Q. Small drops of the same size are charged to V volt each. If $n$ such drops coalesce to form a single large drop, its potential will be
A) $Vn$
B) $V/n$
C) $Vn^{1/3}$
D) $Vn^{2/3}$
Explanation
(d) $V = \frac{1}{4\pi\varepsilon_{0}}\frac{q}{r}$
$V^{'} = \frac{1}{4\pi\varepsilon_{0}}\frac{q^{'}}{r^{'}} = \frac{1}{4\pi\varepsilon_{0}}\frac{nq}{n^{\frac{1}{3}}r}\ \ \ \ \ $
$\ (\because q^{'} = nq,r^{'} = n^{\frac{1}{3}}r)$
Or $V^{'} = n^{2/3}V$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.