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  4. n small drops of same size are charged to V volt each. If they coalesce to form a single large drop, then its potential will be

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Q. $n$ small drops of same size are charged to $V$ volt each. If they coalesce to form a single large drop, then its potential will be

Electrostatic Potential and Capacitance

Solution:

As $\frac{4}{3} \pi R^{3}=n \times \frac{4}{3} \pi r^{3} $
$\therefore R=n^{1 / 3} r$.
New potential $V'=\frac{n q}{4 \pi \varepsilon_{0} R}$
$=\frac{n q}{4 \pi \varepsilon_{0}\left(n^{1 / 3} r\right)}$
$=n^{2 / 3} \frac{q}{4 \pi \varepsilon_{0} r}=n^{2 / 3} V$