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The relation between the field just outside a charged conductor and its local surface charge density is

  • A.\( E = 0 \)
  • B.\( E = \rho_s/\epsilon_0 \), directed normally
  • C.\( E = \rho_s/(2\epsilon_0) \)
  • D.\( E = \rho_s\epsilon_0 \)

Answer: B

A small Gaussian box with one face in the metal and one outside receives flux through the outer face only, since the interior field is zero. That gives the whole of the density over the permittivity, twice what an isolated sheet would give.

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