Q. 1000 similar electrified rain drops merge together into one drop so that their total charge remains unchanged. How is the electric energy affected?
A) 100 times
B) 102 times
C) 200 times
D) 400 times
Explanation
(a) Let q be charge on each small drop of radius r. If R is radius of big drop, then
$\frac{4}{3}\pi R^{3} = 1000 \times \frac{4}{3}\pi r^{3}$
$\therefore\ \ R = 10\ r$
C‘=10 C
Initial energy${\ E}_{1} = 1000 \times \frac{q^{2}}{2C^{'}}$
Final energy $E_{2} = \frac{(1000q)^{2}}{C^{'}}$
$\frac{E_{2}}{E_{1}} = \frac{1000 \times C}{C^{'}}$
$= 1000 \times \frac{1}{10} = 100$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.