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.

中文翻译：

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Ramo-Shockley 定理的相对论和电磁修正

经典的 Ramo-Shockley (RS) 定理给出了由附近电荷的运动在完美导体上感应出的电流，假设这些电荷在静电场中是非相对论运动。本文通过一些简单的例子说明了相对论和电磁效应如何修改 RS。具体来说，我们提出了麦克斯韦方程的显式闭合形式解析解，用于完美导电板上的感应电流分布，这是由于线电荷的运动平行和垂直于板。结果已通过多种方法验证，包括细胞内粒子模拟。它们与用于推导 RS 的经典静电理论进行了比较。提供了对 RS 的局限性和有效性的新见解。