(a) A rod of length is moved horizontally with a uniform velocity `'v'` in a direction perpendicular to its length through a region in which a uniform magnetic field is acting vertically downward. Derive the exprwession for the `emf` induced across the ends of the rod. (b) How does one understand this motional `emf` by invoking the Lorentz force on the free charge carries of the condutor ? Explain.

Explanation

The conductor is moving in a direction perpendicular to the field with constant velocity under the influence of some external agent.
The electrons in the conductor experience a force
`vecF=q(vecvxxvecB)`
That is directed along the length `l` perpendicular to both `v` to `B`
Under the influence of this force, the electrons move to the lower end of the conduction and accumulate there leaving a net positive charge at the upper end.As a result of this charge separation an electric field is product inside the conductor.The charges accumulate at both ends until the downward magnetic force `qvB` is balanced by the upward electric force `qE`.At this point, electrons stop moving .The condition of equilibrium requires that
`q [vecE+(vecvxxvecB)]=0`
`vecE=-(vecvxxvecB)`
`V=-int vecE.dvecl`
`DeltaV=(vecvxxvecB).vecl`
`=V_|_l_|_v`
`B_|_` is the component of magnetic field perpendicular to the velocity.
(a)`phi_(B)=Blx`
`epsilon=(-dphi_(B))/(dt)=-d/(dt)(Blx)`
`epsilon=Blv`