Motional

Electromotive force

or motional emf:





 

1) Consider a system have magnetic field of strength B. A rectangular conductor ABCD is placed perpendicular to the magnetic field



2) Where CD arm of the rectangle can move to and fro.



3) CD arm has length l.

CB distance is say x.

CD arm is moving toward AB arm with a constant velocity v.




4) As CD moves towards AB arm,

Area of rectangle ABCD changes. Area change means magnetic flux linked with the rectangle also changes.



5) This magnetic flux changes develops an emf to the CD arm.

We know that magnetic flux is

f  = B A

f  = B (l x)



Here A is the area of the rectangle ABCD

From Faraday’s Law

       

          

e  = - B l (-v )           

 

e  = B l v           

This emf is called the motional electromotive for or motional emf

 



Be remember, Here

       

 


 

Energy consideration:

 

1) During the motional electromotive force, suppose CD arm has resistance r,

Then current flowing through the circuit is


 



2) We know the force acting on a current carrying wire in a magnetic field is

F = B I l            

F = I B l     






 3) Now power required to push the wire is

P = F v

 






4) This power can also be derived from the equation that