Review of Least Action Principle in Electromagnetics: Part II: Derivation of Maxwell's Equations

Abstract

The 2nd paper in three-part study deals with a derivation of Maxwell's equations by using Hamilton's principle in electromagnetics and Noether's theorem for fields. Kinematical Maxwell's equations are derived from gauge symmetry, while two dynamical Maxwell's equations are derived by minimizing the functional of electromagnetic energy. The corresponding Lagrangian is given as difference between energy stored in the magnetic and electric field respectively.