Question

216 drops of same radius are charged to 10 volt each . These drops coalesce to form a bigger drop. Calculate the potential of bigger drop.

Answer 1

answer : 360 volts

explanation : 216 drops of same radius coalesce to form a bigger drop.

so, 216 × volume of smaller drop = volume of bigger drop

or, 216 × 4/3 πr³ = 4/3 πR³

or, 216r³ = R³

or, R³ = (6r)³ => R = 6r

now, potential on each smaller drop, V = kq/r = 10 volts

or, q = 10r/k

total charge on 216 smaller drops = 216q = 216 × 10r/k = 2160r/k.....(1)

again, potential on bigger drop = k(216q)/(6r)

from equation (1),

= k(2160r/k)/6r

= 360 volts.