# relativistic electrodynamics

## Relativistic electrodynamics

The study of the interaction between electrically charged particles and electromagnetic fields when the velocities involved are comparable to that of light.

A group of charged particles in motion can be represented by a distribution in charge and distribution in current. During the latter part of the eighteenth century and the early part of the nineteenth century, experiments by C. A. Coulomb, M. Faraday, A. M. Ampère, and others showed that electric and magnetic fields are produced by charge and current distributions. These fields, in turn, act on other charges and currents. The interaction between charges and currents on the one hand and electric and magnetic fields on the other is the topic of study of electrodynamics. This field of study was established as a quantitative and self-contained subject in 1864 when J. C. Maxwell formulated his equations for the electromagnetic field. Maxwell conjectured that a time-varying electric field is equivalent to an electric current in its effect of producing a magnetic field, and named it the displacement current. The inclusion of this displacement current enabled Maxwell to combine all the previously established laws of electromagnetism into a coherent whole in his equations. *See* Classical field theory, Displacement current, Maxwell's equations

With the inclusion of the displacement current, the Maxwell equations are relativistically covariant, meaning that they are valid for all velocities, even those approaching the velocity of light. However, the implications of the covariance of the equations were not fully appreciated until A. Einstein formulated the special theory of relativity in 1905. Relativistic electrodynamics was then rapidly developed into a powerful and precise field of physics. It describes and predicts all macroscopic electrodynamic phenomena to the minutest detail and with perfect accuracy, and now forms the foundation on which the entire electrical industry is based. However, its limitations soon became evident when attempts were made to apply it to atomic phenomena: Straightforwardly applied, relativistic electrodynamics failed to explain many of these phenomena, and its predictions frequently disagreed with experimental observations. For these microscopic phenomena, quantum electrodynamics (QED) was developed in the 1930s to replace classical relativistic electrodynamics. In 1967 quantum electrodynamics was further unified by S. Weinberg and A. Salam with the theory of weak interactions to form the electroweak theory. *See* Quantum electrodynamics, Relativity, Weak nuclear interactions

Electrodynamic problems generally fall into one of two categories:

1. Finding the electromagnetic field produced by prescribed charge and current distributions. For example, one may want to determine the electromagnetic field produced or radiated by a given oscillatory electric current in a transmitting antenna, or the field radiated by an accelerating electron.

2. Finding the effect of a predetermined electromagnetic field on the motion of charges and currents. This is the inverse problem corresponding to that of the receiving antenna or of the motion of charged particles in an accelerator.

All other electrodynamic problems are combinations or iterations of these two basic types. For instance, the scattering of light (electromagnetic radiation) by a charged particle is composed of, first, the incident light shaking the charge and, second, the subsequent emission of the scattered light by the shaken charge. *See* Scattering of electromagnetic radiation