Question

Derive equation of induced emf in the rod which is sliding on two sides of U shaped frame placed

perpendicular to magnetic field.​

Answer 1

Explanation:

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 ϕB enclosed  by the loop PQRS

ϕB=Blx

As x is changing with time, the rate of change of flux ϕB will induce an emf given according to Faraday's law of electromagnetic induction  :

ϵ=−dtdϕB=−dtd(Blx)=−Blv

This induced emf Blv is motional emf.

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