Q148 / 160 · TS EAMCET 2021 (04 Aug Shift 1) · Physics

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
$4 π ε_{0} R$
Correct answer
B
$8 π ε_{0} R$
C
$\frac{8 π ε_{0}}{R}$
D
$\frac{4 π ε_{0}}{R}$

Solution

In the above case, the formula of spherical capacitor consists of two concentric spherical conductors of radius, $r_{1}$ and $r_{2}$ is, $C = \frac{4 π ε_{0} r_{1} r_{2}}{r_{1} - r_{2}}$

Here $r_{1} = R$ and $r_{2} = 2 R$ , now put the values in the above formula,
$C = \frac{4 π ε_{0} (R) (2 R)}{2 R - R} = 8 π ε_{0} R$

Hence, the correct answer is option: 'B'.

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

Solution

Relevant Questions

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 $R .$