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Two concentric closed surfaces S₁ and S₂ are arranged such that S₁ is completely inside S₂ . The inner surface S₁ encloses a point charge q₁ . The region between S₁ and S₂ contains a charge q₂ . If the electric flux passing through the outer surface S₂ is 4 times the electric flux passing through the inner surface S₁ , the ratio of the charges q₁ : q₂ is:

Options

  1. A1 : 4
  2. B4 : 1
  3. C3 : 1
  4. D1 : 3

Correct answer

D. 1 : 3

Step-by-step solution

According to Gauss's law, the electric flux through a closed surface is equal to the net charge enclosed by the surface divided by ₀ . For the inner surface S₁ , the enclosed charge is q₁ . Thus, the flux is: ₁ = q₁ ₀ For the outer surface S₂ , the total enclosed charge is the sum of the charge inside S₁ and the charge in the region between S₁ and S₂ . Thus, the enclosed charge is q₁ + q₂ , and the flux is: ₂ = q₁ + q₂ ₀ We are given that ₂ = 4 ₁ . Substituting the expressions for the fluxes, we get: q₁ + q₂ ₀ = 4

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