Give the explanation of reason behind the origin of motional induced emf.

Explanation

When a conducting rod is moving in to a magnetic field as shown in figure the positive ions and electrons move along with it.

In the figure such particles will be in motion with velocity `vecv` perpendicular to the magnetic - field `vecB` and hence they experience a Lorentz force `vecF = q(vecvxxvecB)` .
Here positive ions will experience force from Q to P but as they remain fixed at their lattice positions no motion is produced. Now the force acting on electrons will be from P to Q. since electrons are free to move they accumulate at end Q.
Due to this positive charge opens up at end Q i.e. end P becomes positive and end Q becomes negative and hence the rod behaves as a battery of emf Bvl.