Explain mutual induction and derive equation of induced emf.

Explanation

As shown in figure when current from coil `C_2` changes then flux linked with coil `C_1` also get changed and emf is induced in coil`C_1`.

If number of turns in `C_1` is `N_1` then net flux
`N_1Phi_1 prop I_2`
`therefore N_1Phi_1=MI_2`
According to Faraday.s law an emf `epsilon_1` is induced in coil-1 which is given by
`epsilon_1=-(dN_1Phi_1)/(dt)-d/(dt)(M_12I_2)`
`therefore epsilon_1=-M_12(dI_2)/(dt)`
Similarly we can prove `epsilon_2=-M_21(dI_1)/(dt)`