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