Question

1000 drops ofwater each of radius r and charged to a potential V coalesce together to form a big drop. The potential of big drop will be

• A. 10 V
• B. 100 V
• C. 1000V
• D. $\frac{V}{100}$

Answer 1

Answer: (B)

100 V

Vol. of the big drop =1000 *vol. of each small drop
$\frac{4}{3}\pi R^3=1000\times \frac{4}{3}\pi r^3$
$\Rightarrow R^3=(10r{)}^3$
$\Rightarrow$ R =10r
Potential of each charged sphere for small drop, V = $\frac{q}{c}$
$\therefore$ Potential for the big drop = $1000\frac{q}{C}$
We have, $C=4\pi {ϵ}_{0}R=4\pi {ϵ}_0\times 10r$
$\therefore$ Potential of the big drop
=$\frac{1000}{10}.\frac{q}{4\pi {ϵ}_{0}r}=100V$