Question

obtain an expression for the emf induced across a conductor which is moved in a uniform magnetic field which is perpendicular to the plane of motion​

Answer 1

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

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=−  dt d ϕB​ =−  dt d  (Blx)=−Blv

This induced emf Blv is motional emf.