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) :

Question

$\begin{array}{1 1}(1) \sigma_1 = \varepsilon_0 \upsilon B, \sigma_2 = -\varepsilon_0 \upsilon B \\ (2) \sigma_1 = \frac{\varepsilon_0 \upsilon B}{2}, \sigma_2 = \frac{-\varepsilon_0 \upsilon B}{2} \\ (3) \sigma_1 = \sigma_2 = \varepsilon_0 \upsilon B \\ (4) \sigma_1 = \frac{-\varepsilon_0 \upsilon B}{2}, \sigma_2 = \frac{\varepsilon_0 \upsilon B}{2} \end{array} $