \( C = Q/V \) depends only on its radius.
\( \displaystyle C = 4\pi\varepsilon_0 R = \frac{R}{9\times10^{9}} \)
\( \displaystyle R = 6400\,\mathrm{km} = 6.4\times10^{6}\,\mathrm{m} \)
\( \displaystyle C = \frac{6.4\times10^{6}}{9\times10^{9}} = 7.11\times10^{-4}\,\mathrm{F} = 711\,\mu\mathrm{F} \)