Faraday’s law of induction predicts how a magnetic field will interact with an electric circuit to produce the electromotive force. This law is the fundamental principle of transformers, inductors, generators and solenoids which allow them to operate.

Electromagnetic induction was first discovered by Michael Faraday and Joseph Henry independently in 1831. Faraday published the results of his findings first.¹ He explained electromagnetic induction using a concept he called "line of force". Scientist at the time rejected his theoretical ideas. This was due to the lack of mathematical formulation.

Faraday’s law of induction makes use of magnetic flux through a hypothetical surface whose boundary condition is a wire loop. The magnetic flux is defined by a surface integral. The Maxwell-Faraday equation is:

∇ x E = -∂B/ ∂t

The fields are usually functions of position r and time t. The Maxwell-Faraday equation is one of the four Maxwell’s equations, and therefore plays a fundamental role in the theory of classical electromagnetism.

Reference:

1. Ulaby, Fawwaz (2007). Fundamentals of applied electromagnetics. (5th ed.). Pearson:Prentice Hall. p. 255. ISBN 0-13-241326-4