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enter image description here

According to the question voltage across the inductor in left circuit is given by

$$V_1 = L\frac{di_1}{dt} \pm M\frac{di_2}{dt}$$ Where $i_1$ is the current in left circuit and $i_2$ is the current in the right circuit.

Similarly voltage across the inductor in the right circuit is given by

$$V_2 = L\frac{di_2}{dt} \pm M\frac{di_1}{dt}$$

Now, how do I find whether the mutually induced emf is added or subtracted?

Question is taken from JEE Advanced 2020, they have given the answer by assuming that mutually induced emf is positive.

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2 Answers 2

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Unless they are obvious from context, the polarities of coupled inductors should normally be indicated by dots on the "positive" terminal of each inductor, like in the diagram below (image credit). This means that if inductor currents are defined as entering the positive terminals, the mutual inductance will be positive.

enter image description here

In your case, the polarities are ambiguous. It sounds like they just want to take the currents as being defined in the diagram and take $M > 0$, but know that this isn't normally a given and ideally in the real world you would be given more information.

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  • $\begingroup$ In my diagram current enters L1 from down and L2 from up (As per the Given Directions). So does it mean that if currents in the coil are in opposite directions, then they are aiding each other and M>0? Also, If current enters both the coils in same direction then they are not aiding each other and M<0? $\endgroup$
    – MMS 05
    May 22, 2023 at 13:31
  • $\begingroup$ @MMS05 Even if the inductors are placed next to each other and the currents are flowing in opposite directions (up and down), the sign of the mutual inductance also depends on the way the coils are wound (i.e. clockwise or counterclockwise as seen from above). If they are both wound the same way, yes, $M > 0$ if the currents are in opposite directions (as defined in your diagram) and $M < 0$ if they are in the same direction. $\endgroup$
    – Puk
    May 22, 2023 at 17:01
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By ancient convention lost in the fog of history $M$ itself is a signed quantity, so here it is to be taken with a positive sign.

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