The Principle of Stationary Action is
extremely useful and plays a central role in deriving
physics equations. One of the demanding aspects of this
topic, difficult to explain, is how it connects with
electrodynamic equations. This paper presents a simple
derivation of classical electrodynamic equations based on
Stationary action principle in which the Lagrangian
formalism of a nonrelativistic mechanical system is
extended to obtain the relativistic Lagrangian equation
of a free particle in an external field. Lorentz invariance
and appropriate action integrals for the moving particles
in static fields, moving fields, and matter-field
interaction are constructed to obtain the equations of
motion of charged particles. Inhomogeneous Maxwell’s
equations of the electromagnetic field are obtained using
electromagnetic field tensor with six independent
components of electric field (E) and magnetic field (B) in
matrix form via the electromagnetic Lagrangian density.
It is also considered that the homogeneous part and the
Bianchi identity are derived by introducing a dual field
tensor. The continuity equation of motion is presented by
introducing electromagnetic 4-divergence.
Keywords : Electrodynamics, Maxwell’s Equations, Bianchi Identity, Lorentz Force And Least Action Principle.