Two spherical conductors of radii $r$ and $R$ are separated by distance “ $b$ ” $(b>>r, R)$ capacitance of the system is

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$\frac{4 π \in_{0}}{\frac{1}{r} + \frac{1}{R} - \frac{1}{b}}$

$\frac{4 π \in_{0} rR}{R - r}$

$4 π \in_{0} (r+R)$

$\frac{4 π \in_{0}}{\frac{1}{r} + \frac{1}{R} - \frac{2}{b}}$

answer is B.

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Detailed Solution

$\frac{Q^{2}}{2C}$ = $\frac{Q^{2}}{8 π \in_{0} r} + \frac{Q^{2}}{8 π \in_{0} R} - \frac{Q^{2}}{4 π \in_{0} b}$
$\Rightarrow \frac{4π \in_{0} R}{\frac{1}{r} + \frac{1}{R} - \frac{2}{b}}$

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