Consider I₁ and I₂ are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L₁ = self inductance of coil 1, M₁₂ = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be

The total induced emf in coil 1 arises from both self-induction and mutual induction.

The self-induced emf in coil 1 due to its own changing current is given by:

• $$e_{\text{self}} = -L_1 \frac{dI_1}{dt}$$

The mutual inductance between the coils causes an additional induced emf in coil 1 due to the changing current in coil 2:

• $$e_{\text{mutual}} = -M_{12} \frac{dI_2}{dt}$$

The net induced emf in coil 1 is the sum of both contributions:

$$e_1 = -L_1 \frac{dI_1}{dt} - M_{12} \frac{dI_2}{dt}$$