# Motional EMF from Faraday’s law | definition, formula derivation

According to Faraday’s law, Whenever the magnetic flux linked with the coil changes, an EMF is induced in the coil called induced EMF. Due to this induced EMF, a current is set up in the coil called induced current.

And further, Lenz’s law gives the direction of the induced current in the coil. According to Lenz’s law, the direction of the induced current in the coil is such that it opposes the change in magnetic flux that produces it.

We know that the formula of magnetic flux can be given by $\phi =B\cdot A$, In order to change the magnetic flux linked to any coil, we have to just change either strength of the magnetic field or area of the coil or both.

In this article, we will discuss motional EMF, which is developed in the loop or a coil by changing the area of the loop in the external magnetic field. The area of the loop or coil is changed here to create a change in magnetic flux linked with the coil.

So let’s get started… with the article.

## What is motional EMF?

Motional EMF – The EMF induced across the ends of the conductor due to its motion in magnetic field is called motional EMF.

In simple words, motional EMF means EMF due to motion. When one breadth of a rectangular coil is cut down and that piece of breadth is slid over both the length of the rectangle in an external magnetic field which is normally directed into the loop, then an EMF is induced across the ends of the conductor (cut piece). This induced EMF across the ends of the conductor due to its motion over the length of the rectangular loop is called motional EMF.

## Motional EMF formula derivation

Let’s consider a conductor of length $l$ which is free to move on U-shaped conducting rails, situated in uniform and time-independent external magnetic field $B$. The direction of the magnetic field is normally in the plane of the paper.

Let the conductor PQ moved inwards with its speed $v$. As the conductor, slides towards the left, the area of the rectangular loop PQRS decreases. This decreases the magnetic flux linked with the closed-loop.

Hence, an EMF is developed across the ends of the conductor PQ. Due to this induced EMF, an induced current flows through the loop along the path PQRS. The direction of induced current can be determined by using Fleming’s right-hand rule.

Suppose, a length $x$ of the loop lies inside the magnetic field at any instant of time $t$. Then the magnetic flux linked with rectangular loop PQRS is $$\phi=B\cdot A=Blx$$

According to the Faraday’s law of electromagnetic induction, induced EMF is given as $${\mathcal {E}}=-\frac{d\phi}{dt}=-\frac{d}{dt}(Blx)=-Bl\frac{dx}{dt}$$

or $${\mathcal {E}}=Blv$$ Where $dx/dt =-v$ because the velocity $v$ is in decreasing direction of $x$. The induced EMF $Blv$ is called the motional EMF because this EMF is induced due to the motion of the conductor in an external magnetic field.

## Frequently Asked Questions – FAQs

##### What is motional emf and write its formula?

The EMF induced across the ends of the conductor due to its motion in a magnetic field is called motional EMF. This is represented by the equation ${\mathcal {E}}=Blv$, where $l$ is the length of the object moving at speed $v$ relative to the strength of the magnetic field B.

##### What is the difference between motional emf and induced emf?

The EMF induced across the ends of the conductor due to its motion in a magnetic field is called motional EMF. But, in general terms. By Faraday’s Law, induced emf whenever there’s a changing magnetic flux through a loop.

##### Why does motional emf happen?

Motional EMF happens because when the conductor slides over the conducting rails, the area of the loop changes. This changing area leads to the changing magnetic flux. From faraday’s law, the rate of change of magnetic flux is EMF.
The induced EMF $Blv$ is called the motional EMF because this EMF is induced due to the motion of the conductor in an external magnetic field.

##### What is the unit of motional emf?

Despite its name, an electromotive force is not actually a force. It is commonly measured in units of volts.

##### What is the direction of motional emf?

The direction of induced emf is determined by the right-hand rule. As per the rule, if the thumb is pointed in the direction of motion of the conductor and the first finger is pointed in the direction of the magnetic field (north to south), then the second finger represents the direction of the induced current.

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