Mathematical Formulation Of Electromagnetic Radiation Using Vector Potential Expressions Derived From Maxwell's Equations

The electric vector potential 𝐹 plays a significant role in electromagnetic field analysis when magnetic current sources are introduced through the equivalence principle. Although magnetic currents do not exist physically, their mathematical representation greatly simplifies the analysis of radiation, scattering, and aperture problems in electromagnetics and antenna theory. This work presents a detailed derivation of the electric vector potential 𝐹 directly from Maxwell's equations by incorporating magnetic current density into the generalized field equations. Starting from the curl relations of Maxwell's equations, the electric field is expressed in terms of the curl of the electric vector potential, ensuring automatic satisfaction of Gauss's law in source-free regions. By applying appropriate vector identities and imposing a suitable gauge condition, a vector wave equation governing 𝐹 is obtained. The solution of this wave equation leads to the retarded electric vector potential, which explicitly relates the magnetic current distribution to the radiated electromagnetic fields. The derived formulation provides physical insight into the radiation mechanism of equivalent magnetic current sources and establishes a dual framework to the conventional magnetic vector potential approach used for electric currents. The electric vector potential formulation is particularly advantageous for analyzing slot antennas, aperture radiation, electromagnetic scattering, and computational electromagnetics methods such as the Method of Moments and Finite Element Method. Overall, this derivation highlights the mathematical elegance and practical relevance of the electric vector potential in advanced electromagnetic radiation analysis.