Self and Mutual Inductance: General Concepts

The core idea shared by both. A changing current in ANY coil sets up a changing magnetic field, and hence a changing flux, in the space around it. By Faraday's law, that changing flux induces an emf wherever it links a closed circuit -- and there are exactly two closed circuits it can link: the SAME coil that is carrying the changing current (self-inductance), or a SEPARATE, nearby coil that happens to sit in the same magnetic field (mutual inductance). Both ideas are captured by the general notion of INDUCTANCE: a fixed constant of proportionality, fixed purely by geometry (and by any magnetic material present), relating a flux linkage to the current producing it.

Self-inductance $L$. For a single coil of $N$ turns carrying current $I$, the flux linkage $N\Phi_B$ that the coil's OWN current produces through the coil ITSELF is directly proportional to $I$ (since $\Phi_B$ itself is proportional to the field, which is proportional to $I$):

The constant of proportionality $L$ is called the coil's self-inductance, or coefficient of self-induction. As the current $I$ changes, so does this flux linkage, and by Faraday's law an emf is induced BACK in the very same coil, called the back emf or self-induced emf:

By Lenz's law, this self-induced emf always OPPOSES the change in the coil's own current -- opposing an increase by acting against it, and opposing a decrease by trying to sustain it -- so a coil's self-inductance behaves rather like electrical inertia, resisting any change in the current through it exactly as mechanical inertia resists any change in an object's velocity.

Mutual inductance $M$. For two separate, nearby coils (labelled 1 and 2), a current $I_2$ in coil 2 produces a flux that partly links coil 1 as well. The flux linkage this produces in coil 1, $N_1\Phi_1$, is again proportional to $I_2$:

$N_1\Phi_1 = MI_2$ …