show that the mutual induction between a pair of coils is same ( M12 = M21)
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Answer:
Mutual induction: When an electric current passing through a coil changes with time, an emf is induced in the neighbouring coil. This phenomenon is known as mutual induction and the emf is called mutually induced emf. Consider two coils which are placed close to each other. If an electric current ii is sent through coil 1, the magnetic field produced by it is also linked with coil 2. Let Φ21 be the magnetic flux linked with each turn of the coil 2 of N2 turns due to coil 1, then the total flux linked with coil 2 (N2 Φ21 ) is proportional to the current i1 in the coil 1. The constant of proportionality M21 is the mutual inductance of the coil 2 with respect to coil 1. It is also called as coefficient of mutual induction. If i1 = 1A, then M21 = N2 Φ21 . Therefore, the mutual inductance M21 is defined as the flux linkage of the coil 2 when 1A current flows through coil 1. When the current changes with time, an emf ε2 is induced in coil 2. From Faraday’s law of electromagnetic induction, this mutually induced emf ε2 is given by The negative sign in the above equation shows that the mutually induced emf always opposes the change in current i, with respect to time. If didldidl = 1AS-1,then M21 = -ε2 . Mutual inductance M21 , is also defined as the opposing emf induced in the coil 2 when the rate of change of current through the coil 1 is 1 As-1 . Similarly, if an electric current i2 through coil 2 changes with time, then emf ε1 is induced in coil 1. Therefore, where M12 is the mutual inductance of the coil 1 with respect to coil 2. It can be shown that for a given pair of coils, the mutual inductance is same, i.e., M21 = M12 = M. In general, the mutual induction between two coils depends on size, shape, the number of turns of the coils, their relative orientation and permeability of the coil
