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Explain the motional emf by the Lorentz ...

Explain the motional emf by the Lorentz force acting on the free charge carriers of conductor.

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Consider any arbitrary charge q in the conductor PQ shown in figure. When the rod moves with speed v, the charge will also be moving with speed v in the magnetic field B.

The Lorentz force on this charge is qvB in magnitude, and its direction is towards Q. All charges experience the same force in magnitude and direction, irrespective of their position in the rod PQ.
The work done in moving the charge from Q to P is W = qvBl
Since emf is the work done per unit charge,
`epsilon=W/q=Blv`
which is equation of motional emf.
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