Faraday's law of induction gives the relation between the rate of change of the magnetic flux through the area enclosed by a closed loop and the electric field induced along the loop:

<math>\oint_S \mathbf{E} \cdot d\mathbf{s} = -{d\Phi_B \over dt}<math>

where E is the induced electric field, ds is an infinitesimal element of the closed loop and dΦ_B/dt is the rate of change of the magnetic flux. Or, in differential form in terms of magnetic field B:

<math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}<math>

In the case of an inductor coil where the electric wire makes N turns, the formula becomes:

<math>V=-N{\Delta \Phi \over \Delta t}<math>

where V is the induced electromotive force and ΔΦ/Δt denote the change of magnetic flux Φ during the time interval Δs. The direction of the electromotive force (the negative sign in the above formula) was first given by the Lenz's law.

Faraday's law, along with the other laws of electromagnetism, was later incorporated into Maxwell's equations, unifying all of electromagnetism.

Faraday's law of induction is based on Michael Faraday's experiments 1831.

See also electromagnetic induction.

ja:ファラデーの電磁誘導の法則 sl:indukcijski zakon