Faraday's law of induction

Faraday's law of induction is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators.[1] The law states that:

The induced electromotive force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.[1]

Or alternatively:

The EMF generated is proportional to the rate at which flux is linked.

Electromagnetic induction was discovered independently by Michael Faraday and Joseph Henry in 1831, however Faraday was the first to publish the results of his experiments. Expanding on Faraday’s work, James Clerk Maxwell formulated the law quantitatively in the form: [2][3][4]

|\mathcal{E}| = \left|{{d\Phi_B} \over dt}\right|.

where:

|\mathcal{E}| is the magnitude of the electromotive force (EMF) in volts
ΦB is the magnetic flux through the circuit (in webers).[5]

The direction of the electromotive force is given by Lenz's law. The meaning of "flux through the circuit" is elaborated upon in the examples below.

Traditionally, two different ways of changing the flux through a circuit are recognized. In the case of transformer EMF the idea is to alter the field itself, for example by changing the current originating the field (as in a transformer). In the case of motional EMF, the idea is to move all or part of the circuit through the magnetic field.