TYPES OF INDUCTION

There are two types of inductions that is SELF INDUCTION & MUTUAL INDUCTION. The detail of these types are as under.
Self Induction: - When electric current is passed through a coil, the magnetic flux produced by the current is
linked with the coil itself.
When the current in the coil is changed, the magnetic flux linked with the coil also changes inducing emf in the coil called self induced emf. This phenomenon is called self induction. The self inductance, L, of the coil is given by
L = {(number of turns in a coil) (magnetic flux linked with each turn)} / current through the coil
The self inductance of a coil attains a very large value if the coil is wound around insulated soft iron core.
So therefore the self inductance of the circuit can be defined as under.

“The self induced electromotive force produced per unit rate of change of the current in the circuit is called self inductance of the circuit.”
“The self induced electromotive force produced per unit rate of change of the current in the circuit is called self inductance of the circuit.”
The unit of self inductance is henry ( H ). If e is in volt, I  in ampere and t in second, then L is in henry. Self induced emf is also called ‘back emf’.
Circuit symbol of an inductor is as shown in the figure above. The end of the inductor where the current enters is taken as positive and the other end negative. The potential difference between the positive and negative ends of the inductor is given by
V = L {derivative of current / derivative of time} This p.d. is opposite to the p.d. of the battery providing current.Net power at time t between two ends of the inductor, V I = L I (dI /dt).
This equation shows that if the current increases by d I   in time dt, the electrical energy consumed is
L I ( d I ).

DEPEND: -
( i ) size and shape of the coil,
( ii ) number of turns of the coil and
( iii ) magnetic property of the medium of the space within the coil.

Mutual Induction: -Consider two conducting coils having arbitrary shapes placed near each other with arbitrary inclination with each other as shown in the figure.
Coil 1 has N1 turns and coil 2 has N2 turns. When current I1 flows through coil 1, some of the magnetic field lines generated in it will be linked with coil 2.
According to Biot-Savart law, for given positions of the coils, flux F2 linked with the coil 2 will be proportional to the current I1 in coil 1.
F2 is directly proportional to I1 so therefore F2 =   M21 I1 … ( 1 )
From Faraday’s law, the induced emf produced in coil 2 is given by
induced emf 2 = - dF2 / dt = - derivative of M21 I1 with respect to t
                      = - M21 (d I1 / dt) ----------------- ( 2 )
It can be proved that M21 = M12 = M. This result is called the reciprocity theorem. M is termed the mutual inductance of the system formed by the two coils. It can be defined on the basis of equation ( 1 ) or ( 2 ).
Taking I1 = 1 unit in equation ( 1 ), F2 = M21
Thus, “the magnetic flux linked with one of the coils of a system of two coils per unit current passing through the other coil is called mutual inductance of the system formed by the two coils.”
If current is in ampere, flux in Wb, then the unit of mutual inductance is WbA exp(- 1) = henry ( H ).
Depend: -
( i ) shapes and sizes,
( ii ) their number of turns,
( iii ) distance between them,
( iv ) their mutual inclination angle and
( v ) the material on which they are wound.