Last update: October 2, 2025

Equation of electromagnetic induction

Electromagnetic induction: EMF = -N * dΦ/dt

Electromagnetic induction was discovered by Michael Faraday (1791-1867) in 1831. It is based on the relationship between electricity and magnetism.
When a magnetic field changes the intensity or direction of the field, it creates a magnetic flux that passes through the circuit. This magnetic flux induces an electromotive force (EMF) in the circuit, which can generate an electric current if the circuit is closed. Electromagnetic induction is the basis of many applications, such as electromechanical alternators, electric generators, electric transformers, electric motors, wireless communication systems and many others.

For example, in an alternator the mechanical energy of rotation is converted into electrical energy using electromagnetic induction.
When the alternator spins at a certain speed, it generates a magnetic field using permanent magnets or exciter coils. This magnetic field varies in intensity and direction depending on the configuration and specific operation of the alternator. When a coil is placed inside this magnetic field and is subjected to relative movement with respect to this field (rotation of the alternator), an electric current is induced in the coil.

The current induced in the coil of the alternator is proportional to the speed of rotation of the alternator and to the intensity of the magnetic field. In general, the higher the rotational speed of the alternator, the greater the induced current will be, provided that the intensity of the magnetic field remains constant. Similarly, the higher the intensity of the magnetic field, the greater the induced current will be, provided that the speed of rotation remains constant.

The mathematical equation that describes the relationship between rotational speed (v) and magnetic field strength (B) in an alternator is given by Faraday's law of electromagnetic induction.
EMF = -N * dΦ/dt
EMF is the induced electromotive force (in volts), N is the number of turns of the coil in the alternator, Φ is the magnetic flux through the coil (in webers), and dt/dt is the time rate of change of the magnetic flux (in webers per second).

According to this equation, the emf induced in the alternator (i.e. the voltage generated) is directly proportional to the rate of change of the magnetic flux through the coil. The magnetic flux depends both on the intensity of the magnetic field B generated by the alternator and on the surface of the loop of the coil through which the magnetic field passes. Thus, the complete equation could be expressed as follows:
EMF = -N * A * dB/dt
A is the coil loop area (in square meters) and dB/dt is the rate of change of magnetic field strength over time (in teslas per second).
It is important to note that this equation is a simplification and does not take into account other factors such as internal coil resistance, circuit impedance, and energy losses, which can also influence performance. an alternator in a real system. The design and operation of an alternator is generally more complex and requires more detailed modeling for a full understanding of its behavior.