Question

Twenty seven drops of same size are charged at $220\, V$ 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 $n q=27 q(n=27)$
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 $V=\frac{q}{4 \pi \epsilon_{0} r}=220 V$
Potential of the big drop,
$V=\frac{n q}{4 \pi \in_{0} R}=\frac{n q}{4 \pi \in_{0} n^{1 / 3} r}=n^{2 / 3} \frac{q}{4 \pi \in_{0} r} $
$V=(27)^{2 / 3} \times 220 V$
$=9 \times 220=1980 V$