In the figure, a very large plane sheet of positive charge is shown. P₁ and P₂ are two points at distance l and 2l from the charge distribution. If σ is the surface charge density, then the magnitude of electric fields E₁ and E₂ at P₁ and P₂ respectively are :

Solution

Physics sir · 4 steps

An infinite sheet has no length scale, so its field is the same at every distance from it.

1. Pick a Gaussian surface. Take a cylinder that pierces the sheet, with flat end caps of area A on either side. By symmetry the field is perpendicular to the sheet, so no flux leaves through the curved side.
2. Apply Gauss's law. Flux leaves through both end caps, EA each. The charge enclosed is σ A, so 2EA = σ A / ε₀.

   E = σ/2ε₀

3. No distance appears. The result does not contain l at all. The cap could sit at l or at 2l and the flux balance would be identical, so the field cannot change with distance.
4. So. E₁ = E₂ = σ / 2ε₀, which is option (c).

The idea to keep. For an infinite sheet of charge, E = σ/2ε₀ at any distance. Use σ/ε₀ only next to a conductor's surface, where the field exists on one side only.

Answer from the NTA final answer key. Solution by PrepWiser.