A large spherical liquid drop is charged to a potential of 500 V . It breaks up into N identical smaller spherical drops. If the potential of each of the smaller drops is found to be 20 V , what is the value of N ?

Step-by-step solution

Let the radius of the large drop be R and its charge be Q . Its potential is given by V_ large = kQ R . When it breaks into N identical smaller drops of radius r and charge q , the total charge and total volume are conserved. Charge conservation: Q = Nq Volume conservation: 4 3 R^3 = N 4 3 r^3 R = N^ 1/3 r The potential of each small drop is V_ small = kq r . Taking the ratio of the potentials: V_ large V_ small = kQ R kq r = ( Q q ) ( r R ) = (N) ( 1 N^ 1/3 ) = N^ 2/3 Given V_ large = 500 V and V_ small = 20 V : N