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. $ Vn^{2/3}$
• B. $ Vn^{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
$V=\frac{q}{4 \pi \varepsilon_{0} r}$
The potential on a large drop is
$=\frac{n q}{4 \pi \varepsilon_{0} R}=\frac{n q}{4 \pi \varepsilon_{0}\left(n^{1 / 3} r\right)}$
$=\frac{q}{4 \pi \varepsilon_{0}} n^{2 / 3}$
$=V n^{2 / 3}$