Twenty seven drops of same size are charged at $200 ext{ V}$ each. They combine to form a bigger drop. Calcu

Question

Twenty seven drops of same size are charged at $200 	ext{ V}$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

Accepted Answer

Electric potential due to a charged sphere = $\frac{kQ}{R}$. For smaller drop, $V = \frac{kq}{r} = 200 	ext{ V}$. As volume remains the same, $(\frac{4}{3}\pi r^3) 	imes 27 = \frac{4}{3}\pi R^3 \Rightarrow R = \sqrt[3]{27} r = 3r$. Using charge conservation, $Q = 27q$. $V_{	ext{big drop}} = \frac{kQ}{R} = \frac{k(27q)}{3r} = 9(\frac{kq}{r}) = 9 	imes 220 = 1980 	ext{ V}$.

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