1.8
Summary
Electromagnetic fields, whether they be inside a transistor, on the surfaces of an antenna or in the human nervous system, are defined in terms of the forces they produce. In every example involving electromagnetic fields, charges are moving somewhere in response to electromagnetic fields. Hence, our starting point in this introductory chapter is the Lorentz force on an elementary charge, (1.1.1). Represented by this law is the effect of the field on the charge and current (charge in motion).
The subsequent sections are concerned with the laws that predict how the field sources, the charge, and current densities introduced in Sec. 1.2, in turn give rise to the electric and magnetic fields. Our presentation is aimed at putting these laws to work. Hence, the empirical origins of these laws that would be evident from a historical presentation might not be fully appreciated. Elegant as they appear, Maxwell's equations are no more than a summary of experimental results. Each of our case studies is a potential test of the basic laws.
In the interest of being able to communicate our subject, each of the basic laws is given a name. In the interest of learning our subject, each of these laws should now be memorized. A summary is given in Table 1.8.1. By means of the examples and demonstrations, each of these laws should be associated with one or more physical consequences.
From the Lorentz force law and Maxwell's integral laws, the units of variables and constants are established. For the SI units used here, these are summarized in Table 1.8.2. Almost every practical result involves the free space permittivity
o and/or the free space permeability
o. Although these are summarized in Table 1.8.2, confidence also comes from having these natural constants memorized.
A common unit for measuring the magnetic flux density is the Gauss, so the conversion to the SI unit of Tesla is also given with the abbreviations.
A goal in this chapter has also been the use of examples to establish the mathematical significance of volume, surface, and contour integrations. At the same time, important singular source distributions have been defined and their associated fields derived. We will make extensive use of point, line, and surface sources and the associated fields.
In dealing with surface sources, a continuity condition should be associated with each of the integral laws. These are summarized in Table 1.8.3.
The continuity conditions should always be associated with the integral laws from which they originate. As terms are added to the integral laws to account for macroscopic media, there will be corresponding changes in the continuity conditions.
TABLE 1.8.1 SUMMARY OF MAXWELL'S INTEGRAL LAWS IN FREE SPACE
| Name | Integral Law | Eq. Number |
|---|---|---|
| Gauss' Law |  | 1.3.1 |
| Ampère's Law |  | 1.4.1 |
| Faraday's Law |  | 1.6.1 |
| Magnetic Flux Continuity |  | 1.7.1 |
| Charge Conservation, |  | 1.5.2 |
TABLE 1.8.2 DEFINITIONS AND UNITS OF FIELD VARIABLES AND CONSTANTS
(basic unit of mass, kg, is replaced by V-C-s2/m2)
| Variables OR Parameter | Nomenclature | Basic Units | Derived Units |
|---|---|---|---|
| Electric Field Intensity | E | V/m | V/m |
| Electric Displacement Flux Density | oE | C/m2 | C/m2 |
| Charge Density |  | C/m3 | C/m3 |
| Surface Charge Density |  s | C/m2 | C/m2 |
| Magnetic Field Intensity | H | C/(ms) | A/m |
| Magnetic Flux Density | oH | Vs/m2 | T |
| Current Density | J | C/(m2s) | A/m2 |
| Surface Current Density | K | C/(ms) | A/m |
| Free Space Permittivity | o = 8.854 x 10-12 | C/(Vm) | F/m |
| Free Space Permeability | o = 4 x 10-7 | Vs2/(Cm) | H/m |
Unit Abbreviations
| Ampère | A | Kilogram | kg | Volt | V |
| Coulomb | C | Meter | m | ||
| Faraday | F | Second | s | ||
| Henry | H | Tesla | T (104 Gauss) |
TABLE 1.8.3 SUMMARY OF CONTINUITY CONDITIONS IN FREE SPACE
| Gauss' Law |  | 1.3.17 |
| Ampère's Law |  | 1.4.16 |
| Faraday's Law |  | 1.6.14 |
| Magnetic Flux Continuity |  | 1.7.6 |
| Charge Conservation |  | 1.5.12 |