Explain mutual induction and derive equation of mutual $\mathrm{emf}$.
Explain mutual induction and derive equation of mutual $\mathrm{emf}$.
As shown in figure when current from coil $\mathrm{C}_{2}$ changes then flux linked with coil $\mathrm{C}_{1}$ also get changed and emf is induced in coil $\mathrm{C}_{1}$.
If number of turns in $\mathrm{C}_{1}$ is $\mathrm{N}_{1}$ then net flux
$\mathrm{N}_{1} \phi_{1} \propto \mathrm{I}_{2}$
$\therefore \mathrm{N}_{1} \phi_{1} =\mathrm{MI}_{2}$
According to Faraday's law an emf $\varepsilon_{1}$ is induced in coil-1 which is given by
$\varepsilon_{1}=-\frac{d \mathrm{~N}_{1} \Phi_{1}}{d t}-\frac{d}{d t}\left(\mathrm{M}_{12} \mathrm{I}_{2}\right)$
$\therefore \varepsilon_{1}=-\mathrm{M}_{12} \frac{d \mathrm{I}_{2}}{d t}$
Similarly we can prove $\varepsilon_{2}=-\mathrm{M}_{21} \frac{d \mathrm{I}_{1}}{d t}$
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