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Combination of Charged Drops

Suppose we have n identical drops each having radius r, capacitance c, charge q, potential v and energy u. If these drops are combined to form a big drop of radius R, capacitance C, charge Q, potential V and energy U, then
  • Charge on big drop: Q = nq
  • Radius of big drop: Volume of big drop = n × volume of a single drop, i.e.,
    63537.png, R = n1/3r
  • Capacitance of big drop: C = n1/3c
  • Potential of big drop: 63549.png V = n2/3v
  • Energy of big drop: 63555.png = n5/3u
  • Energy difference: Total energy of big drop is greater than the total energy all smaller drop. Hence, energy difference,
    ΔU = Unu 63563.png

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