Question

A charge of $10^{-9}C$ is placed on each of the $64$ identical drops of radius $2cm$. They are then combined to form a bigger drop. Its potential will be

• A. $7.2\times 10^{3}V$
• B. $7.2\times 10^{2}V$
• C. $1.44\times 10^{2}V$
• D. $1.44\times 10^{3}V$

Answer 1

Answer: (A)

Volume of bigger drop = volume of $64$ small drops
ie., $\frac{4}{3}\pi R^3=64\times \frac{4}{3}\pi r^3$
or $R=4r$
Potential on small drop
$V_1=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$
Potential on bigger drop
$V_2=\frac{1}{4\pi {\epsilon }_0}\frac{64q}{R}$
$V_2=\frac{1}{4\pi {\epsilon }_0}\frac{64q}{4r}$
$=\frac{9\times 10^9\times 64\times 10^{-9}}{4\times 2\times 10^{-2}}$
$=7.2\times 10^{3}V$