# Electromagnetic induction

Electromagnetic induction is the production of an electrical potential difference (or voltage) across a conductor situated in a changing magnetic flux.

Michael Faraday discovered the induction phenomenon in 1831. He found that the electromotive force (EMF) produced along a closed path is proportional to the rate of change of the magnetic flux through any surface bounded by that path. In practice, this means that an electrical current will flow in any closed conductor, when the magnetic flux through a surface bounded by the conductor changes. This applies whether the field itself changes in strength or the conductor is moved through it. Electromagnetic induction underlies the operation of generators, induction motors, transformers, and most other electrical machines.

For a coil of wire in a changing magnetic field, Faraday's law of electromagnetic induction states that

[itex] \epsilon= - N{{d\Phi} \over dt}[itex] or [itex] U= {-{d\Phi} \over dt}[itex]

where

[itex]\epsilon[itex] is the electromotive force (emf) in volts
N is the number of turns of wire
Φ is the magnetic flux in webers
U is the induced voltage

Further, Lenz's law gives the direction of the induced emf, thus:

The emf induced in an electric circuit always acts in such a direction that the current it drives around the circuit opposes the change in magnetic flux which produces the emf.

Lenz's law is therefore responsible for the minus sign in the above equation.

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