Consider a conducting rod of length l moving with velocity v perpendicular to a uniform magnetic field B. In time dt the rod sweeps an area dA = l (v dt), so the change in flux is d(flux) = B dA = B l v dt. By Faraday's law, the induced emf e = d(flux)/dt = B l v. Alternatively, the free electrons in the rod experience a force qvB that pushes them to one end, setting up an emf e = B v l across the rod.

e = B l v

Self-inductance is the property of a coil by virtue of which it opposes any change in the current flowing through it, by inducing an opposing emf (back emf). It is defined as the flux linkage per unit current (N flux = L I) or from the induced emf e = -L (dI/dt), where L is the self-inductance. Its SI unit is the henry (H).

e = -L dI/dt

Mutual inductance is the property by which a change of current in one coil (primary) induces an emf in a neighbouring coil (secondary) due to the change in flux linkage. It is defined by e2 = -M (dI1/dt), where M is the mutual inductance, whose SI unit is the henry. It depends on the number of turns of the coils, their geometry (area and length), the distance and orientation between them, and the permeability of the core material.

e2 = -M dI1/dt