Phenomenon by which an emf is induced in a circuit (and hence current flows when the circuit is closed) when magnetic flux linking with it changes is called electro-magnetic induction.
This law explains the working principle of most of the electrical motors, generators, electrical transformers and inductors.
Relationship between electric circuit and magnetic field.
Faraday’s first law:
Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil.
This emf induced is called induced emf and if the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.
Method to change magnetic field:
By moving a magnet towards or away from the coil
By moving the coil into or out of the magnetic field
By changing the area of a coil placed in the magnetic field
By rotating the coil relative to the magnet
Faraday’s second law:
It states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil.
The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil. \[\epsilon=-N\dfrac{\partial\Phi}{\partial t}\]
Usually, a minus sign is given to the right-hand side expression which indicates that emf is induced in such a direction which opposes the cause (i.e., change in flux) that produces it (according to Lenz’s law).