Deduce an expression for the motional EMF of by considering the Lorentz force acting on the free charge carriers of a conductor moving in a perpendicular magnetic field. Also deduce expressions for the induced current, force necessary to pull the conductor, power delivered by the external source, and power dissipated as Joule loss. Hence discuss the energy conservation
Answers
Answer:
Let us consider a straight conductor moving in a uniform and time-independent magnetic field.
The figure shows a rectangular wire PQRS in which the conductor PQ is free to move.
Rod PQ is moved towards the left with a constant velocity v.
PQRS forms closed circuit enclosing an area that changes as PQ moves.
It is placed in a uniform magnetic field B perpendicular to the plane of our system.
Let the length RQ =x and RS =l,
the magnetic flux ϕ
B
enclosed by the loop PQRS
ϕ
B
=Blx
As x is changing with time, the rate of change of flux ϕ
B
will induce an emf given according to Faraday's law of electromagnetic induction :
ϵ=−
dt
dϕ
B
=−
dt
d
(Blx)=−Blv
This induced emf Blv is motional emf.
Explanation: