Obtain an expression for motional emf from Lorentz force.

Explanation

Motional emf from Lorentz force:Consider a strsight conducting rod AB of length l in a uniform magnetic field `overlineB` which is directed perpendicularly into the plane of the paper.The length of the rod is normal to the magnetic field .Let the rod move with a constant velocity `overlinev`towards right side .When the rod moves ,the free electrons present in it also move with same velocity `overlinev`in `overlineB`.As a result,the LorentZ force acts on free electrons in the direction fromB to A and is given by the relation `overlineF_B=-e(overlinev xx overlineB)`
The action of this Lorentz is to accumlate the free electrons at the end A.This accumulation of free electrons produces a potential difference across the rod which in turn establishes an electric field `overlineE` directed along BA.Due to the electric field `overlineE`,the colulomb force starts acting on the free electrons along AB and given by `overlineF_E=-e overlineE`
The magnitude of the electric field `overlineE` keeps on increasing as long as accumulation of electrons at the end A coninues.The force `overlineF_E` also increases untill equilibrium is reached.at equilibrium,the magnetic of free electrons at the end A takes place i.e
`|overlineF_B|=|overlineF_E|`
`|-e(overlinevxxoverlineB)|=|-eoverlineE|`
`vB sin 90^@)=E`
vB=E
The potential difference between two ends of the rod is
V=El
V=vBl
Thus the Lorentz force on the free electrons is responsible to maintains this potential difference and hence produces an emf
`epsilon=Blv`
As this emf is produced due to the movement of the rod,it is often called as motional emf.