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MHT CET202020 Oct 2020Evening 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 ( E ₀= . permittivity of free space )

Options

  1. A12 ₀ V A
  2. B4 ₀ V A
  3. C2 ₀ V A
  4. D8 ₀ V A

Correct answer

A. 12 ₀ V A

Step-by-step solution

If we assume shape of earth be solid spherical. Then, the volume of earth =4 / 3 R ³ where R is radius of earth. Given, volume of earth = V =4 / 3 R ³ surface area of earth = A =4 R ² So, V / A= (4 / 3 R³ ) / 4 R² or V / A = R / 3 or, R =3 ~V / A Now, capacitance of earth =4 ₀ R =4 ₀ 3 V ~A = 12 ₀ V ~A .

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