One thousand similar electrified raindrops merge into a single one so that their total charge remains unchanged. Find the change in the total electrostatic energy of the drops, assuming that all the drops are spherical and the small drops were initially at large distances from one another.

Explanation

Suppose, each drop of radius r contains a charge Q.
Capacitance, C= r and energy, `E_1 = (1)/(2)*(Q^2)/(C )= (Q^2)/(2r)`
Total energy of 1000 drops, `E= 1000E_1 (500Q^2)/(r )`
If R be the radius of the large drop then,
`(4)/(3) pi R^3= 1000xx(4)/(3)pi r^3 " or "R = 10r`
Charge of the large drop = 1000Q
Energy of the large drop,
`E_2= (1)/(2)*((1000Q)^2)/(R )= (5xx10^(5)Q^2)/(10r)= (5xx10^(4)Q^2)/(r )`
`:. (E_2)/(E) = (5xx10^(4))/(500) = 100 " or " E_2= 100E`
Change in electrostatic energy of the drops
`E_2 -E = 100E - E = 99E = 99xx " initial energy "`.