Question:
512 identical drops of mercury are charged to a potential of $2 \mathrm{~V}$ each. The drops are joined to form a single drop. The potential of this drop is___ V.
Solution:
(128)
Let charge on each drop $=\mathrm{q}$
radius $=r$
$v=\frac{k q}{r}$
$2=\frac{k q}{r}$
radius of bigger
$\frac{4}{3} \pi R^{3}=512 \times \frac{4}{3} \pi r^{3}$
$R=8 r$
$v=\frac{k(512) q}{R}=\frac{512}{8} \frac{k q}{r}=\frac{512}{8} \times 2$
$=128 \mathrm{~V}$