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# Electromagnetic induction

Electromagnetic induction is the production of an electrical potential difference (or voltage) across a conductor situated in a changing magnetic field. Michael Faraday was the first to describe this phenomenon mathematically: he found that the size of the voltage produced is proportional to the rate of change of the magnetic flux. This applies whether the flux itself changes in strength or the conductor is moved through it. Electromagnetic induction underlies the operation of generators, induction motors, and most other electrical machines[?].

Faraday's law of electromagnetic induction states that

$e=N{{d\Phi} \over dt}$
where e is the electromotive force (emf) in volts, N is the number of turns of wire, and Φ is the magnetic flux in webers.

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.

See Maxwell's equations for further mathematical treatment.

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