MAXWELL'S EQUATIONS, CONSTITUTIVE RELATIONS, WAVE EQUATION, AND POLARIZATION

This chapter provides the details of Maxwell's equations, constitutive relations, wave equation, and polarization. The compact form of Maxwell's equations in vector notation was originally given by Oliver Heaviside. Maxwell's equations have had a profound impact on society through their role in paving the way for many major technological inventions. Ferromagnetic, antiferromagnetic and super‐paramagnetic materials exhibit strong magnetic moments even in the absence of an applied electromagnetic (EM) field. The analysis of EM problems can often be simplified by separating or suppressing the time variation of the fields and sources using the Fourier transform as is commonly done in the analysis of electric circuits. The chapter discusses Kramers‐Kronig relationship, vector and scalar wave equations, and describes the separable solutions of the source‐free wave equation in rectangular coordinates and for isotropic homogeneous media. It provides separable solutions of the source‐free wave equation in cylindrical and spherical coordinates and for isotropic homogeneous media.