Electromagnetic Induction: Definition, Principles, Examples

Electromagnetic Induction is the phenomenon due to which an emf is induced in a conducting loop, placed in a magnetic field when there is a change in the magnetic flux associated with the loop. It is also the phenomenon due to which an emf is induced across the ends of a conductor when it is moving through a region of a magnetic field. Simply put, electromagnetic induction is a phenomenon due to which an emf is produced with the help of a magnetic field. Michael Faraday discovered electromagnetic Induction in \(1831,\) and later James Clerk Maxwell mathematically described it as Faraday’s law of induction. Let us understand this phenomenon in detail with the help of this article.

What is Electromagnetic Induction?

Electromagnetic induction is a process in which an emf (or a current) is induced in a conducting loop due to a change in the magnetic flux associated with the coil. The emf is known as induced emf and the current driven by it is known as induced current.

Scientists like Oersted and Ampere had demonstrated that electric current through a conductor produces a magnetic field around it. Michael Faraday, an English physicist, thought that the reverse could also happen, that is, a current could be produced by a magnetic field. Finally, after many experiments, he could demonstrate that it was possible.

Faraday’s Experiment to Demonstrate Electromagnetic Induction

1. Connect a conductor in the form of a coil to a galvanometer. A galvanometer is used to detect the presence of current.
2. Move a strong magnet towards the coil. The needle of the galvanometer moves momentarily and comes back to zero.
3. Move the magnet in the reverse direction. The galvanometer needle moves in the opposite direction and again comes back to zero. It means that the current direction is reversed.
4. Keep the magnet stationary but move the coil. We see that there is a deflection in the needle.
5. Keep both the coil and the magnet stationary. There is no deflection.

This experiment shows that an emf (or current) is induced in a conductor only when there is a change in magnetic flux associated with the coil, which is established here by either moving the magnet or the coil.

Faraday’s Law of Electromagnetic Induction

Whenever the flux of a magnetic field associated with a conducting coil changes, an emf is induced in the coil whose magnitude is equal to the rate of change of the magnetic flux. Magnetic flux associated with a coil is simply a measure of the number of magnetic field lines through the coil. Mathematically it is given by

\( \Phi = NBA\cos \theta \)

where,

\(\left( \Phi \right)\) is the magnetic flux ( SI unit weber \((Wb)\) )

\(N\) is the number of turns in the coil.

\(B\) is the strength of magnetic field ( SI unit tesla \((T)\) )

\(A\) is the area of the surface through which the field lines pass. It is measured in \({{\rm{m}}^{\rm{2}}}.\)

\(\theta \) is the angle made by the area vector of the surface with the magnetic field lines.

From Faraday’s Law, emf \((e)\) induced in a coil is,

\(e = – N\frac{{d\Phi }}{{dt}}\)

where,

\(\frac{{d\Phi }}{{dt}}\) is the time rate of change in flux

Here negative sign implies that the induced emf (or current) opposes the cause of its production. Let’s learn about it a bit more with Lenz’s law.

Lenz’s Law

It states that the emf induced in a coil is such that it opposes the cause (change in flux) of its production. Let’s understand it with the help of an example. Suppose the north pole of a bar magnet is moved towards a coil with a closed circuit. Then, according to Faraday’s law, an emf is induced in it which drives a current through the coil and creates a magnetic field. Now, Lenz’s law says that this field (produced by the induced current) will be in such a direction that it will oppose the incoming north pole. This means the face of the coil towards which the north pole is moving will become a north pole to repel the incoming magnet. If the magnet is pulled away, the induced current changes its direction to create a south pole at this end in order to attract the magnet.

Self Induction

We all know that a current-carrying coil produces a magnetic field and there is a flux of this magnetic field through the coil itself. When there is a change in the current through the coil, there will be a change in the magnetic flux through the coil and hence according to faraday’s law, an emf will be induced. This phenomenon due to which an emf is induced in a current-carrying coil due to a change in its own current is known as self-induction. Mathematically it is given as

\(e = -L\frac{{di}}{{dt}}\)

where the proportionality constant \(L\) is called inductance. It is a geometrical quantity, meaning, it depends on the shape and size of the coil. The SI unit of inductance is henry. Any conducting loop which can exhibit self-induction is called an inductor.

Mutual Induction

When a current-carrying coil is placed near another conducting coil, there is a magnetic flux through the second coil due to the magnetic field of the first coil. Now, if there is a change in the current in the first coil, there will be a change in the magnetic flux associated with the second coil and hence according to faraday’s law, an emf will be induced in the second coil. This phenomenon due to which an emf is induced in the second coil due to a change in the current in the first coil is known as mutual induction.

Fleming’s Right-hand Rule to Find the Direction of Current

According to Faraday’s experimental results, when a conductor moves in a magnetic field such that its length is moving perpendicular to the magnetic field, emf is induced in it. A current will flow through it if the circuit is closed. 

The direction of current depends on –

1. The direction of the movement of the conductor
2. The direction of the magnetic field

When the directions of these three parameters are perpendicular to each other, The direction of the current can be found using Fleming’s right-hand rule.

If we hold the right hand such that the thumb, forefinger, and the middle finger are perpendicular to each other, and –

1. if the forefinger points in the field direction (north to south),
2. if the thumb points the direction of movement of the conductor,
3. then the middle finger points in the current direction.

Applications of Electromagnetic Induction

Transformers, alternating current (AC) generators, induction cooktops are a few examples from our day-to-day life which function on the principle of electromagnetic induction.

Transformer

It is a device that transforms or changes the voltage level from higher to lower or vice versa. It works on the principle of mutual induction, so it can operate only for alternating current. It consists of two coils wound over an iron core. AC is passed through one of the coils which we call the primary coil. Its varying magnetic flux links with the second coil called the secondary coil and induces an emf in it. Based on the ratio of turns in primary and secondary, the voltage can be increased or decreased.

AC Generator

At the simplest level, it consists of a rectangular coil between two magnetic poles. The ends of the coil are connected to two slip rings. They are connected to the external circuit through carbon brushes. The coil is rotated at an angular speed \(\omega\) using an external force. At any time \(t\), the plane of the coil makes an angle \(\theta = \omega t\) with the direction of the field lines. The magnetic flux linked with the coil is

\(\Phi = NBA\cos \theta = NBA\cos \omega t\)

From Faraday’s law, induced emf is

\(e =\) – \(\frac{{d\Phi }}{{dt}}\)

\(e =\) – \(\frac{{d(NBA\cos \omega t)}}{{dt}}\)

The number of turns \((N)\), Flux density \((B)\) and area \((A)\) are constant for a given generator.

Therefore,

\(e =\) \(-NBA\frac{{d(\cos \omega t)}}{{dt}}\)

Differentiating,

\(e =\) \(NBA\omega \sin \omega t\)

When the coil face is perpendicular \(({90^{\rm{o}}})\) to the field lines, induced emf is maximum \(\left({{e_0}}\right).\)

\({e_0} = NBA\omega \) when \(\sin \omega t = \pm 1\)

Therefore, induced emf is

\(e = {e_0}\sin \omega t\)

The induced emf follows a sine wave function. Since the emf regularly alternates between positive and negative values, the induced current is called alternating current (AC).

Solved Examples- Electromagnetic Induction

Q.1. A rectangular coil of sides \({\rm{20}}\,{\rm{cm}}\) and \({\rm{10}}\,{\rm{cm}}\) rotates in a magnetic field of density \(0.1{\rm{T}}{\rm{.}}\) What is the maximum and minimum flux linked with the coil?
Ans: Given,
Flux density, \(B = 0.1{\rm{T}}\)
Area, \(A = 20\;{\rm{cm}} \times 10\;{\rm{cm}} = 0.2\;{\rm{m}} \times 0.1\;{\rm{m}} = 0.02\;{{\rm{m}}^2}\)
Flux linking with a conductor is given by
\(\Phi = BA\cos \theta \)
It is minimum when the coil face is parallel to the field lines, that is, \(\theta = {90^{\rm{o}}}\)
Then, induced emf is \(\Phi = 0\)
Flux is maximum when the coil face is perpendicular to the field lines, that is, \(\theta = {0^{\rm{o}}}\)
Then, induced emf is \(\Phi = 0.1 \times 0.02 \times 1 = 0.002\;{\rm{Wb}}\)
Maximum emf induced is \({\rm{2}}\,{\rm{milliweber}}{\rm{.}}\)

Summary

In this article, we have seen the connection between electricity and magnetism and how they are related to each other. We have seen that current induces a magnetic field, as well as a magnetic field inducing a voltage, thereby creating a current in a conductor. This mutual relationship goes a long way in the working of the various common devices we use and see daily, from motors, generators to transformers. We are able to use the machines in our routine lives due to the research of Faraday, Lenz, Ampere and the other scientists.

FAQs

Q.1. Why is a current set up when a magnet is pushed into a closed coil?
Ans: The moving magnetic field induces emf that sets up a current.

Q.2. Will emf be induced in a conductor if both the field and the conductor are stationary?
Ans: No. For emf to be induced, either the magnetic field or the conductor must move.

Q.3. Why is a negative sign used for the equation of induced emf in Faraday’s equation?
Ans: The negative sign tells that the emf induced sets a current to create a field opposing the cause of the induced emf. This is according to Lenz’s law.

Q.4. When using Fleming’s right-hand rule, what direction is signified by the thumb?
Ans: The thumb signifies the direction of the conductor movement.

Q.5. What property does a transformer use?
Ans: A transformer uses the property of mutual induction between two coils.

We hope this detailed article on Electromagnetic Induction helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.