Liénard-Wiechert equations

The Liénard-Wiechert equations describe how electromagnetic signals, like light or radio waves, are emitted from a moving charged particle—such as an electron—reaching an observer at a specific point in space and time. They account for the fact that changes in the particle’s velocity and position influence the observed fields, including how the signals are delayed and distorted due to the particle's motion. Essentially, these equations provide a precise way to determine the electric and magnetic fields produced by a moving charge at any point in space and time, considering the finite speed of light and the particle’s past trajectory.