Equações de Maxwell – as leis fundamentais do magnetismo

Abstract

The work presents a theoretical construction of Maxwell's equations, which constitute the fundamental equations for the description of electromagnetic phenomena. The study begins with electrostatics, in which the electric field is defined from Coulomb's law, followed by the formulation of Gauss's law in both differential and integral forms. From the conservative nature of the electric field, the scalar potential and Poisson's equation are introduced. Next, magnetostatics is addressed, establishing the magnetic scalar potential, the Biot-Savart law, Gauss's law for magnetism, and Ampère's law, culminating in the definition of the vector potential. The work then advances to the context of electrodynamics, in which electromotive force, Faraday's law, and the displacement current introduced by Maxwell are discussed — a development that generalizes Ampère's law for non-stationary regimes and allows the complete formulation of Electromagnetism. Subsequently, the behaviors of fields in conductive materials, dielectrics, and magnetic materials are analyzed, with emphasis on electric polarization, the electric displacement vector, magnetization, and boundary conditions. Finally, after establishing Maxwell's equations in vacuum and in material media, the work converges to the electromagnetic wave equation, a result that unifies Optics and Electromagnetism.