# Electromagnetic induction & Faraday’s law of induced EMF

Scientist Oersted first observed that a current carrying wire produces magnetic field around it. One can find the magnitude of this magnetic field by using Biot-Savart law and Ampere’s circuital law. Again, the direction of this magnetic field is given by Fleming’s right hand Thumb rule and Maxwell’s corkscrew rule. Now, the question is that is the reverse case possible? Will a current flow through the wire if we place it in a magnetic field? If yes, then what are the conditions? In this article, we are going to discuss this fact by the Faraday’s law of electromagnetic induction for induced EMF. This will be helpful for the students of class 10 and class 12.

• What is electromagnetic induction?
• What is Induced EMF
• Definition of Induced current
• Laws of Electromagnetic Induction
• Faraday’s Law of electromagnetic induction
• Lenz’s Law of Electromagnetic Induction
• Expression for induced EMF in a coil
• Direction of Induced EMF by Fleming’s right hand rule
• Law of conservation of energy from Lenz’s law

## What is Electromagnetic Induction?

Electromagnetic induction is an electromagnetic process in which an EMF induces in a conducting coil when it is placed in a varying magnetic field. If there is a relative velocity between the magnetic field and the coil, the magnetic flux linked with the coil changes and due to this change in magnetic flux, an EMF induces in the coil.

## What is Induced EMF?

The EMF that appears in a coil due to the change in magnetic flux through the coil is called the induced EMF. Now, the magnetic flux in the coil may change due to varying magnetic filed or the relative motion between the coil and the magnet.

## Induced Current

We already know that if there is a change in magnetic flux through a coil, an EMF induces in that coil. Now, if the coil is closed one, then a current will flow through the coil due to this induced EMF. This current is known as the induced current. This is similar to the conduction current we know, but the origin is different from that.

## Laws of Electromagnetic Induction

There are three laws of electromagnetic induction – two Faraday’s law and one Lenz’s Law. These laws give the cause, equation or magnitude and the direction of induced EMF and current.

## Faraday’s law of Electromagnetic induction

Scientist Michael Faraday first observed that an EMF induces and thereby a current flows in a closed coil if there is any change in magnetic flux through the coil. Then he has given two laws on this. His first law gives the cause of induced EMF and the second law gives an equation to find magnitude of the induced EMF.

### Faraday’s First law of Electromagnetic Induction

Faraday’s first law states that whenever the magnetic flux linked with a coil changes, an EMF induces in that coil and the induced EMF exists as long as the change in magnetic flux continues.

So, this law gives the origin or the cause of induced EMF in a coil placed in external magnetic field.

Explanation:

Number of magnetic field lines passing through the coil gives the amount of magnetic flux in the coil. In the diagram one can see that the number of magnetic field lines passing through the coil is 8 when it is at the position-A. Now when the coil is moved from position-A to position-A’, the number of field lines passing through it reduced to 3 . That means the magnetic flux through the coil changes due to the relative motion of the coil with respect to the magnetic field or magnet. Faraday said, this will induce an EMF in the coil. But if we stop the relative motion of coil, the induced EMF vanishes.

### Faraday’s second law of Electromagnetic Induction

Faraday’s second law gives an equation to find the magnitude of Induced EMF. The second law states that the magnitude of induced EMF is directly proportional to the rate of change in magnetic flux linked with the coil.

If d$\phi$ is the change in flux through the coil in the time interval dt, then according to Faraday’s second law, the magnitude of Induced EMF in the coil is $\varepsilon \propto \frac{d\phi }{dt}$.

## Lenz’s Law of Electromagnetic Induction

Lenz’s law of electromagnetic induction gives the direction of induced EMF. This law states that the direction of induced EMF in the coil will be such that it will oppose the cause of its generation in the coil. That means induced EMF will oppose the change in flux through the coil or it opposes the relative motion between the coil and the magnet. So, induced EMF and change in magnetic flux in the coil are opposite effect to each other.

## Expression for Induced EMF in a coil

From second law of Faraday we get the magnitude of induced EMF and from Lenz’s law we get the direction of induced EMF. Combining both laws we have the equation for induced EMF in a coil due to electromagnetic induction as, $\varepsilon = - N \frac{d\phi }{dt}$. Where, N is the number of turns in the coil. The negative sign arises from Lenz’s law which states that induced EMF will oppose the change in magnetic flux. Induced EMF has the unit of Volt.

If R be the resistance of the closed coil, then induced current through the coil will be i(t) = -N$\frac{1}{R}\frac{d\phi }{dt}$. Induced current has the unit of Ampere. Induced EMF and induced current both are the function of time.

## Direction of Induced EMFby Fleming’s right hand rule

One can determine the direction of induced EMF or induced current by using Fleming’s right hand rule. This is the best rule to use in this purpose.

### Fleming’s right hand thumb rule

This rule states that if we stretch the thumb, forefinger and the middle finger of right hand perpendicularly, then if forefinger points the direction of motion (relative motion) of the conductor (coil) and the middle finger points the direction of magnetic field, then the thumb will point the direction of induced current in the conductor.

This rule is also known as the dynamo rule.

## Law of conservation of energy from Lenz’s law

Lenz’s law obeys the law of conservation of energy. One can obtain the explanation of law of conservation of energy from Lenz’s law.

Lenz’s law states that induced EMF or the current opposes its cause i.e. change in magnetic flux which occurs due to the relative motion between the coil and the magnet. Thus, the induced current opposes the relative motion of the coil. So, to move the coil an external mechanical work is to be done. Again, this movement will induce current in the coil. So, the external mechanical energy is converting into the electrical energy (current) in the coil. This is nothing but the law of conservation of energy.

## Summary

1. An EMF induces in a coil if there is a change in magnetic flux through the coil.
2. This flux change may occur due to change in magnetic filed or the relative motion between the coil and the magnet.
3. If the coil is a closed coil then a current will flow in the coil due to this induced EMF.
4. Faraday’s laws and Lenz’s law give the cause, magnitude and direction of the induced EMF and current in the coil.
5. Lenz’s law obeys the law of conservation of energy.

This is all from this article on Faraday’s law of induced EMF. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

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