Time-dependent generalizations of the Biot–Savart and Coulomb laws

Strictly, Coulomb’s law and the Biot–Savart law determine the electric and magnetic fields for static sources only. Time-dependent generalizations of these two laws, introduced by Jefimenko, are used here to explore the applicability of Coulomb and Biot–Savart outside the static domain. The fact that Biot–Savart holds for some classes of time-dependent currents has led to much confusion in the literature, which this paper endeavors to dispel. To illustrate Jefimenko’s equations, the standard Liénard–Wiechert fields of a point charge are derived.