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 \({\sigma _1}\) and \({\sigma _2}\) are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)

1. A \({\sigma _1} = \frac{{ - { \in _0}\,vB}}{2}\,,\,{\sigma _2} = \frac{{{ \in _0}\,vB}}{2}\)
2. B \({\sigma _1} = { \in _0}\,vB\,,\,{\sigma _2} =  - { \in _0}\,vB\)
3. C \({\sigma _1} = \frac{{{ \in _0}\,vB}}{2}\,,\,{\sigma _2} = \frac{{ - { \in _0}\,vB}}{2}\)
4. D \({\sigma _1} = {\sigma _2} = { \in _0}\,vB\)