**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 in the loop:

**E**is the induced electric field, d

**s**is an infinitesimal element of the closed loop and dΦ

_{B}/dt is the rate of change of the magnetic flux.

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

*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 the Lenz's law.

The **Faraday's law**, as the others laws of electromagnetism was later incorporated into Maxwell's equations, unifying all of electromagnetism.