Definition

Self-inductance

ε = - L \frac{d I}{d t}

Statement

The back-emf induced in a coil by its own changing current, with L the inductance characterizing that coil's geometry.

Symbols and units

$ε$	self-induced back-emf	V
$L$	self-inductance	H
$d I / d t$	rate of change of current	A/s

When it applies

Any coil or circuit element with self-inductance L, for a changing current.

Don't use when

Inductance opposes a change in current, not the current itself — a steady current through an ideal inductor produces no back-EMF at all.

Derivation

A changing current changes the coil's own flux; applying Faraday's law to that self-generated flux and defining L as the constant of proportionality gives:

ε = - L \frac{d I}{d t}

Watch out for

Inductance opposes CHANGE in current, not the current itself — a steady current through an inductor produces no back-emf at all, however large.

Connects to

Faraday's law