Faraday’s Laws of Induction: Definition, Laws, Applications

Faraday’s Laws of Induction: The phenomena of electricity and magnetism were considered to be mutually exclusive for a long period of time. Scientists like oersted and ampere performed various experiments to prove that these two concepts were related. They found that a compass needle gets deflected when placed close to a current-carrying wire, proving that a magnetic field is associated with the moving charges or electricity. At that time, there were several other questions that scientists had to answer, like – is the converse of this effect true? Can there be an electric field associated with moving magnetic charges are electricity and magnetism mutually inclusive?

English scientist Michael Faraday performed several experiments involving electricity and magnetism. Based on the observations made during those experiments, in \(1832\), he gave a quantitative relationship between a changing magnetic field and the corresponding changes in an electric field associated with it. The results of his experiments were computed and established in the form of Faraday’s laws of electromagnetic induction. Faraday’s laws are the basic laws that established the understanding of electromagnetism. He explained the phenomena of electromagnetic induction that helps us predict the nature of the interaction between the magnetic field and an electric circuit that leads to an electromotive force or EMF. To learn in detail about the laws of induction as given by Faraday, let us read further.

Faraday’s Laws of Induction

According to electromagnetic induction, a change in the magnetic field around an electric circuit induces a current in the circuit. The amount of current induced in the wire will vary with the strength of the magnetic field or due to the relative motion between the magnetic field and the electric circuit.

When Faraday’s results that the relative motion between a bar magnet and loop of wire generates a small current through the wire were made public, he had to answer many questions. The basis and usefulness of this discovery were questioned, and he answered that his experiments were just the beginning of something huge. Indeed, the phenomenon of electromagnetic induction has transformed the world as we see it. Can you imagine a world without electricity, trains, telephones or computers? We have Faraday and Henry to thank for it. Henry discovered EMI a year after Faraday, and both of them worked on several experiments to conceptualise it.

Faraday’s law of electromagnetic induction, also known as the law of electromagnetism, forms the basis for the working of electric generators, motors, transformers and inductors.

First Experiment

Faraday and Henry performed several experiments to understand electromagnetic induction.
As we can see from the diagram above, the set-up for the experiment consists of a bar magnet, a coil attached in a circuit containing wire attached to a galvanometer. When the magnet is pushed towards the coil, with its north pole pointing towards it, a deflection is observed in the galvanometer. This deflection proves that the current is flowing through the coil. The deflection in the galvanometer persists as long as the magnet is moving, and as soon as the magnet comes to rest, deflection dies out. The deflection is observed in the galvanometer but in the opposite direction when the magnet is pulled away, indicating a reversal in the current direction. Opposite results were obtained when the bar magnet was pushed towards to away from the coil, with its South Pole pointing towards the coil.
The deflection produced in the galvanometer is large when the magnet is pushed away or towards the coil faster, indicating a large amount of current flow. Similar observations were made when the magnet is kept stationary while the circuit is moved towards or away from it. Thus, proving that the relative motion between the coil and the magnet generates electric current through the coil.

Second Experiment

For the second experiment, Faraday and henry replaced the bar magnet with another electric coil connected to a battery, shown in the figure below. We know that a magnetic field is associated with moving electric charges. Thus, the steady flow of current through the second coil will produce and uniform magnetic field around it. A deflection is produced in the galvanometer when the second coil is moved towards the first coil, indicating the flow of electric current through the first coil. The deflection stops as soon as the second coil comes at rest, and the direction is deflection is revered when the second coil is moved away from the first coil.  Similar results were obtained if the second coil was kept at rest and the first coil was moved towards it. Thus, the current is induced due to the relative motion between the coils.

Third Experiment

From the first two experiments, it became apparent that the electric current is induced whenever there is a relative motion between the magnet and the coil or between the two coils. But in his third experiment, Faraday proved that this relative motion is not essential for the flow of current through the coil. For his third experiment, he took two coils; the first coil connected to a galvanometer and the second coil connected to a battery and a tapping key, as shown in the figure below:

He observed that when the two coils are kept close and the tapping key attached to the second coil is pressed, the circuit is completed and the current flows through the coil, and a momentary deflection is observed in the galvanometer attached to the first coil. A momentary deflection is observed in the opposite direction when the key is released. The deflection in the galvanometer increases when an iron rod is inserted along the axis of the coils. The presence of an iron rod enhances the strength of the electromagnet. Thus, the magnitude of current flowing through the coil increases, as indicated by the increased deflection in the galvanometer.

Conclusion from the Experiments

Based on the three experiments, Faraday stated that whenever there occurs relative motion between the coil and the magnetic field, the total magnetic flux associated with the coil varies accordingly. This varying magnetic field would generate a voltage across the coil. Also, an electromotive force is generated across the coil due to the variation of magnetic flux with time.

Magnetic Flux

The amount of (number of magnetic field lines) passing through a closed surface is defined as magnetic flux. It gives an estimation of the total magnetic field passing through a given surface. Mathematically, the magnetic flux through a plane surface having an area \(A\), kept in a uniform magnetic field \(B\) is:
\({\Phi _B} = B \cdot A = BA\cos \theta \)
Here, \(\theta \) is the angle between the magnetic field and the area vector. Magnetic flux has only magnitude and no direction. Thus, it is a scalar quantity. The SI unit of magnetic flux is weber\({\rm{(Wb)}}\) or tesla meter squared \(\left( {{\rm{T}}{{\rm{m}}^2}} \right)\).

Faraday’s First Law

According to Faraday’s first law of electromagnetic induction, an electromotive force is developed across the conductor when a conductor is placed in a varying magnetic field. When this circuit is closed, a current gets induced in the circuit, and this current is known as Induced current.
Methods of varying the magnetic field:
The magnetic field across a circuit can be varied in four different ways:

1. By rotating the coil with respect to the magnet.
2. By moving the coil towards or away from the magnetic field.
3. By altering the area of the coil within the magnetic field.
4. By moving the magnet towards or away from the coil.

Faraday’s Second Law

Faraday’s second law states that the magnitude of the emf induced in an electric coil equals the rate of change of electric flux linked with the coil. The flux associated with the coil is determined by the product of the number of turns in the coil and the flux linked with it.
In simple terms, the amount of emf generated in the coil depends upon the rate of change of magnetic flux through it. Mathematically, Faraday’s law can be given as:
\(\varepsilon = – \frac{{Nd\Phi }}{{dt}}\)
Here,
\(\varepsilon \): EMF generated
\(\Phi \): Magnetic flux associated with the coil
\(N\): Number of turns in the coil

Note:
1. EMF is nothing but the potential difference generated across an unloaded loop that occurs when the resistance through a circuit attains a very high value.
2. The negative sign in the equation is according to energy conservation.

Lenz’s Law

Heinrich Lenz postulated the lenz law in \(1834\). Faraday’s law of electromagnetic induction gave the idea regarding the magnitude of electromotive force generated across the circuit; Lenz’s law helps us determine the direction of flow of electric current through the circuit. According to Lenz’s law, the direction of induced current in the coil is such that it opposes the change which is responsible for the induced emf. Or it can be stated simply as the direction of current will be opposite to the direction of flux that produces it.

It can be understood as the inertia of the loop due to which it opposes the change that causes the electrons to flow through it. The field produced by the “induced current” is opposite in direction to change in the main magnetic field that induces the current. We can use Fleming’s right-hand rule to determine the direction of this current flow.

Applications of Faraday’s Law of Electromagnetic Induction

1. This law constitutes the principle of operation of devices like Transformers and electric motors.
2. Faraday’s law of induction helps in understanding the working of the Induction cooker.
3. We can measure the speed of flow of liquids using an electromagnetic flowmeter.

Summary

Force is developed across the conductor when a conductor is placed in a varying magnetic field. When this circuit is closed, a current gets induced in the circuit, and this current is known as Induced current.
Faraday’s second law of motion states that the magnitude of the emf induced in an electric coil equals the rate of change of electric flux linked with the coil. The flux associated with the coil is determined by the product of the number of turns in the coil and the flux linked with each turn.

Lenz law: According to Lenz’s law, the direction of induced current in the coil is such that it opposes the change which is responsible for the induced emf. Or it can be stated simply as the direction of current will be opposite to the direction of flux that produces it.

The EMF generated through the coil when placed in a changing magnetic field can be mathematically given as \(\varepsilon = – \frac{{Nd\Phi }}{{dt}}\)

Frequently Asked Questions on Faraday’s Laws of Induction

Q.1. State Lenz’s law of electromagnetic induction.
Ans: According to Lenz’s law, the direction of induced current in the coil is such that it opposes the change which is responsible for the induced emf.

Q.2. Based on the experiments performed by Faraday, describe how the emf generated across the coil can be increased.
Ans: EMF through the coil can be increased by:
1. Increasing the number of turns in the coil
2. Increasing the strength of the magnetic field
3. Increasing the speed of relative motion between the coil and the source of the magnetic field.

Q.3. Give a few devices based on Faraday’s law of induction.
Ans: Electric generator, motor and inductor.

Q.4. State Faraday’s first law.
Ans: According to Faraday’s first law, an emf or electromotive force is developed across the conductor whenever a conductor is placed in a varying magnetic field.

Q.5. Give the mathematical relation of Faraday’s second law of electromagnetic induction.
Ans: The mathematical expression of Faraday’s second law of electromagnetic induction,  \(\varepsilon = \frac{{Nd\Phi }}{{dt}}\).

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