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Derive the expression for motional EMF induced in a conductor moving in a uniform magnetic field.

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Derive the expression for motional EMF induced in a conductor moving in a uniform magnetic field.

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Updated on : 2022-09-05

Let  us  consider  a  straight  conductor  moving  in  a  uniform  and  time-independent magnetic field.

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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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Derive an expression for motional emf induced in a conductor moving in a magnetic field.

Derive an expression for motional emf induced in a conductor moving in a magnetic field.

Derive an expression for motional emf induced in a conductor moving in a magnetic field.

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Derive the expression for motional EMF induced in a conductor moving in a uniform magnetic field.

Derive the expression for motional EMF induced in a conductor moving in a uniform magnetic field.. Ans: Hint: The magnetic flux enclosed in area A is given by\\[\\Phi = BA\\]If the length of the conductor is l and displacement be x then the area A i...

Derive the expression for motional EMF induced in a conductor moving in a uniform magnetic field.

Last updated date: 16th Mar 2023

• Total views: 205k • Views today: 2.85k Answer Verified 205k+ views 6 likes

Hint: The magnetic flux enclosed in area A is given by

Φ=BA Φ=BA

If the length of the conductor is l and displacement be x then the area A is given by

A=lx A=lx Hence, Φ=Blx Φ=Blx

Complete step by step solution:

1) Consider a straight conducting wire placed in an uniform magnetic field. The length of the wire is AB= l.

2) Now it is shifted x distance to another point CD.

3) Hence the flux associated with the loop ABCD is given by

Φ B =Blx ΦB=Blx

4) As the displacement x changes with time, then there is a rate of change of induced flux. According to Faraday’s law, this rate of change of flux will induce an emf in the conductor. The rate of change of flux is hence given by

ε=− d Φ B dt ε=− d dt (Blx) ε=−Bl d dt x ε=−Blv

ε=−dΦBdtε=−ddt(Blx)ε=−Blddtxε=−Blv

This induced emf is called the motional emf.

Note: The negative sign given here indicates that this emf opposes the cause of its generation. Faraday’s law of electromagnetic induction gives the concept of motional emf which is different from the emf of the cell and opposes it.

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