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Mutual Induction

Whenever the current passing through a coil or circuit changes, the magnetic flux linked with a neighbouring coil or circuit will also change. Hence, an emf will be induced in the neighboring coil or circuit. This phenomenon is called mutual induction.
Fig. 14

Coefficient of mutual induction

Total flux linked with the secondary due to current in the primary is N2φ2 and N2φ2 i1 N2φ2 = Mi1 where N1 is the number of turns in primary; N2 is the number of turns in secondary; φ2 is the flux linked with each turn of secondary; i1 is the current flowing through primary; and M is the coefficient of mutual induction or mutual inductance.
  • According to Faraday’s second law, emf induces in secondary, 88807.png; 88813.png
  • If 88819.png then |e2| = M. Hence, coefficient of mutual induction is equal to the emf induced in the secondary coil when rate of change of current in primary coil is unity.
Units and dimensional formula Similar to self-inductance (L).

Dependence of mutual inductance

  • Number of turns (N1N2) of both coils
  • Coefficient of self inductances (L1L2) of both the coils
  • Area of cross section of coils
  • Magnetic permeability of medium between the coils (μr) or nature of material on which two coils are wound
  • Distance between two coils (as d increases so M decreases)
  • Orientation between primary and secondary coil (for 90o orientation no flux relation M = 0)
  • Coupling factor K between primary and secondary coil

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