Chapter-6|Electromagnetic Induction (EMI)| NCERT 12th Physics:
The phenomenon according to which an opposing EMF is produced in a primary coil as a result of change in current or magnetic flux linked with a neighbouring coil is called mutual induction.
If I₁ is changing, then B in primary coil also changes, B in secondary also changes. Thus magnetic flux in secondary coil changes. So we obtained induced EMF as results induced current is generated in secondary coil.
Let a current I₁ flows in primary coil, due to this current, the magnetic flux linked with each turn of the coil be Φ₂. If N₂ be the number of turns in the secondary coil, then the number of flux linked with the secondary coil will be N₂Φ₂.
This number of flux is proportional to the current I₁, flowing in the primary coil.
Note: M depends upon geometry of two coils, and their orientation, separation and medium etc.
If on changing the current in primary coil, the EMF induced in the secondary coil is e₂, then according to Faraday’s law
Mutual Inductance of Two Long Co-axial Solenoid:
Let current in outer solenoid be i₁, then magnetic field B inside the outer solenoid along the axis
Since, these field lines also passes through the inner solenoid, so magnetic flux Φ linked with the each turn of the inner solenoid will be