Consider $I_1$ and $I_2$ are the currents flowing simultaneously in two nearby coils $1$ and $2$,respectively. If $L_1$ is the self-inductance of coil $1$ and $M_{12}$ is the mutual inductance of coil $1$ with respect to coil $2$,then the value of the induced emf in coil $1$ will be:

• A
  $\varepsilon_1 = -L_1 \frac{dI_1}{dt} + M_{12} \frac{dI_2}{dt}$
• B
  $\varepsilon_1 = -L_1 \frac{dI_1}{dt} - M_{12} \frac{dI_1}{dt}$
• C
  $\varepsilon_1 = -L_1 \frac{dI_1}{dt} - M_{12} \frac{dI_2}{dt}$
• D
  $\varepsilon_1 = -L_1 \frac{dI_2}{dt} - M_{12} \frac{dI_1}{dt}$