Introduction to Electromagnetic Engineering

Roger E. Harrington

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486432410
• eBook ISBN: 9780486151953
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

This study of electromagnetic theory introduces students to a broad range of quantities and concepts, imparting the necessary vector analysis and associated mathematics and reinforcing its teachings with several elementary field problems. Based on circuit theory rather than on the classical force-relationship approach, the text uses the theory of electric circuits to provide a system of experiments already familiar to the electrical engineer; a series of field concepts are then introduced as a logical extension of circuit theory. Virtually unobtainable elsewhere, this text was written by a prominent professor whose recognition includes the prestigious IEEE Electromagnetics Award. It is appropriate for advanced undergraduate and graduate students with a background in calculus and circuit theory. 176 Figures. 9 Tables.

CHAPTER 1

BASIC CONCEPTS

1-1. Units and Dimensions.

The measurement of a quantity involves a unit and a number. The unit is a reference amount of the quantity, and the number expresses the ratio of the magnitude of that quantity to the magnitude of the unit. When the unit of a quantity is assigned an arbitrary value, that unit is called a fundamental unit and the quantity a fundamental quantity. When the unit of a quantity is defined in terms of other units, that unit is called a secondary unit and the quantity a secondary quantity.

In mechanics length, mass, and time are usually chosen as fundamental quantities. In the mks (meter-kilogram-second) system the meter is the unit of length, the kilogram is the unit of mass, and the second is the unit of time. To describe electrical phenomena, it is convenient to consider an additional quantity to be fundamental. The quantity taken is usually electric charge. In the mksc (meter-kilogram-second-coulomb) system the coulomb is the unit of charge, the other fundamental units being those of the mks system. Throughout this book, we shall use the mksc system of units. It is especially convenient because the units of electrical quantities in this system are identical with those used in engineering practice.

The equations of physics express the relationships among numbers associated with quantities. These equations are valid for any choice of units for the fundamental quantities. If the fundamental units are changed, the secondary units change in accordance with their defining equations. A dimensional equation is an equation which expresses the manner in which the unit of a quantity changes as the fundamental units are changed. The symbols L, M, T, and Q denote ratios between possible new units of length, mass, time, and charge, and their respective units in the mksc system. Such ratios have been given the name dimensions. The terminology “mass has the dimension M,” symbolically written [mass] = M, means that the unit of mass can be chosen independently. The quantities length, mass, time, and charge in the mksc system are said to have fundamental dimensions because their units are arbitrary. All other quantities are said to have secondary dimensions because their units depend upon the fundamental units. For example, the dimensional equation for voltage is [voltage] = ML²/T²Q. This equation specifies the change in the unit of voltage which must be made when the fundamental units are changed if the same system of equations is to be used. For example, if the unit of mass is doubled, the unit of voltage must be doubled; if the unit of time is doubled, the unit of voltage must be quartered. The dimensions of a secondary quantity can be determined from any equation relating this secondary quantity to quantities of known dimensions.

Because equations are written so as to be valid for any choice of fundamental units, they must “ check dimensionally.” This means that quantities equal to one another must have the same dimensions and that quantities added together in the same equation must have the same dimensions. The argument of any function expressible as a power series must be dimensionless if successive terms of the series are to have the same dimensions. Examination of an equation to verify that these conditions are met is called a dimensional check. We can be sure that an equation that fails to check dimensionally is not generally valid, but a successful check is no assurance that an equation is correct.

A table of quantities considered in this book, their symbolic representation, their units, and their dimensions, is given in Appendix A.

1-2. Linearity and Superposition.

Suppose two quantities, f and g, are interrelated such that for each “stimulus” g there corresponds a “response” f. Let f_i be the response to the specific stimulus g_i. If the application of stimulus g_i + g_j produces the response f_i + f_j, i and j arbitrary, then the system is linear and the principle of superposition applies. In other words, a system is linear if the total response is the sum of the partial responses.

The linearity of a system is reflected in the linearity of the equations representing it. Consider the equation

where

is an operator.

may be as simple as constant times f, or it may involve integration, differentiation, powers, and roots of functions of f. Basically, the above equation states merely that f and g are interrelated. If

then

is a linear operator, the preceding equation is a linear equation, and the principle of superposition applies. Applying this test to possible operators, we can construct a list of common linear operations. For example, successive differentiation of f and successive integration of f are linear operations.

1-3. Circuit Quantities.

In the theory of electric circuits we are usually interested in voltage and current, occasionally in electric charge and magnetic flux. The basic concepts of these four quantities are summarized in this section.

Electric charge is the quantity by which “amount” of electricity is measured. T...

Table of contents

• Title Page
• Copyright Page
• PREFACE
• Table of Contents
• CHAPTER 1 - BASIC CONCEPTS
• CHAPTER 2 - CHARGE DENSITY AND CURRENT DENSITY
• CHAPTER 3 - ELECTRIC INTENSITY AND MAGNETIC FLUX DENSITY
• CHAPTER 4 - ELECTRIC FLUX DENSITY AND MAGNETIC INTENSITY
• CHAPTER 5 - THE FIELD OF STATIC CHARGES
• CHAPTER 6 - THE FIELD OF STEADY CURRENTS
• CHAPTER 7 - SOME FIELD CONCEPTS
• CHAPTER 8 - THE BOUNDARY-VALUE PROBLEM
• CHAPTER 9 - CIRCUIT ELEMENTS
• CHAPTER 10 - THE ELECTROMAGNETIC FIELD
• APPENDIX A - UNITS AND DIMENSIONS
• APPENDIX B - SUMMARY OF VECTOR ANALYSIS
• APPENDIX C - CONSTITUTIVE PARAMETERS OF MATTER
• BIBLIOGRAPHY
• INDEX - Numbers in boldface type refer to problems
• A CATALOG OF SELECTED DOVER BOOKS IN SCIENCE AND MATHEMATICS
• DOVER BOOKS ON ENGINEERING