# Inductance

## (9) Mutual Inductance of two co-axial solenoids

• Consider a long solenoid of length l and area of crossection A containing Np turns in its primary coil
• Let a shorter secondary coil having N2 number of turns be wounded closely over the central portion of primary coil as shown below in the figure.

• If Ip is the current in the primary coil then magnetic field due to primary coil would be

• So flux through each turn of secondary coil would be

where A is the area of crossection of primary coil
• Total magnetic flux through secondary coil is

• Emf induced in secondary coil is

Thus from equation 24

So

## (10) Relation between Mutual inductance and self inductance

• Consider two coils of same length l and same area of cross-section placed near each other as shown below in the figure

• Let there are N1 number of turns in primary coil and N2 number of turns in secondary coil
• A current I1 in the primary coil produces a magnetic field

which in turns gives rise to flux?

in primary coil and

in the secondary coil due to current in primary coil.
• By the definition of self induction

and by definition of mutual induction

• Reversing the procedure if we first introduce the current I2 in secondary coil then we get

• So L1 is the self inductance of primary coil,L2 is the self induction of secondary coil and M21=M12=M is the mutual inductance between two coils

• Product of L1 and L2 is

• In practice M is always less than eq due to leakage which gives

Where K is called coefficient of coupling and K is always less then 1.