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Two infinite parallel plane sheets are located at x = a and x = b (where b > a ). The x -component of the net electric field, E_x , in the surrounding space is found to be -E₀ for x b . The surface charge densities of the sheets at x = a and x = b are respectively:

Options

  1. A4 ₀ E₀ and -2 ₀ E₀
  2. B8 ₀ E₀ and -4 ₀ E₀
  3. C2 ₀ E₀ and 4 ₀ E₀
  4. D3 ₀ E₀ and ₀ E₀

Correct answer

A. 4 ₀ E₀ and -2 ₀ E₀

Step-by-step solution

Let the surface charge densities be ₁ at x = a and ₂ at x = b . The electric field due to a single infinite sheet with charge density is 2 ₀ directed away from the sheet. For x E_x = - ₁ 2 ₀ - ₂ 2 ₀ = -E₀ ₁ + ₂ = 2 ₀ E₀ ... (i) For a E_x = ₁ 2 ₀ - ₂ 2 ₀ = 3E₀ ₁ - ₂ = 6 ₀ E₀ ... (ii) Adding equations (i) and (ii): 2 ₁ = 8 ₀ E₀ ₁ = 4 ₀ E₀ Subtracting equation (ii) from (i): 2 ₂ = -4 ₀ E₀ ₂ = -2 ₀ E₀ Alternatively, using the boundary condition that the jump in the normal component of the electric field across a surfac

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