Faraday's Law of Electromagnetic Induction

Michael Faraday (B. 22 September 1791 D. 25 August 1867)
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On April 21, 1820 Danish Physicist Hans Christian Oersted discovered the magnetic field produced by an electric field. After this discovery scientists began to search for the converse phenomena. that is production of electric current from magnetic field about 1821 onward. The problem they put to themselves was conversion of magnetism into electricity. Michael Faraday was one of those scientist. Michael Faraday had a habit of keeping magnets in his pocket while walking to remind himself of the problem. After 9 years of continuous experiment and research he succeeded to obtain the electricity by converting magnetic field. He postulated the two laws of electromagnetism which is the basis of Electrical Engineering and serves as the laws upon which the working of most of the electrical equipments like motor, generator, transformer, etc are based.

Laws of Electromagnetic Induction  

Any change in the magnetic field of a coil of wire will cause a voltage(emf) to be induced in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic  field strength by moving a magnet toward or away from the coil, rotating the coil relative to the magnet. The expression for emf induced is as follows,

where e = generated emf

                        N = number of turns of coil

                                                                        Φ = flux

Above equation can be mathematically proved as below.

Suppose a coil has N number of turns and the flux through it changes from an initial value of Φ₁ Webers to final value Φ₂ Webers in time "t" seconds.

Initial flux linkages = NΦ₁

Final flux linkages = NΦ₂

Therefore,

Negative sign signify the fact that the induced emf sets up current in such a direction that the magnetic effect produced by it opposes the very cause of producing it. The induced emf in the coil is equal to the negative rate of change of magnetic flux times the number of turns in the coil. It involves interaction of charge with magnetic field. 

First Law:- Whenever a conductor is placed in a varying magnetic field and emf gets induced across the conductor and if the conductor is closed circuit then induced current flows through it.

Second Law:- It states that, "the emf induced is equal to the rate of change of flux linkages with the coil. 

Note:- 

1. The flux linkages is the product of number of turns and the flux associated with the coil.
2. The direction of induced emf is given by Fleming's Right Hand and Left Hand rule,