Question

Suppose Earth has a volume 'V' and surface area 'A'; then its becomes a large capacitor having the value of capacitance as

• A. $12\pi {\in }_0\frac{V}{A}$
• B. $4\pi {\in }_0\frac{V}{A}$
• C. $4\pi {\in }_0\frac{A}{V}$
• D. $12\pi {\in }_0\frac{A}{V}$

Answer 1

The correct option is A $12\pi {\in }_0\frac{V}{A}$

Capacitance of spherical conductor is given as $=4\pi {ϵ}_{0}R$

Now, $\frac{V}{S}=\frac{\frac{4}{3}\pi R^3}{4\pi R^2}=\frac{\perp }{3}R\Rightarrow R=\frac{3V}{A}$

$\Rightarrow C=4\pi {ϵ}_0\left(\frac{V}{A}\right)\times 3=12\pi {ϵ}_0\left(\frac{V}{A}\right)$