The capacitance of a sphere of radius R₁ is increased 3 times when it is enclosed by an earthed sphere of radius R₂. The ratio $R_{2} / R_{1}$ is

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$2$

$\frac{3}{2}$

$\frac{4}{3}$

$3$

answer is B.

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Detailed Solution

$C_{1} = 4 π ε_{0} R_{1}$
$C_{2} = \frac{4 π ε_{0} (R_{1} R_{2})}{(R_{2} - R_{1})}$
Given $C_{2} = 3 C_{1}$ Hence
$\frac{4 π ε_{0} (R_{1} R_{2})}{(R_{2} - R_{1})} = 3 \times 4 π ε_{0} R_{1}$
which gives $\frac{R_{2}}{R_{1}} = \frac{3}{2}$

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