Interference of outgoing electromagnetic waves generated by two point-like sources

TL;DR

This paper calculates the energy-momentum of electromagnetic fields from two point charges, revealing how their wave interactions include both radiation and mutual forces, highlighting the interplay between emitted waves and source interactions.

Contribution

It introduces a detailed calculation of electromagnetic energy-momentum considering both radiation and mutual interactions for two point charges.

Findings

Energy-momentum includes Larmor radiation terms.

Interaction involves work done by Lorentz forces.

Wave motions lead to source interactions.

Abstract

An energy-momentum carried by electromagnetic field produced by two point-like charged particles is calculated. Integration region considered in the evaluation of the bound and emitted quantities produced by all points of world lines up to the end points at which particles' trajectories puncture an observation hyperplane $y^0=t$. Radiative part of the energy-momentum contains, apart from usual integrals of Larmor terms, also the sum of work done by Lorentz forces of point-like charges acting on one another. Therefore, the combination of wave motions (retarded Li\'enard-Wiechert solutions) leads to the interaction between the sources.