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MHT CET202611 April 2026Evening ShiftPhysicsCapacitanceActual

The earth is assumed to be a charged conducting sphere having volume 'V' and surface area 'A'. The capacitance of the earth in free space is ( ₀ = permittivity of free space)

Options

  1. A2 ₀ V/A
  2. B4 ₀ V/A
  3. C8 ₀ V/A
  4. D12 ₀ V/A

Correct answer

D. 12 ₀ V/A

Step-by-step solution

The capacitance of a spherical conductor of radius R is given by C = 4 ₀ R . The volume of the sphere is V = 4 3 R^3 and its surface area is A = 4 R^2 . Taking the ratio of volume to surface area: V A = 4 3 R^3 4 R^2 = R 3 This gives R = 3V A . Substituting the value of R in the expression for capacitance: C = 4 ₀ ( 3V A ) = 12 ₀ V A Answer: 12 ₀ V/A

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