## 15.0Introduction

In developing the study of electromagnetic fields, we have followed the course summarized in Fig. 1.0.1. Our quest has been to make the laws of electricity and magnetism, summarized by Maxwell's equations, a basis for understanding and innovation. These laws are both general and simple. But, as a consequence, they are mastered only after experience has been gained through many specific examples. The case studies developed in this text have been aimed at providing this experience. This chapter reviews the examples and intends to foster a synthesis of concepts and applications.

At each stage, simple configurations have been used to illustrate how fields relate to their sources, whether the latter are imposed or induced in materials. Some of these configurations are identified in Section 15.1, where they are used to outline a comparative study of electroquasistatic, magnetoquasistatic, and electrodynamic fields. A review of much of the outline (Fig. 1.0.1) can be made by selecting a particular class of configurations, such as cylinders and spheres, and using it to exemplify the material in a sequence of case studies.

The relationship between fields and their sources is the theme in Section 15.2. Again, following the outline in Fig. 1.0.1, electric field sources are unpaired charges and polarization charges, while magnetic field sources are current and (paired) magnetic charges. Beginning with electroquasistatics, followed by magnetoquasistatics and finally by electrodynamics, our outline first focused on physical situations where the sources were constrained and then were induced by the presence of media. In this text, magnetization has been represented by magnetic charge. An alternative commonly used formulation, in which magnetization is represented by "Ampèrian" currents, is discussed in Sec. 15.2.

As a starting point in the discussions of EQS, MQS, and electrodynamic fields, we have used idealized models for media. The limits in which materials behave as "perfect conductors" and "perfect insulators" and in which they can be said to have "infinite permittivity or permeability" provide yet another way to form an overview of the material. Such an approach is taken at the end of Sec. 15.2.

Useful as these idealizations are, their physical significance can be appreciated only by considering the relativity of perfection. Although we have introduced the effects of materials by making them ideal, we have then looked more closely and seen that "perfection" is a relative concept. If the fields associated with idealized models are said to be "zero order," the second part of Sec. 15.2 raises the level of maturity reflected in the review by considering the "first order" fields.

What is meant by a "perfect conductor" in EQS and MQS systems is a part of Sec. 15.2 that naturally leads to a review in Sec. 15.3 of how characteristic times can be used to understand electromagnetic field interactions with media. Now that we can see EQS and MQS systems from the perspective of electrodynamics, Sec. 15.3 is aimed at an overview of how the spatial scale, time scale (frequency), and material properties determine the dominant processes. The objective in this section is not only to integrate material, but to add insight into the often iterative process by which a model is made to both encapsulate the essential physics and serve as a basis of engineering innovation.

Energy storage and dissipation, together with the associated forces on macroscopic media, provide yet another overview of electromagnetic systems. This is the theme of Sec. 15.4, which summarizes the reasons why macroscopic forces can usually be classified as being either EQS or MQS.