# 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 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

- <math> \epsilon= - N{{d\Phi} \over dt}</math>

where <math> \epsilon</math> 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.*

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

See Maxwell's equations for further mathematical treatment.

## Applications

- Induction motors
- Electrical generators
- Transformers
- Contactless charging of rechargeable batteries
- Electric cookers with induction hobs.
- Induction welding
- Inductors

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