A Relativistic and Electromagnetic Correction to the Ramo–Shockley Theorem

The classical Ramo–Shockley (RS) theorem gives the current induced on perfect conductors by the motion of nearby charges, assuming nonrelativistic motion of those charges in electrostatic fields. This article illustrates how relativistic and electromagnetic effects modify RS in some simple examples. Specifically, we present explicit, closed form analytic solutions of Maxwell’s equations for the induced current distribution on perfectly conducting plates due to the motion of a line charge moving parallel and perpendicular to the plates. The results have been verified by several methods, including particle-in-cell simulations. They are compared with the classical electrostatic theory used to derive RS. New insights into the limitation and validity of RS are provided. Electromagnetic shocks are explicitly calculated in closed form when the line charge strikes a parallel plate transmission line.