Mutual Induction—Mutual induction of two coil can be defined as the magnetic flux linked to the secondary coil due to the flow of induced current in primary coil. Mathematically, it can be written as,
Where, M is a proportionally constant which is called mutual inductance.
Hence, mutual induction of two coils is the ratio of magnetic flux changes in secondary coil to the induced current produced in primary coil.
Mutual inductance of two coils is numerically equal to change in magnetic flux in secondary coil provided induced current produced in primary coil is 1A
According to Faraday's second law
Hence, mutual inductance of two coils is the ratio of induced emf produced in secondary coil to the rate of lose of induced current produced in primary coil with respect to time
Therefore, mutual inductance of two coils is numerically equal to induced emf produced in secondary coil provided rate of loss of induced current produced in secondary coil with respect to time is 1AS–1.
1 henry = 1 weber /1 ampere
Solenoid—Prove that M12 = M21 = M
N-turns coil wrapped around soft iron core is called solenoid two solenoid S1 and S2 are placed co-axially as shown in next page. The magnetic field of solenoid S1 can be expressed as,
For solenoid S1 , N, is the total number of turns, n1 is the total number of turns per unit lenght and the since they are placed co-axially.
:. I1 = I2 = I ..(3)
For solenoid S2, N2 is the total number of turns, n2 is the total no. of turns per unit lenght.
By defn of mutual inductance, for primary coil
By defn of mutual inductance for secondary coil.
Conclusion—Mutual inductance of primary coil is numericlly equl to mutual inductance of secondary coil with respect to primary coil which is simply called mutual inductance of two coil.
