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What is Motional emf | Faraday Law

August 6, 2022

The emf induced by the linear motion of a conductor across a magnetic field is called Motional Emf. Faraday’s law state that The average emf induced in a conducting coil of N loops is equal to the negative of the rate at which the magnetic flux through the coil is changing with time.

Motional emf

Consider a conducting rod of length L placed on two parallel metal rays separated by a distance of L. A galvanometer is connected between the ends c and d of the rails. It forms a complete conducting loop abcd. A uniform magnetic field B is applied to the paper.

When the rod is at rest galvanometer shows no deflection. If the rod is pulled to the right with constant velocity V the galvanometer indicates the current flowing through the loop.Thus the moving rod is acting as a source of emf;

E=v b– v a=âˆ†v

When the rod moves a change q within the rod also moves with the same velocity v in the magnetic field B and experiences a force.

F=q (V*B)

having magnitude.

F=q V B sin

F=q V B

According to the right-hand rule, the direction of F is from a to b. Hence a uniform magnetic field E is induced along the rod having magnitude.

Fe= Fb

q E = q V B

E=v B

The direction of electric intensity is also from a to b. As the electric intensity is equal to the negative potential gradient

E=-âˆ†V/L

E=-Ô‘/L

v B=- Ô‘/L

Ô‘=-vBL

This is the magnitude of motional emf. If Î¸ is the angle between v and B then

Ô‘=-v BL sin Î¸

Factors increasing motional emf:

Motional emf can be increased by;

When v=0Ô‘ =0 no motional emf is developed in a stationary rod.

Due to induced EMF positive charge will flow along the path abcda therefore the induced current is anti-clockwise.

The average emf induced in a conducting coil of N loops is equal to the negative of the rate at which the magnetic flux through the coil is changing with time.

Ô‘=-N Î” Ï•/ Î”t

Explanation:

A conducting rod L move from position 1 to position 2 in time Î”t and covers a distance

Î”x=x2-x1

The velocity of the rod is given by

v= Î”x/Î”t

The emotional emf induced in the rod perpendicular to the magnetic field is

Ô‘= -vBL

Ô‘= -(Î”x/Î”t)BL

When the rod covers the distance Î”x increase in the area of the loop is

Î”A= Î”x .L

And the increase in the flux through the loop is

Î” Ï• =B Î”A

Î” Ï• =B Î”x L

Becomes,

Ô‘= – Î” Ï•/ Î”t

For a coil of N, the induced emf will become N time so,

Ô‘= -N(Î” Ï• / Î”t)

This is called the faradays law of electromagnetic induction. The â€“ve sign show that the direction of induced emf is such that it opposes the change in flux.

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