Question

Explain reciprocity theorem of mutual induction?

Answer 1

Suppose two coils are placed near each other,And current I-1 is passed through coil 1 , then there is magnetic field (B₁) produced in it. Using right hand thumb rule, we can see the direction of Magnetic field. As the current is AC, the field also changes, and Field (B₁) times number of turn N₁ is magnetic flux(Φ), so flux changes,

Since the two coils are close to each other, some of the magnetic field lines through coil 1 will also pass through coil 2.Then there will be an induced emf associated with the changing magnetic flux in the second coil,given by Faraday's Law:

The rate of change of magnetic flux in coil 2 is proportional to the time rate of change of the current in coil 1:

where the proportionality constant M₂₁ is called the mutual inductance. It can also be written as

similarly if we pass current from coil two:

There will be production of emf in first coil due to AC current in coil 1, given by

and comparing it to the emf generated due to a inductor's changing current

so mutual inductance is

By principle of reciprocity means Mutual inductance is reciprocate from one side to other in equal manner.