LiénardWiecher

The Liénard-Wiechert potentials are a set of equations in classical electromagnetism that describe the electromagnetic field generated by a moving point charge. Developed by Alfred-Marie Liénard and Emil Wiechert in the early 20th century, these potentials are fundamental for understanding how the motion of a charged particle influences the electromagnetic fields around it.

The potentials consist of two parts: the scalar potential and the vector potential. The scalar potential, denoted by V, is related to the electric field, while the vector potential, denoted by A, is related to the magnetic field. Unlike the simpler expressions for static charges, the Liénard-Wiechert potentials account for the finite speed of light. This means the fields at a given point and time depend on the position and velocity of the charge at an earlier, "retarded" time. This retardation is crucial because electromagnetic influences propagate at the speed of light, not instantaneously.

The Liénard-Wiechert potentials are derived from Maxwell's equations and are expressed in terms of the charge's position, velocity, and acceleration at the retarded time. These potentials can then be used to calculate the electric and magnetic fields at any point in space and time. The formulas are complex, involving derivatives of the charge's trajectory. Despite their complexity, they provide a complete description of the electromagnetic radiation emitted by a single accelerating point charge, a key result in classical electrodynamics.