Faraday’s Law of induction is the fundamental law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromagnetic induction. It is the core operating principle of transformers, inductors, and many types of electrical motors, generators, and solenoids.
The Maxwell-Faraday equation describes a spatially varying and time magnetic field, while Faraday's law states that there is EMF work done on a unit charge when it has traversed one round upon the conductive loop when the magnetic flux throughout the surface enclosed by the loop varies in time. The equation of Faraday's Law can be derived from The Maxwell-Faraday equation and the Lorenth Force.