Review of Maxwell's Equations

This chapter provides an overview of Maxwell's equations. Maxwell's equations govern the interaction of charged matter, and the behavior of electromagnetic fields. They provide a fundamental understanding of a wide range of phenomena including the magnetic interactions. Maxwell's equations are presented in both differential and integral form, along with constitutive relations and boundary conditions. Further, scalar and vector potentials are introduced and it is highlighted that they provide an alternate tractable formulation of electromagnetic field theory. The chapter also deals with the explanation of quasi-static field theory. Here, there is a partial uncoupling of the field equations that simplifies their solution. Quasi-static field theory applies at low frequencies (long wavelengths) when the dimensions of the region of interest are small relative to the wavelength of the electromagnetic field that permeates it. Finally, static field theory in which all time dependence is negligible is studied. It is found that the magnetic and electric fields uncouple into separate magnetostatic and electrostatic field equations. Permanent magnet and electromechanical devices are analyzed using magnetostatic and quasistatic field theory, respectively.