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MHT CET202311 May 2023Evening ShiftPhysicsCapacitanceActual

Two spherical conductors of capacities 3 F and 2 F are charged to same potential having radii 3 ~cm and 2 ~cm respectively. If ' ₁ ' and ' ₂ ' represent surface density of charge on respective conductors then ₁ ₂ is

Options

  1. A1 3
  2. B1 2
  3. C2 3
  4. D3 4

Correct answer

C. 2 3

Step-by-step solution

We know, C = Q V As both the charged spheres are at the same potential, the charge on both spheres is aligned & Q₁=C₁ ~V & Q₂=C₂ ~V aligned The charge densities of both spheres are ₁= Q ₁ ~A ₁ = C ₁ ~V 4 r ₁^2 Similiarly, ₂= Q ₂ ~A ₂ = C ₂ ~V 4 r ₂^2 Taking the ratios, aligned ₂ ₁ & = C ₂ r ₁^2 C ₁ r ₂^2 ₂ ₁ & = 2 10⁻⁶ (0.03)^2 3 10⁻⁶ (0.02)^2 = 3 2 ₁ ₂ & = 2 3 aligned

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