Question

Twenty seven drops of same size are charged at $220V$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

• A. 660 V
• B. 1320 V
• C. 1520 V
• D. 1980 V

Answer 1

Answer: (D)

If each drop has a charge ' $q$ ' and radius ' $r$ '.
Then from conservation of charge, charge on the big drop is $nq=27q(n=27)$
from conservation of volume $\frac{4}{3}\pi r^{3}n=\frac{4}{3}\pi R^3$
$R=n^{1/3}r$
Now potential of the small drop $V=\frac{q}{4\pi {ϵ}_{0}r}=220V$
Potential of the big drop,
$V=\frac{nq}{4\pi {\in }_{0}R}=\frac{nq}{4\pi {\in }_0{n}^{1/3}r}=n^{2/3}\frac{q}{4\pi {\in }_{0}r}$
$V=(27{)}^{2/3}\times 220V$
$=9\times 220=1980V$