Question

In an experiment, $n$ small drops of same size are charged to $V$ volts each, if they form a single large drop, then it potential is:

• A. $V{n}^{2/3}$
• B. $V{n}^{1/3}$
• C. $\sqrt{Vn}$
• D. $\frac{V}{n}$

Answer 1

Answer: (A)

Here: Number of small drops $=n$
Charge on each drop $=V$ volt
Volume of $n$ drops $=$ Volume of single large drop
$n\times \frac{4}{3}\pi r^3=\frac{4}{3}\pi R^3$
$R=n^{1/3}r$
The potential on a small drop is
$V=\frac{q}{4\pi {\epsilon }_{0}r}$
The potential on a large drop is
$=\frac{nq}{4\pi {\epsilon }_{0}R}=\frac{nq}{4\pi {\epsilon }_0\left(n^{1/3}r\right)}$
$=\frac{q}{4\pi {\epsilon }_0}{n}^{2/3}$
$=V{n}^{2/3}$