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For an infinite sheet of charge the surface of choice is

  • A.a single flat surface parallel to the sheet
  • B.a rectangular box straddling the sheet
  • C.a sphere with the sheet passing through its centre
  • D.a cylinder with its axis lying in the plane of the sheet

Answer: B

Correct answer: a rectangular box straddling the sheet

The field of an infinite sheet is uniform, perpendicular to the sheet and outward on both sides. A box with two faces parallel to the sheet therefore has flux through those two faces only - the sides being parallel to the field - and the enclosed charge is the sheet area they span. That gives \( E = \sigma/2\varepsilon_0 \) immediately.

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