So, Faraday found that the instantaneous voltage produced around a closed path was directly proportional to the rate of change of magnetic flux through any surface bounded by that path.
In plain and simple terms it means that whenever a conductor was placed in a changing magnetic field or is moved through a constant magnetic field EMF will be generated across its ends.
Faraday was able to mathematically formulate the above observation.So, mathematically we have:

e is the emf in volts
ΦB is the flux in Webers.
If the conductor is a coil of wire with N loops the equation becomes:

e = emf in volts.
N = number of turns in the coil each having the same area.
ΦB is the flux through each coil in Webers.
Note that e denotes an instantaneous voltage i.e., voltage a certain instant of time.It doesnsinglequotet denote a steady and stable voltage.
The negative sign indicates that the production of emf or the direction of current in the conductor is such that it opposes the change in the flux through the conductor.
Also, we know that the magnetic field produced by a wire due to current flowing through it is perpendicular to the wire and the magnetic flux intensity changes with the amount of current flowing through it, it was found an emf is generated in the conductor simply by a time-varying current flowing through it. This phenomenon is called self induction. That is, a changing current in a wire produces emf in the same wire. Often the wire is bent in the shape of a coil or wrapped with material of high permeability to increase the value of magnetic flux so that the self-induced voltage is higher. This property is used in devices called inductors.
Applications of Electromagnetic Induction:
The principle of electromagnetic induction is used in most of the electrical machines. A few examples are generators, transformers, electric motors, induction motors, synchronous motors and solenoids.

