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If the uniform surface charge density on an infinite plane sheet is σ, the electric field near the surface will be

Asked in GUJCET 2007 · Infinite sheet and sheet combinations

• (1) σ/(2ε₀)
• (2) (3σ)/(ε₀)
• (3) σ/(ε₀)
• (4) (2σ)/(ε₀)

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives (3σ)/(ε₀). Gauss's law with a pillbox gives 2EA=(σ A)/(ε₀), so E=σ/(2ε₀).
• (3) This is the field just outside a charged conductor, where all the flux leaves through one face. A thin sheet sends flux out through both faces of the pillbox, so its field is half as large.
• (4) Puts the 2 on the wrong side: from 2EA=(σ A)/(ε₀) the 2 belongs with E, giving E=σ/(2ε₀), not (2σ)/(ε₀).

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