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Electromagnetism
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Magnetostatics
Ampère's law
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Electrodynamics
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(EM) Electromagnetic induction
Faraday-Lenz law
Displacement current
Maxwell's equations
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Electromagnetic induction is the production of voltage across a conductor situated in a changing magnetic field or a conductor moving through a stationary magnetic field.

Michael Faraday is generally credited with having discovered the induction phenomenon in 1831 though it may have been anticipated by the work of Francesco Zantedeschi in 1829. Around 1830 [1] to 1832 [2] Joseph Henry made a similar discovery, but did not publish his findings until later.

Faraday found that the electromotive force (EMF) produced around 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 be induced in any closed circuit 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.

Faraday's law of electromagnetic induction states that:

,

where

is the electromotive force (emf) in volts

Φ_B is the magnetic flux in webers

For the common but special case of a coil of wire, comprised of N loops with the same area, Faraday's law of electromagnetic induction states that

where

is the electromotive force (emf) in volts

N is the number of turns of wire (per metre)

Φ_B is the magnetic flux in webers through a single loop.

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.

Two videos demonstrating Faraday's and Lenz's laws can be watched at EduMation.

The principles of electromagnetic induction are applied in many devices and systems, including:

• Induction Sealing
• Induction motors
• Electrical generators
• Transformers
• Contactless charging of rechargeable batteries
• Induction cookers
• Induction welding
• Inductors
• Electromagnetic forming
• Magnetic flow meters
• Transcranial magnetic stimulation
• Faraday Flashlight
• Graphics tablet
• Wireless energy transfer

• Maxwell's equations for further mathematical treatment.
• Faraday's law of induction
• Inductance
• Eddy current
• Moving magnet and conductor problem

• Induction - Animation made by bigs
• A free java simulation on motional EMF

• David J. Griffiths (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X. 
• Paul Tipler (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8. 
• J.S. Kovacs and P. Signell, Magnetic induction (2001), Project PHYSNET document MISN-0-145.