Question

A spherical drop of mercury of radius r has capacitance given by= 4πɛ0r. if 2 such drops combine to form a big drop, what is its capacitance?

Answer 1

Let potential f 1 drop = Kq/r =V 

        Volume of n drops = volume of bigger drop 

            n  4/3 pi (r)^3  = 4/3 pi (R)^3

          Therefore ,  R = ( (n)^1/3) r 

also charge remains conserved 

charge on 1 drop = q 

charge on big drop containing n drops = (nq) 

Therefore potential on big drop = K (nq)/ ((n)^1/3)r

                                              =(( n)^2/3) Kq/r

                                             = (( n)^2/3) V