Question

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)

• A. $\sigma _{1}=\frac{- ϵ_{0} vB}{2}, \, \sigma _{2}=\frac{ϵ_{0} vB}{2}$
• B. $\sigma _{1}=ϵ_{0}vB, \, \sigma _{2}=-ϵ_{0}vB$
• C. $\sigma _{1}=\frac{ϵ_{0} vB}{2}, \, \sigma _{2}=\frac{- ϵ_{0} vB}{2}$
• D. $\sigma _{1}=\sigma _{2}=ϵ_{0}vB$

Answer 1

Answer: (B)

$\sigma _{1}=-\sigma _{2}$ [due to magnetic force]
$E=\frac{\sigma }{\epsilon _{0}}=vB$
$\sigma =\epsilon _{0}vB$