# what is Difference between motional and induced emf?

This post also includes:

- Motional emf definition
- The formula of motional emf
- Induced emf definition
- Lot’s more

Let’s Dive right in…

## What is Motional EMF?

“The emf induced by the motion of a conductor across a magnetic field is called motional emf”.

In the previous section we have studied that when a conductor is moved across a magnetic field, an emf induced between its ends. The emf of the moving conductor is similar to that of a battery,i.e., if the ends of the conductor are joined by a wire to make a closed circuit, a current flow through it.

### Motional emf formula

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

When the rod is stationary, the galvanometer indicates no current loop. If the rod is pulled to the right with constant velocity **v**, the galvanometer indicates a current flowing through the loop. Obviously, the current is induced due to the motion of the conducting rod across the magnetic field. The moving rod is acting as a source *E *=*V _{b }*–

*V*

_{a }= ∆

*V.*

When the rod moves, a charge q within the rod also moves with the same velocity **v** in the magnetic field **B** and the experiences a force given by

** F =**q**v × B**

The magnitude of the force is:

F = qv B sinθ

Since angle θ between v and B is 90°, so

F = q vB

Applying the right-hand rule, we see that **F** is directed from a to b in the rod. This suggests a uniform electric field **E** is induced along the rod. Its magnitude is given by:

E =F/q

substituting F =q v B in equation E=F/q,we have:

E =qvB/q

E =vB ……..(1)

The direction of electric intensity is that of force **F** i.e., it is directed from a to b. As the electric intensity is given by negative of the potential gradient, therefore

E = -ΔV/L

E=-ε/L ………..(2)

Comparing equation (1) and (2) we get:

-ε/L =vB

ε =-vBL ………..(3)

This is the magnitude of motional emf. However, if the angle between v and B is θ, then

ε =vBL sinθ ……….(4)

Read Also: Coulomb’s law

### Motional emf equation

The above equation shows that when v=0,∑=0, that means no motional emf is developed in the stationary rod. It is also obvious that by increasing the speed of rod and using a stronger field, emf can be increased.

Due to induced emf, positive charges would flow along the path , therefore the induced current is anticlockwise the diagram.

**Motional emf Vs induced emf video**

**See also:**

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