Obtain an expression for the emf induced across a conductor which is moved in a uniform magnetic field which is perpendicular to the plane of motion.

1. Consider a straight conductor (PQ) moving in uniform magnetic field
2. If the rod (PQ) is moved towards right with a constant velocity (V) area of cross section changes
 

3. The magnetic flux enclosed by the loop PQRS is $\mathrm{\varphi }=\mathrm{B}\cdot \mathrm{A}=\mathrm{B}\left(lx\right)$
4. According to faraday’s law, the induced e.m.f is
$\begin{array}{l}\mathrm{\epsilon }=\frac{\mathrm{d\varphi }}{\mathrm{dt}}=\frac{\mathrm{d}\left(Blx\right)}{\mathrm{dt}}\\ =Bl\frac{\mathrm{dx}}{\mathrm{dt}}=Blv\end{array}$
This is known as motional induced e.m.f.