In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay (retarded time) of the fields due to the finite speed of light and relativistic effects. Therefore they can be used for moving charges and currents. They are the particular solutions to Maxwell's equations for any arbitrary distribution of charges and currents. Equations Electric and magnetic fields Jefimenko's equations give the electric field E and magnetic field B produced by an arbitrary charge or current distribution, of charge density ρ and current density J: where r′ is a point in the charge distribution, r is a point in space, and is the retarded time. There are similar expressions for D and H. These equations are the time-dependent generalization of Coulomb's law and the Biot–Savart law to electrodynamics, which were originally true only for electrostatic and magnetostatic fields, and steady currents. Origin from retarded potentials Jefimenko's equations can be found from the retarded potentials φ and A: which are the solutions to Maxwell's equations in the potential formulation, then substituting in the definitions of the electromagnetic potentials themselves: and using the relation replaces the potentials φ and A by the fields E and B. Heaviside–Feynman formula The Heaviside–Feynman formula, also known as the Jefimenko–Feynman formula, can be seen as the point-like electric charge version of Jefimenko's equations. Actually, it can be (non trivially) deduced from them using Dirac functions, or using the Liénard-Wiechert potentials. It is mostly known from The Feynman Lectures on Physics, where it was used to introduce and describe the origin of electromagnetic radiation. The formula provides a natural generalization of the Coulomb's law for cases where the source charge is moving: Here, and are the electric and magnetic fields respectively, is the electric charge, is the vacuum permittivity (electric field constant) and is the speed of light. The vector is a unit vector pointing from the observer to the charge and is the distance between observer and charge. Since the electromagnetic field propagates at the speed of light, both these quantities are evaluated at the retarded time . The first term in the formula for represents the Coulomb's law for the static electric field. The second term is the time derivative of the first Coulombic term multiplied by which is the propagation time