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MHT CET202525 Apr 2025Morning ShiftPhysicsElectrostaticsActual

'n' identical small spherical drops of water, each of radius 'r' and charged to the same potential ' v ' are combined to form a big drop. The potential of a big drop is

Options

  1. Anv
  2. Bn v
  3. Cn ^ 1 / 3 ~v
  4. Dn ^ 2 / 3 ~v

Correct answer

D. n ^ 2 / 3 ~v

Step-by-step solution

The potential of a small drop with radius r and charge q is V = 1 4 ₀ q r . When n such drops combine to form a large drop, charge is conserved: Q = nq . The volume is also conserved, so n 4 3 r^3 = 4 3 R^3 , which simplifies to R = n^ 1/3 r . The potential of the large drop is V' = 1 4 ₀ Q R . Substituting Q = nq and R = n^ 1/3 r gives V' = 1 4 ₀ nq n^ 1/3 r = n^ 2/3 1 4 ₀ q r . Since 1 4 ₀ q r = V , the potential of the large drop is V' = n^ 2/3 V . The correct answer is D.

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