Stationary dielectrics and stationary magnetic materials

Abstract

So far in this book we have always assumed that the relative permittivity ε _r and the relative permeability µ _r were both equal to unity everywhere. We shall now go on to discuss the form Maxwell’s equations take at points inside stationary dielectrics and stationary magnetic materials. Dielectrics are polarized in the presence of an applied electric field and make contributions to the total electric field. Magnetic materials are magnetized in the presence of an applied magnetic field and make contributions to the total magnetic field. The development of Maxwell’s equations for field points inside dielectrics and magnetic materials from the Maxwell-Lorentz equations, namely equations (1.137), (1.138), (1.139) and (1.140) of Chapter 1 is covered comprehensively in the literature, for example Russakoff [1] and in the text books such as Robinson [2]. Consequently we shall confine our remarks to a few headlines and comments to indicate how Maxwell’s equations for field points inside dielectrics and magnetic materials can be interpreted in a way consistent with the approach we developed in Chapter 4. We shall not go through the full processes of averaging the microscopic variables using equation (1.147) of Chapter 1 to determine the corresponding macroscopic variables, but we shall just use simplistic arguments to illustrate the plausibility of the final results. We shall find it convenient to introduce two new macroscopic variables to describe the dielectric and magnetic properties of materials, namely the polarization vector P and the magnetization vector M. We shall illustrate how a knowledge of the vectors P and M is sufficient for us to determine the contributions of polarized dielectrics and magnetized bodies to the macroscopic electric and magnetic fields. We shall also develop the form Maxwell’s equations take in a material medium that has both dielectric and magnetic properties.