MIT OpenCourseWare http://ocw.mit.edu Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207. Please use the following citation format: Haus, Hermann A., and James R. Melcher, Electromagnetic Fields and Energy. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed [Date]). License: Creative Commons Attribution-NonCommercial-Share Alike. Also available from Prentice-Hall: Englewood Cliffs, NJ, 1989. ISBN: 9780132490207. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms15 OVERVIEW OF ELECTROMAGNETIC FIELDS 15.0 INTRODUCTION In developing the study of electromagnetic fields, we have followed the course sum-marized 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 exam-ples. 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) mag-netic 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 “Amp`erian” 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 12 Overview of Electromagnetic Fields Chapter 15 “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 macro-scopic media, provide yet another overview of electromagnetic systems. This is the theme of Sec. 15.4, which summarizes the reasons why macroscopic forces can usu-ally be classified as being either EQS or MQS. 15.1 SOURCE AND MATERIAL CONFIGURATIONS We can use any one of a number of configurations to review physical phenomena outlined in Fig. 1.0.1. The sections, examples, and problems associated with a given physical situation are referenced in the tables used to trace the evolution of a given configuration. Incremental Dipoles. In homogeneous media, dipole fields are simple solu-tions to Laplace’s equation or the wave equation in two or three dimensions and have been used to represent the range of situations summarized in Table 15.1.1. As introduced in Chap. 4, the dipole represented closely spaced equal and opposite electric charges. Perhaps these charges were produced on a pair of closely spaced conducting objects, as shown in Fig. 3.3.1a. In Chap. 6, the electric dipole was used to represent polarization, and a distinction was made between unpaired and paired (polarization) charges. In representing conduction phenomena in Chap. 7, the dipole represented a closely spaced pair of current sources. Rather than b eing a source in Gauss’ law, the dipole was a source in the law of charge conservation. In magnetoquasistatics, there were two types of dipoles. First was the small current loop, where the dipole moment was the product of the area, a, and the circulating current, i. The dipole fields were
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