i. When an electric current passing through a coil changes with time, an emf is induced in the neighbouring coil. This phenomenon is called mutually induced emf.
ii. Consider two coils which are placed close to each other. If an electric current i 1 is sent through coil 1, the magnetic field produced by it is also linked with coil 2 as shown i Figure (a).
iii. Let `Phi_(21)` be the magnetic flux linked with each turn of the coil 2 of `N_(2)` turns due to coil 1, then the total flux linked with coil 2 `(N_(2)Phi_(21))` is proportional to the current `i_(1) in the coil 1.
`N_(2)Phi_(21)propi_(1)`
`N_(2)Phi_(21)=M_(21)i_(1)`
`(or)M_(21)=(N_(2)Phi_(21))/(i_(1))`
iv. The constant of proportionality `M_(21)` is the mutual inductance of the coil 2 with respect to coil 1. It is also called as coefficient of mutual induction. If `i_(1)=1A," then "M_(21)=N_(2)Phi_(21).`
v. Therefore, the mutual inductiance `M_(21)` is defined as the flux linkage of the coil 2 when 1 A current flows through coil 1.
vi
When the current `i_(1)` changes with time, an emf `epsilon_(2)` is induced in coil 2. Form Faraday's law of electromagnetic induction induction, this mutually induced emf `epsilon_(2)` is given by
`epsilon_(2)=(d(N_(2)Phi_(21)))/(dt)=(d(M_(2)i_(1)))/(dt)`
`epsilon_(2)=-M_(21)(di_(1))/(dt)`
`(or)M_(21)=(-epsilon_(2))/((di)/(dt))`
vii. The negative sign in the above equation shows that the mutually induced emf always opposes the change in current `i_(1)` with respect to time. If `(di_(1))/(dt)=1As^(-1)," then "M_(21)=epsilon_(2).`
viii. Mutual inductance `M_(21)` is also defined as the opposing emf induced in the coil 2 when the rate of change of current through the coil 1 is `1As^(-1).`
ix. Similarly, if an electric current `i_(2)` through coil 2 changes with time, then emf `epsilon_(1)` is induced in coil 1. Therefore,
`M_(12)=(N_(1)Phi_(12))/(i_(1))andM_(12)=(-epsilon_(1))/((di_(2))/(dt))`
where `M_(12)` is the mutual inductance of the coil 1 with respect, to coil 2. It can be mutual inductance is same.
`i.e.,M_(21)=M_(12)=M`
x. In general, the mutual induction between two coils of turns of the coils, their relative orientation and permeability of the medium.
