' n ' small spherical drops of the same size which are charged to 'V' volt each coalesce to form a single big drop. The potential of a big drop is

Step-by-step solution

Let the radius of each small drop be r and its charge be q . The potential of each small drop is V = 1 4 ₀ q r . When n such drops coalesce, the total charge of the big drop is Q = nq . The volume is conserved, so the volume of the big drop is equal to the sum of the volumes of the n small drops. 4 3 R^3 = n ( 4 3 r^3 ) R^3 = n r^3 R = n^ 1 3 r The potential of the single big drop is: V' = 1 4 ₀ Q R V' = 1 4 ₀ nq n^ 1 3 r V' = n^ 1 - 1 3 ( 1 4 ₀ q r ) V' = n^ 2 3 V