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Let there be two coils, L1 (with self inductance L1), and L2, with self inductance L2. The first coil is connected to a sinusoidal supply, and the second one is connected to a resistor load, as shown in the image:

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As we know There is a changing current in coil 1, therefore a changing magnetic flux (which goes through the second coil). Because of the changing magnetic flux, we have an emf induced in the second coil, and because it is a close circuit with a resistor we have also got a changing current in the second coil.

My questions - As the formula shows the induced emf in the second coil is: $\varepsilon_2 =-L_2\frac{\mathrm{d}I_2 }{\mathrm{d} t} - L_{21}\frac{\mathrm{d} I_1}{\mathrm{d} t}$ but because of the changing current in the second coil, we have a changing magnetic flux which induces an emf on the first coil, therefore we have a changing current in the first coil, a magnetic flux which induces a changing current in the second coil and so on.... the first coil induces an emf on the second and the second on the first... So how come we don't take into account these infinity number of emf on each other into this formula? Is my assumption of induced emf which creates an induced emf on the other coil which then again creates an induced emf on the first coil even true? is this process goes on and on?

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  • $\begingroup$ The equation $\epsilon_2 = -L_2(dI_2/dt) - L_{21}(dI_1/dt)$ means exactly what it says: at each instant in time, the voltage on coil 2 is given by that equation. If you want to compute how the voltage on coil 2 depends on time, then you have to think about the back-and-forth you mention, but really you'd just solve the differential equation. $\endgroup$
    – DanielSank
    Commented Jan 13, 2021 at 22:55

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The infinite process you suggest exists but only for non-zero intervals of time. At a single time instant, there are only two induced effects on coil 1: that due to the coil 1, and that due to coil 2. That is what the equation

$\varepsilon_2 =-L_2\frac{\mathrm{d}I_2 }{\mathrm{d} t} - L_{21}\frac{\mathrm{d} I_1}{\mathrm{d} t}$

correctly takes into account.

When we solve the equations numerically or using some formal method, the functions $I_1(t), I_2(t)$ can be determined, in which the infinite number of effects of the past events can be seen. But this is not necessary for writing the equations down or solving them.

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