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The field on either side of an infinite sheet of charge of surface density \( \rho_s \) is

  • A.\( \rho_s/(2\pi\epsilon_0 z) \), falling with distance from the sheet
  • B.\( \rho_s/(4\pi\epsilon_0 z^2) \), falling as the inverse square
  • C.\( \rho_s/(2\epsilon_0) \), independent of distance
  • D.\( \rho_s/\epsilon_0 \), the whole of the flux emerging on one side

Answer: C

Gauss's law applied to a box straddling the sheet gives equal flux out of two faces whose area does not change with distance, so the field is uniform. It is directed away from the sheet on both sides for a positive density.

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