Faraday's Law of Electromagnetic Induction

Faraday's Law of electromagnetic induction is the basic principle behind the operation of Transformer, Induction motor, DC motor, DC generator and several other special machines.

It states that, the electromotive force (EMF) produced in a conductor is proportional to rate of change of magnetic flux linked with the conductor.

In other words,

For a transformer, Induction motor:
"Whenever a conductor is placed in a varying magnetic field, an emf is induced in the conductor."

i.e. in transformer and induction motor, varying magnetic flux is produced by exciting a coil with a time varying (AC) supply which links with the secondary (in transformer) or with the rotor conductors (in induction motor).

For a Generator:
"Whenever a conductor moves in a magnetic field such that it cuts the magnetic field, an emf is induced in the conductor."

Here in generator, flux linked with the conductors is varied by means of a mechanical force. i.e. the conductors are moved into and away from the magnetic field which means that when conductor moves towards a magnetic pole(field), flux linkage increases and when it moves away from a pole, flux linkage decreases thus a varying flux linkage is achieved mechanically.

For a motor (Converse):
"Whenever a current carrying conductor is placed in a magnetic field, it experiences a force."

Here, assume there is magnet (stator) and a current carrying conductor wound on a core(rotor). Current carrying conductor will behave as an electromagnet with it own poles. Now, the interaction of the stator and rotor poles produces a force (attractive or repulsive) which is directed in a rotational path to produce rotating motion of the motor.