Capacitance of an isolated conducting sphere of radius R 1 becomes n times when it is enclosed by a concentric conducting sphere of radius R 2 connected to earth. The ratio of their radii R 2 R 1 is:

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Aicharya · Accepted Answer

Capacitance of isolated conducting sphere $C = 4 π ε_{0} R_{1}$
By enclosing inside another sphere of radius $R_{2}$ , new capacitance $C^{'} = \frac{4 π ε_{0} R_{1} R_{2}}{(R_{2} - R_{1})}$
Given: $\frac{4 π ε_{0} R_{1} R_{2}}{(R_{2} - R_{1})} = n \times 4 π ε_{0} R_{1}$
$\Rightarrow \frac{R_{2}}{(R_{2} - R_{1})} = n \Rightarrow \frac{\frac{R_{2}}{R_{1}}}{(\frac{R_{2}}{R_{1}} - 1)} = n$
$\Rightarrow \frac{R_{2}}{R_{1}} = n \frac{R_{2}}{R_{1}} - n \Rightarrow \frac{R_{2}}{R_{1}} = \frac{n}{(n - 1)}$

Capacitance of an isolated conducting sphere of radius R 1 becomes n times when it is enclosed by a…

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