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Statement of a problem № 3722

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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:
Let n identical droplets, each of radius r and charge q , coalesce to form a lar

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