Modern Physics

Electromagnetic induction: formula, how it works, examples

The electromagnetic induction is defined as the induction of a force (pressure) means an electromotive force or near the body, due to the presence of a changing magnetic field. This phenomenon was discovered by the British physicist and chemist Michael Faraday, in 1831, by Faraday’s law of electromagnetic induction.

Faraday conducted experimental tests with a permanent magnet surrounded by a coil of wire and observed the induction of a voltage in that coil and the circulation of an underlying current.

Michael Faraday

This law indicates that the voltage induced in a closed circuit is directly proportional to the rate of change of the magnetic flux when crossing a surface, in relation to time. Thus, it is possible to induce the presence of a voltage difference (voltage) in an adjacent body due to the influence of varying magnetic fields.

In turn, this induced voltage generates the circulation of a current corresponding to the induced voltage and the impedance of the object of analysis. This phenomenon is the principle of action of energy systems and devices for everyday use, such as: motors, generators and electrical transformers, induction furnaces, inductors, batteries, etc.

formula and units

The electromagnetic induction observed by Faraday was shared with the world of science through mathematical modeling that allows replicating these types of phenomena and predicting their behavior.


To calculate the electrical parameters (voltage, current) associated with the phenomenon of electromagnetic induction, you must first define the value of the magnetic induction, currently known as the magnetic field.

To find out what magnetic flux passes through a particular surface, you must calculate the product of magnetic induction in that area. Thus:

Electromagnetic induction: formula, how it works, examples 2


Flux: Magnetic flux [Wb]

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B: Magnetic induction [T]

S: Surface [m 2 ]

Faraday’s law indicates that the electromotive force that is induced in the surrounding bodies is given by the rate of change of the magnetic flux with respect to time, as detailed below:

Electromagnetic induction: formula, how it works, examples 3


ε: electromotive force [V]

By substituting the magnetic flux value in the previous expression, you have the following:

Electromagnetic induction: formula, how it works, examples 4

If integrals are applied to both sides of the equation to delimit a finite path for the area associated with the magnetic flux, a more accurate approximation of the necessary calculation is obtained.

Furthermore, in this way, the calculation of the electromotive force in a closed circuit is also limited. Thus, when applying the integration to the two members of the equation, it is obtained that:

Electromagnetic induction: formula, how it works, examples 5

Unit of measurement

Magnetic induction is measured in the International System of Units (SI) in Teslas. This unit of measure is represented by the letter T and corresponds to the set of the following basic units.

Electromagnetic induction: formula, how it works, examples 6

One tesla is equivalent to a uniform magnetic induction that produces a magnetic flux of 1 weber on a surface of one square meter.

According to the Cegesimal System of Units (CGS), the measurement unit of magnetic induction is the gauss. The equivalence relationship between the two units is as follows:

1 tesla = 10,000 gauss

The unit of measurement for magnetic induction owes its name to the Serbo-Croat engineer, physicist and inventor Nikola Tesla. It was named in the mid-1960s.

How it works?

It is called induction because there is no physical connection between the primary and secondary elements; consequently, everything happens through indirect and intangible connections.

The phenomenon of electromagnetic induction occurs due to the interaction of lines of force from a variable magnetic field on the free electrons of a nearby conducting element.

For this, the object or medium in which the induction takes place must be arranged perpendicular to the lines of force of the magnetic field. Thus, the force exerted on free electrons is greater and, consequently, the electromagnetic induction is much stronger.

In turn, the direction of circulation of the induced current is given by the direction given by the lines of force of the changing magnetic field.

On the other hand, there are three methods by which the magnetic field flux can be varied to induce an electromotive force in a nearby body or object:

1- Modify the magnetic field modulus, due to flux intensity variations.

2- Change the angle between the magnetic field and the surface.

3- Modify the inherent surface size.

Then, once a magnetic field is changed, an electromotive force is induced in the surrounding object which, depending on its resistance to current flow (impedance), will produce an induced current.

In this order of ideas, the proportion of said induced current will be greater or less than the primary, depending on the physical configuration of the system.


The principle of electromagnetic induction is the basis for the operation of electrical voltage transformers.

The transformation rate of a voltage transformer (reducer or elevator) is given by the number of windings each transformer winding has.

Thus, depending on the number of coils, the secondary voltage can be higher (auxiliary transformer) or lower (auxiliary transformer), depending on the application in the interconnected electrical system.

Likewise, the electricity generating turbines in hydroelectric centers also operate thanks to electromagnetic induction.

In this case, the turbine blades mobilize the axis of rotation located between the turbine and the generator. So this results in the mobilization of the rotor.

In turn, the rotor is composed of a series of windings which, when in motion, give rise to a variable magnetic field.

The latter induces an electromotive force on the generator stator, which is connected to a system that allows the energy generated during the process to be transported online.

Using the two examples described above, it is possible to detect how electromagnetic induction is part of our lives in elementary applications of everyday life.

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