Let n identical droplets, each of radius r and charge q , coalesce to form a large drop of radius R and charge Q. Assuming that the droplets are incompressible, show that (a) the radius R = n^1/3r ; (b) the capacitance C of the large drop is C = n^1/3C , where C is the capacitance of the droplet; (c) the potential V of the large drop is given by V = n^2/3 V , where V is the potential of the droplet; (d) the surface charge density s = n^1/3 s ; (e) the energy U stored in the large drop is given by U = n^5/3U where U is the energy stored in the droplet.
Solution:
