A consequence of Maxwell’s equations is that changes in time of currents and charges are not synchronized with changes of the electromagnetic fields. The changes of the fields are always delayed relative to the changes of the sources, reflecting the finite speed of propagation of electromagnetic waves. Under the assumption that this effect can be ignored, it is possible to obtain the electromagnetic fields by considering stationary currents at every instant. This is called the quasi-static approximation. The approximation is valid provided that the variations in time are small and that the studied geometries are considerably smaller than the wavelength (Ref. 5).

The quasi-static approximation implies that the equation of continuity can be written as ∇ ⋅ J = 0 and that the time derivative of the electric displacement ∂D/∂t can be disregarded in Maxwell-Ampère’s law.

There are also effects of the motion of the geometries. Consider a geometry moving with velocity v relative to the reference system. The force per unit charge, F/q, is then given by the Lorentz force equation:

This means that to an observer traveling with the geometry, the force on a charged particle can be interpreted as caused by an electric field E' = E + v × B. In a conductive medium, the observer accordingly sees the current density

where Je is an externally generated current density.