A changing current in one coil creates changing magnetic flux. If some of that flux links a second coil, a voltage is induced in the second coil. The two windings are then magnetically coupled.

Mutual inductance

For a linear pair of coils, the flux linkage of coil 2 produced by current $i_1$ can be written

$$\lambda_{21}=Mi_1,$$

where $M$ is the mutual inductance.

Faraday's law then gives an induced voltage proportional to the rate of change of the other coil's current:

$$|v_2|=M\left|\frac{di_1}{dt}\right|.$$

The polarity is determined by winding orientation and Lenz's law.

Dot convention

Circuit diagrams mark corresponding winding ends with dots. If current enters the dotted terminal of one winding, the dot convention determines which terminal of the other winding becomes instantaneously positive under the chosen voltage references.

The dots encode winding orientation; they do not indicate where the magnetic flux physically enters the core.

Self and mutual inductance

Self-inductance relates a winding's own current to its own flux linkage. Mutual inductance describes the part of the magnetic coupling shared between different windings.

Perfect coupling is an idealization. Real devices also have leakage flux that links one winding but not the other.