Question

The earth has volume 'V' and surface area 'A'. If permeability of earth is ${ϵ}_0$ then find its capacitance.

Answer 1

Capacitance of an isolated spherical capacitor n,

$C=4\pi {ϵ}_{0}R$ (R $\to$ radian of earth)

Now,

$A=4\pi R^2$ and $V=\frac{4}{3}\pi R^3$

$\Rightarrow R=\frac{3V}{A}$

Which gives,

$C=12\pi {ϵ}_0\frac{V}{A}$