Motional EMF means EMF induced at the endpoint due to the motion of the conductor in an external magnetic field. Due to the motion of the conductor, if EMF is induced then this EMF will also induce a current in the conductor. Because this conductor is producing electric current then this conductor is considered as a source.

If this source is attached to a loop then the current produced by it will flow through the loop. As we know that every conductor has some resistance, so the flow of the electrons will be hindered and heat will be produced. In this short piece of the article, we will discuss motional EMF in brief and energy consideration in detail. For a detailed reading of motional EMF, you may like the below article.

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## What is Motional EMF?

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

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.

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## Current induced in the loop

Let $R$ be the resistance of the movable arm PQ of the rectangular loop PQRS shown in the figure above. Suppose that the total resistance of the remaining arm QR, RS, and SP is negligible compared to R, then the current in the loop will be $$I=\frac{{\mathcal {E}}}{R}=\frac{Blv}{R}$$

## Force on the movable arm

The conductor PQ of the length $l$ and carrying current $I$ experiences force $F$ in the perpendicular magnetic field $B$. The force is given by $$F= lIBsin{90^{\circ}}=\left(\frac{Blv}{R}\right)lB=\frac{B^2l^2v}{R}$$

This force (due to the induced current) acts in the outwards direction opposite to the velocity of the arm in accordance with Lenz’s law. Hence, to move the arm with constant velocity $v$, it should be pulled with a constant force $F$.

**Read Also**

- Lenz’s law – statement, formula, application, and experiments
- Faraday’s laws of electromagnetic induction Class 12

## Power delivered by the external force

The power supplied by the external force to maintain the motion of the movable arm is $$F=Fv=\frac{B^2l^2v^2}{R}$$

## Power dissipated as Joule loss

The power dissipated in the loop as Joule heating loss is $$P_j = I^2 R=\left(\frac{Blv}{R}\right)^2 R=\frac{B^2l^2v^2}{R}$$

Clearly, $P_j=P$. Thus, the mechanical energy expended to maintain the motion of the movable arm is first converted into the electrical energy (induced EMF) and then to thermal energy (heat energy). This is consistent with the law of conservation of energy. This fact represents the electromagnetic setup of an equivalent electrical circuit as above.

## Frequently Asked Questions – FAQs

##### What is a motional emf?

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 $E=Blv$.

##### What are energy considerations?

We know that force is the push or pull of an object and performing a day-to-day task. we apply force on our bodies. For exerting our body, we need energy. So, here can find a link between the force and the energy. Also, the thing that provides a link between these two quantities is the energy consideration.

##### Why does motional emf happen?

This induced emf **due to the motion of an electric conductor in the presence of the magnetic field** is called motional emf. Thus, emf can be induced in two major ways: Due to the motion of a conductor in the presence of a magnetic field. Due to the change in the magnetic flux enclosed by the circuit

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