Small mercury drops of the same size are charged to the same potential V. If n such drops coalesce to form a single large drop, then calculate its potential.

Explanation

Let r be the radius of a small drop and R that of the large drop. Then, since the volume remains conserved,
`(4)/(3) pi R^(2) = (4)/(3) pi r^(2) n " " rArr R^(3) = r^(3) n `
R = `r^(3) (n)^(1//3)`
Further, since the total charge remains conserved, we have using Q = CV
`C_("large") V = n C_("small"^(V))`
Where V is the potential of the large drop.
`4 pi epsilon_(0) RV = n (4 pi epsilon_(0) r)_(v)`
V = `("nrv")/(R) = ("nrv")/(r(n)^(1//3))`
`V = vn^(2//3)`