Derive equation of induced emf in the rod which is sliding on two sides of U shaped frame placed
perpendicular to magnetic field.
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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.
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