# What is Motional emf | Faraday Law

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.

F_{e}= F_{b}

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;

- Increasing the speed of the rod
- Using a stronger
**magnetic field**

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.

**FARADAYS LAW **

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=x_{2}-x_{1}

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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