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Using Gauss's law, the electric field due to an **infinite plane sheet of charge** with surface charge density σ is:
AE = σ/(4πε₀r²)
BE = σ/(2ε₀) — **independent of distance from the sheet!**
CE = σr/(2ε₀)
DE = σ/(ε₀r)
Answer & Solution
Correct answer: B. E = σ/(2ε₀) — **independent of distance from the sheet!**
Gaussian cylinder (or pillbox) crossing the sheet, faces parallel to sheet. By symmetry E perpendicular to sheet on both sides. Flux = 2EA = σA/ε₀ → **E = σ/(2ε₀)**. **Independent of distance** — the infinite sheet looks the same from any distance.
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