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Weber-Maxwell electrodynamics is a representation of classical electrodynamics expressed in terms of a generalized Coulomb law that can also be applied to moving and accelerated non-relativistic point charges.

Weber-Maxwell electrodynamics is based on exactly the same field equations as Maxwell's electrodynamics. In contrast to Maxwell's theory of electrodynamics, Weber-Maxwell electrodynamics does not define the Lorentz force with the Lorentz force law, but explains Lorentz force and magnetism by means of a hypothesis by Carl Friedrich Gauss.

Field of the electromagnetic force of an accelerated negative point charge from the perspective of a resting positive test charge in Weber-Maxwell or Maxwell electrodynamics.

Weber-Maxwell electrodynamics is largely equivalent to Maxwell's electrodynamics, as it uses exactly the same fields and only describes the effect of the electromagnetic fields on matter slightly differently. For small relative velocities and negligibly small accelerations, it is compatible with Weber electrodynamics. As a result, Weber-Maxwell electrodynamics is also compatible with André-Marie Ampère's original force law for small relative velocities. In contrast to Weber electrodynamics, Weber-Maxwell electrodynamics is also suitable for describing electromagnetic waves in a vacuum, providing practically identical predictions as Maxwell's electrodynamics.

Weber-Maxwell electrodynamics is not suitable for applications in which charged particles move at almost the speed of light. In such cases, it is necessary to use relativistic mechanics.