Electromagnetic Extension to Ramo's Theorem

Ramo's theorem, or the Ramo-Shockley theorem (RS) [1,2], describes the current induced on perfect conductors by the motion of nearby charges, and is a foundational result in vacuum electronics, discharge physics, and semiconductor devices. The classical theorem ignores relativistic and radiative effects and assumes that the fields are quasi-static. This paper demonstrates, for the first time, how RS is modified by electromagnetic and relativistic effects. Explicit, closed form analytic solutions of Maxwell's equations for the induced current distribution on conducting plates due to the motion of a line charge are presented. These solutions were verified by several methods, including particle-in-cell simulations. Novel features are accounted for that are absent in the classical RS: electromagnetic transients produced by the sudden acceleration of charge, the generation of an electromagnetic shock when a charge strikes a conductor, and the reflections of electromagnetic waves by the conductors. Applications of these new findings and further extensions will be presented.