Advances in Weber and Maxwell Electrodynamics

This text concerns the mathematical development of classical electrodynamics. It is shown that Maxwell’s electrodynamics has two implicit restrictions. By removing these restrictions, and adding two terms to the scalar potential function, Weber’s electrodynamics is obtained. It is further shown that Weber’s electrodynamics can be formulated using scalar and vector potential functions. A set of differential equations, similar to the four well known Maxwell differential equations, is developed for Weber’s electrodynamics. Time retardation is introduced into Weber’s electrodynamics and wave equations are derived that reduce to the Maxwell wave equations when the Maxwell implicit restrictions are applied. Derivations are presented in detail so that students may follow the mathematical development.This text is suitable for advanced undergraduates in physics, engineering, or mathematics that have completed a 1-year course sequence in undergraduate classical electrodynamics. Advanced mathematics beyond undergraduate vector calculus (engineering mathematics) is not required.