Motional EMF from faraday law-

The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf.

Consider a conductor PQ of length l free to move on U-shaped conducting rails situated in a uniform and time independent magnetic field B, directed normally into the plane of paper.The conductor PQ moved inwards with the velocity v.

Now, suppose a length x of the loop inside the magnetic field at any instant of time t.

Then the flux linked with the rectangular loop PQRS is-

Φ = BA = Blx

According to Faraday law of electromagnetic induction, the induced emf is-

ε= -dΦ/dt = -d(Blx)/dt = -Bl.dx/dt

ε= Blv

Here, we take dx/dt= -v, because the velocity v is in the decreasing direction of x.

This induced emf Blv is called motional emf.