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Q.
1000 similar electrified rain drops merge together into one drop so that their total charge remains unchanged. The electric energy gets increased by
JIPMERJIPMER 2015Electrostatic Potential and Capacitance
Solution:
Let $q$ be charge on each small drop of radius $r$. If $R$ is radius of big drop, then
$ \frac{4}{3} \pi R^3 = 1000 \times \frac{4}{3} \pi r^3$
$\therefore \:\:\: R = 10 \, r$
and $C' = 10 \, C$
Initial energy, $E_1 = 1000 \times \frac{q^2}{2C}$
Final energy, $E_2 = \frac{(1000 \, q)^2}{2C'}$
$ \frac{E_2}{E_1} = \frac{1000 \times C}{C'} = 1000 \times \frac{1}{10} = 100$