Question

A spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is $2 R$ and the inner radius is R.

• A. $4 \pi \epsilon_0 R$
• B. $8 \pi \epsilon_0 R$
• C. $\frac{8 \pi \epsilon_0}{ R }$
• D. $\frac{4 \pi \epsilon_0}{R}$

Answer 1

Answer: (B)

Given, outer radius, $b=2 R$
Inner radius, $a=R$
As we know that, capacitance of spherical capacitor,
$ C=4 \pi \varepsilon_0\left(\frac{a b}{b-a}\right) $
$\therefore C=4 \pi \varepsilon_0\left(\frac{R \cdot 2 R}{2 R-R}\right)=4 \pi \varepsilon_0 \frac{2 R^2}{R} $
$ C=8 \pi \varepsilon_0 R$