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Asked in GSEB Board July 2022 · Infinite sheet and sheet combinations
Idea: apply Gauss's law to a cylindrical pillbox that pierces the sheet, with its flat faces of area A at distance r on either side.
By symmetry ⃗E is perpendicular to the sheet, so flux passes only through the two flat faces:
φ=EA+EA=2EA
Charge enclosed: qᵢₙ=σ A
2EA=(σ A)/(ε₀)⇒ E=σ/(2ε₀)
The distance r never enters the result: the field lines of an infinite sheet stay parallel and equally spaced, so they never thin out.
So the field does not depend on r.
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