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:

[itex]\oint_S \mathbf{E} \cdot d\mathbf{s} = -{d\Phi_B \over dt}[itex]

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

[itex]\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}[itex]

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

[itex]V=-N{\Delta \Phi \over \Delta t}[itex]

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

He also states that An EMF is inducted when the magnetic field around a conductor changes in his first law and The magnitude of the induced emf is proportional to the rate of change of the flux linkage in his second.

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 in 1831.

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