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Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed v in a uniform magnetic field B going into the plane of the paper (see figure). If charge densities σ 1 and σ 2 are induced on the left and right surfaces respectively of the sheet, then (ignore fringe effects)

Options

  1. Aσ 1 = - ϵ 0 vB 2 ,   σ 2 = ϵ 0 vB 2
  2. Bσ 1 = ϵ 0 vB ,   σ 2 = - ϵ 0 vB
  3. Cσ 1 = ϵ 0 vB 2 ,   σ 2 = - ϵ 0 vB 2
  4. Dσ 1 = σ 2 = ϵ 0 vB

Correct answer

B. σ 1 = ϵ 0 vB ,   σ 2 = - ϵ 0 vB

Step-by-step solution

σ 1 = - σ 2 [due to magnetic force] E = σ ε 0 = vB σ = ε 0 vB

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