Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed â€˜vâ€™ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities $\sigma $1 and $\sigma $2 are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) :

Question

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed â€˜vâ€™ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities $\sigma $₁ and $\sigma $₂ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) :

$\sigma $₁ = $ \in $₀ $\upsilon $ B, $\sigma $₂ = $-$ $ \in $₀ $\upsilon $ B

$\sigma $₁ = ${{{ \in _0}\upsilon \,B} \over 2},$ $\sigma $₂ = ${{ - { \in _0}\,\upsilon B} \over 2}$

$\sigma $₁ = $\sigma $₂ = ${ \in _0}\,\upsilon B$

$\sigma $₁ = ${{ - { \in _0}\upsilon B} \over 2},$ $\sigma $₂ = ${{ { \in _0}\upsilon B} \over 2},$

Solution

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