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