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Faraday's law of induction

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Faraday's law of induction is a physical law postulated by Michael Faraday in 1831.[1] It is one of the basic laws of electromagnetism. The law explains the operation principles of generators, transformers and also electrical motors.

Faraday's law of induction says that when a magnetic field changes, it causes a voltage.[2] That phenomenon was also found by Joseph Henry in 1831.[3] To describe the law, the magnetic flux and also a surface with a wire loop as border. This leads to the following surface integral:

[math]\Phi_B = \iint\limits_{\Sigma(t)} \mathbf{B}(\mathbf{r}, t) \cdot d \mathbf{A}[/math]

When the flux changes, it produces electromotive force. The flux changes when B changes or when the wire loop is moved or deformed, or when both happens. The electromotive force can then be calculated with the following equation:

[math] \mathcal{E} = -N {{d\Phi_B} \over dt} [/math]
  • [math] \mathcal{E}[/math] is the electromotive force
  • N is the number of loops the wire makes
  • ΦB is the magnetic flux of one loop


  1. "Faraday's Law of Induction >". 2012 [last update]. Retrieved 6 August 2012.
  2. "Faraday's Law". 2004 [last update]. Retrieved 6 August 2012.
  3. "Joseph Henry". 2012 [last update]. Retrieved 6 August 2012.
de:Elektromagnetische Induktion#Induktionsgesetz in Integralform