Faraday's law does not care where a changing flux comes from. Put a second coil near the first, and some of the first coil's flux threads the second. Change the current in coil 1, and a voltage appears across coil 2, with no wire between them. That is mutual induction, and it is the working principle of every transformer, ignition coil and wireless charger.

How strongly the pair is linked is one number, the mutual inductance: $M = k\sqrt{L_1 L_2}$, read aloud M equals k root L-one L-two. $M$ is the mutual inductance in henries, the same unit as any inductance. $L_1$ and $L_2$ are the two coils' own self-inductances in henries; subscript 1 is the coil whose current you change, subscript 2 is the coil that feels it, and for $M$ itself the order makes no difference. $k$ is the coupling coefficient, a bare number from 0 to 1: the fraction of flux the two coils share. At $k = 1$ every line threads both, which is the ideal transformer. Air-cored coils on a bench rarely pass 0.5, and $k = 0$ is two coils that ignore each other completely, which is what the inductor-combination rules quietly assume. Note the shape: $\sqrt{L_1 L_2}$ is the geometric mean of the two coils, it is the ceiling M can never exceed, and $k$ says how close to the ceiling this pair gets.

Then what M does: $\varepsilon_2 = M \dfrac{\Delta I_1}{\Delta t}$, read aloud epsilon-two equals M delta-I-one over delta-t. $\varepsilon_2$ is the EMF induced in coil 2, in volts. $\Delta I_1$ is the CHANGE in coil 1's current, in amperes, and $\Delta t$ is the time that change took, in seconds. It is Faraday's law with the turns and the flux folded into M. As before, $\Delta t$ sits underneath, so speed is everything: interrupt a current in a millisecond and a modest M will throw tens of volts across a coil that is connected to nothing.

Two honest notes. This is the magnitude form. The full law carries a minus sign, which is Lenz's law: the induced EMF drives a current whose own field opposes the change that made it. Get the polarity from the winding sense and the dots on the schematic. And a steady current in coil 1 induces nothing at all, however large it is. Units guide, they do not confess: henries times amperes per second is volts, and the bench shortcut is that mH times A over ms is volts too, because the two millis cancel. Convert one and not the other, and you are out by a thousand.