512 identical drops of mercury are charged to a potential

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

$\frac{4}{3} \pi R^{3}=512 \times \frac{4}{3} \pi r^{3}$

$R=8 r$

$v=\frac{k(512) q}{R}=\frac{512}{8} \frac{k q}{r}=\frac{512}{8} \times 2$

$=128 \mathrm{~V}$

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