First slide

Electrostatic potential

Question

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

Easy

A

V/n
B

V n
C

$V n^{\frac{1}{3}}$
D

$V n^{\frac{2}{3}}$

Solution

Let R be the radius of big drop and r, radius of small drop.
$∴ \frac{4}{3} {πR}^{3} = n \frac{4}{3} {πr}^{3} or R = r (n)^{1 / 3}$
Total charge on big drop = n q
Potential of bigger drop
$\begin{array}{l} = \frac{1}{4 {πε}_{0}} \times \frac{nq}{r (n)^{1 / 3}} \\ = \frac{1}{4 {πε}_{0}} \times \frac{q}{r} \times n^{2 / 3} = {Vn}^{2 / 3} \end{array}$

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