Redistribution of charges and concept of common potential

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Question

1728 drops of mercury of equal radii possessing equal charges combine to from a big drop. Then the capacitance of bigger drop compared to each individual small drop is____times.

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Solution

$V o l u m e o f 1728 s m a l l d r o p s = V o l u m e o f b i g d r o p \Rightarrow 1728 \times \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3} \Rightarrow R = 12 r \Rightarrow A l s o, C' = 4 π ε_{0} R, C = 4 π ε_{0} r \Rightarrow \frac{C'}{C} = \frac{R}{r} = 12$

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