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ELECTROMAGNETIC INDUCTION:
As per previous study, we know that when electric current flows through a conductor, it creates a magnetic field surrounding it.
The reverse is also true. When a conductor situated under a magnetic field, which has a relative motion to the conductor, produces electric current through the conductor. That means the conductor experiences a force of flow of electrons.
The induced emf or current in conductor by cutting magnetic flux is known as electromagnetic induction. This was first discovered by Michael Faraday in the year of 1830.
Application: Motor, Generator, Transformers etc.

INDUCED EMF AND CURRENT BY A MOVING MAGNET:

When a magnet situated in the dotted position, some flux linked with the coil, but there is no deflection in the connected sensitive galvanometer. But when the magnet moves towards the coil from dotted position, the pointer of the sensitive galvanometer deflects in one direction from middle zero position. But when the magnet stops moving, the pointer of the galvanometer return to the zero position.
Again the galvanometer shows the result in other direction, when the magnet moves away from the coil. But again it shows zero position when the magnet become stationary.
Galvanometer deflection indicates the induced emf in the coil. The left and right deflection of galvanometer is for the directional motion of the magnet.
If we move the magnet faster, then induced emf in the coil will be greater. It is seen that the actual cause of this emf is the change of flux linkage with the coil.

By summed up above discussion Faraday states it into two laws known as Faraday’s laws of electromagnetic induction.
FIRST LAW: This law states that, if the magnetic flux changes, which linked with a conductor or a conductor which cuts the magnetic flux, an emf is induced in the conductor.

SECOND LAW: This law states that, the magnitude of induced emf is equal to the rate of change of flux linkage, i.e. the flux which linked with the conductor.

MATHMATICAL EXPLANATION:
If the number of turn of the coil is N,
Initial value of flux = ø1,
Final value of flux = ø2.
Time = t second.
So, initial flux linkage = Nø1 and final flux linkage = N ø2.
As per law, induced emf, e = (Nø2-Nø1)/t volt.
e = N(ø21)/t volt.
After differential, we get, d/dt(Nø) = Ndø/dt volt.
Or, e = -Ndø/dt volt.
The ‘-’ sign indicates that the induced emf sets up the current direction, which produced by the magnetic effect, opposes the very cause of producing, which we will discuss in Lenz’s law.

TYPES OF INDUCED EMF:
Induced emf are two types, 1) Dynamically induced emf and 2) Statically induced emf.

DYNAMICALLY INDUCED EMF: When the emf induced, in the conductor by cutting the flux is known as dynamically induced emf.
If B = flux density of the magnetic field in wb/m2,
l= length of the conductor in meter,
v= velocity of the conductor in meter/ second,
Then, emf induced in the conductor, e = Blv volt.
If the direction of the flux and the moving conductor angle is θ, then,
E = Blv sinθ volts.

STATICALLY INDUCED EMF: When the emf induced by variation of flux linkage, it is called statically induced emf.
Statically induced emf again divided by two types,
(i) Self induced emf and (ii) mutually induced emf.
(i) SELF INDUCED EMF: When an emf induced in the coil by the change of its own flux linkages, it is known as self induced emf.
e = -Ndø/dt
It is also known as counter emf or back emf.
(ii) MUTUALLY INDUCED EMF: If there is two coil nearer to each other, the induced emf in one coil due to current change in nearby coil is called mutually induced emf.