(a) Define the term 'self-inductance' and write its S.I. unit.
(b) Obtain the expression for the mutual inductance of two long co-axial solenoids S1 and S2 wound one over the other, each of length L and radii r1 and r2 and n1 and n2 number of turns per unit length when a current I is set up in the outer solenoid S2.
a) Mutual inductance of two coils is equal to the e.m.f induced in one coil when the rate of change of current through the other coil is unity.
SI unit of mutual inductance is Henry.
b) Consider two long solenoids S1 and S2 of same length ‘l’ such that S2 surrounds S1 completely.
Let,
n1 = Number of turns per unit length of S1
n2 = Number of turns per unit length of S2
I1 = Current passing through solenoid S1
= Flux linked with S2 due to current flowing in S1
is the coefficient of the mutual inductance of two solenoids.
When current is passed through S1, emf is induced in S2 .
Magnetic field inside solenoid S1 is given by, 
Magnetic flux linked with each turn of the solenoid = 
Total magnetic flux linked with S2 is given by,
Similarly, mutual inductance between two solenoids, when current is passed through S2 and emf induced in solenoid S1 is given by, 
Hence, coefficient of mutual induction between the two long solenoids is given by, 
