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Question

Physics Question on electrostatic potential and capacitance

1000 similar electrified rain drops merge together into one drop so that their total charge remains unchanged. The electric energy gets increased by

A

100 times

B

200 times

C

300 times

D

400 times

Answer

100 times

Explanation

Solution

Let qq be charge on each small drop of radius rr. If RR is radius of big drop, then
43πR3=1000×43πr3\frac{4}{3} \pi R^3 = 1000 \times \frac{4}{3} \pi r^3
R=10r\therefore \:\:\: R = 10 \, r
and C=10CC' = 10 \, C
Initial energy, E1=1000×q22CE_1 = 1000 \times \frac{q^2}{2C}
Final energy, E2=(1000q)22CE_2 = \frac{(1000 \, q)^2}{2C'}
E2E1=1000×CC=1000×110=100\frac{E_2}{E_1} = \frac{1000 \times C}{C'} = 1000 \times \frac{1}{10} = 100