Question

$27$ identical drops are charged at $22 \,V$ each. They combine to form a bigger drop. The potential of the bigger drop will be ___$V$.

Answer 1

$q \rightarrow nq$
$n \frac{4}{3} \pi r ^{3}=\frac{4}{3} \pi\left( r ^{\prime}\right)^{3}$
$\Rightarrow r ^{\prime}= n ^{\frac{1}{3} r }$
$V =\frac{ kq }{ r } \propto \frac{ n }{ n ^{1 / 3}} \propto n ^{2 / 3} \propto 27^{2 / 3} $
$\Rightarrow v ^{\prime}=9 V =9 \times 22=198$