Question

The earth has Volume 'V' and surface area 'A' then its capacitance would be

Answer 1

If we assume shape of earth be solid spherical.

Then, the volume of earth$=4/3\pi R^3$

where R is radius of earth.

Given, volume of earth$=V=4/3\pi R^3$

surface area of earth$=A=4\pi R^2$

So, $V/A=\left(4/3R^3\right)/4\pi R^2$

or $V/A=R/3$

or, $R=3V/A$

Now, capacitance of earth$=4\pi {\in }_{0}R$

$=4\pi {\in }_0\frac{3V}{A}$

$=\frac{12\pi {\in }_{0}V}{A}$.