64 identical spherical liquid drops, each carrying a charge and having an electric potential V , coalesce to form a single large drop. What is the electric potential of the new large drop?

Step-by-step solution

Let the radius of each small drop be r and its charge be q . The electric potential of each small drop is given by: V = kq r When 64 such drops coalesce to form a single large drop of radius R , the total volume remains conserved: 4 3 R^3 = 64 4 3 r^3 R^3 = 64r^3 R = 4r By conservation of charge, the total charge on the large drop is: Q = 64q The electric potential of the new large drop will be: V' = kQ R = k(64q) 4r = 16 ( kq r ) = 16V Thus, the potential of the large drop is 16V . Answer: 16V