Fundamentals of Engineering Electromagnetics

by Cheng, David K.

• ISBN13: 9780201566116
• ISBN10: 0201566117
• Edition: 1st
• Format: Paperback
• Copyright: 2019-11-08
• Publisher: Pearson

Summary

This book is designed for use as an undergraduate text on engineering electromagnetics. Electromagnetics is one of the most fundamental subjects in an electrical engineering curriculum. Knowledge of the laws governing electric and magnetic fields is essential to the understanding of the principle of operation of electric and magnetic instruments and machines, and mastery of the basic theory of electromagnetic waves is indispensible to explaining action-at-a-distance electromagnetic phenomena and systems.

Table of Contents

The Electromagnetic Model	2	(10)
Overview	2	(2)
The Electromagnetic Model	4	(4)
SI Units and Universal Constants	8	(4)
Summary	10	(2)
Vector Analysis	12	(60)
Overview	12	(2)
Vector Addition and Subtraction	14	(2)
Vector Multiplication	16	(5)
Scalar or Dot Product	16	(2)
Vector or Cross Product	18	(1)
Products of Three Vectors	19	(2)
Orthogonal Coordinate Systems	21	(18)
Cartesian Coordinates	22	(6)
Cylindrical Coordinates	28	(5)
Spherical Coordinates	33	(6)
Gradient of a Scalar Field	39	(4)
Divergence of a Vector Field	43	(5)
Divergence Theorem	48	(4)
Curl of a Vector Field	52	(7)
Stokes's Theorem	59	(3)
Two Null Identities	62	(2)
Identity I	62	(1)
Identity II	63	(1)
Field Classification and Helmholtz's Theorem	64	(8)
Summary	66	(1)
Problems	67	(5)
Static Electric Fields	72	(78)
Overview	72	(2)
Fundamental Postulates of Electrostatics in Free Space	74	(2)
Coulomb's Law	76	(9)
Electric Field due to a System of Discrete Charges	81	(1)
Electric Field due to a Continuous Distribution of Charge	81	(4)
Gauss's Law and Applications	85	(5)
Electric Potential	90	(7)
Electric Potential due to a Charge Distribution	92	(5)
Material Media in Static Electric Field	97	(8)
Conductors in Static Electric Field	98	(4)
Dielectrics in Static Electric Field	102	(3)
Electric Flux Density and Dielectric Constant	105	(6)
Dielectric Strength	108	(3)
Boundary Conditions for Electrostatic Fields	111	(5)
Capacitances and Capacitors	116	(4)
Electrostatic Energy and Forces	120	(8)
Electrostatic Energy in Terms of Field Quantities	123	(3)
Electrostatic Forces	126	(2)
Solution of Electrostatic Boundary-Value Problems	128	(22)
Poisson's and Laplace's Equations	129	(1)
Boundary-Value Problems in Cartesian Coordinates	130	(2)
Boundary-Value Problems in Cylindrical Coordinates	132	(2)
Boundary-Value Problems in Spherical Coordinates	134	(2)
Method of Images	136	(7)
Summary	143	(1)
Problems	143	(7)
Steady Electric Currents	150	(20)
Overview	150	(1)
Current Density and Ohm's Law	151	(6)
Equation of Continuity and Kirchhoff's Current Law	157	(2)
Power Dissipation and Joule's Law	159	(1)
Governing Equations for Steady Current Density	160	(2)
Resistance Calculations	162	(8)
Summary	166	(1)
Problems	167	(3)
Static Magnetic Fields	170	(58)
Overview	170	(2)
Fundamental Postulates of Magnetostatics in Free Space	172	(6)
Vector Magnetic Potential	178	(2)
The Biot-Savart Law and Applications	180	(6)
The Magnetic Dipole	186	(4)
Magnetization and Equivalent Current Densities	190	(4)
Magnetic Field Intensity and Relative Permeability	194	(2)
Behavior of Magnetic Materials	196	(3)
Boundary Conditions for Magnetostatic Fields	199	(2)
Inductances and Inductors	201	(9)
Magnetic Energy	210	(4)
Magnetic Energy in Terms of Field Quantities	211	(3)
Magnetic Forces and Torques	214	(14)
Forces and Torques on Current-Carrying Conductors	214	(5)
Direct-Current Motors	219	(1)
Forces and Torques in Terms of Stored Magnetic Energy	220	(3)
Summary	223	(1)
Problems	223	(5)
Time-Varying Fields and Maxwell's Equations	228	(44)
Overview	228	(2)
Faraday's Law of Electromagnetic Induction	230	(13)
A Stationary Circuit in a Time-Varying Magnetic Field	231	(1)
Transformers	232	(3)
A Moving Conductor in a Magnetic Field	235	(4)
A Moving Circuit in a Time-Varying Magnetic Field	239	(4)
Maxwell's Equations	243	(8)
Integral Form of Maxwell's Equations	245	(3)
Electromagnetic Boundary Conditions	248	(3)
Potential Functions	251	(4)
Solution of Wave Equations	253	(2)
Time-Harmonic Fields	255	(17)
The Use of Phasors---A Review	255	(4)
Time-Harmonic Electromagnetics	259	(4)
The Electromagnetic Spectrum	263	(4)
Summary	267	(1)
Problems	268	(4)
Plane Electromagnetic Waves	272	(64)
Overview	272	(1)
Plane Waves in Lossless Media	273	(14)
Doppler Effect	279	(2)
Transverse Electromagnetic Waves	281	(2)
Polarization of Plane Waves	283	(4)
Plane Waves in Lossy Media	287	(9)
Low-Loss Dielectrics	290	(1)
Good Conductors	291	(5)
Group Velocity	296	(2)
Flow of Electromagnetic Power and the Poynting Vector	298	(6)
Instantaneous and Average Power Densities	301	(3)
Normal Incidence of Plane Waves at Plane Boundaries	304	(9)
Normal Incidence on a Good Conductor	309	(4)
Oblique Incidence of Plane Waves at Plane Boundaries	313	(23)
Total Reflection	315	(4)
The Ionosphere	319	(2)
Perpendicular Polarization	321	(4)
Parallel Polarization	325	(2)
Brewster Angle of No Reflection	327	(3)
Summary	330	(1)
Problems	330	(6)
Transmission Lines	336	(50)
Overview	336	(2)
General Transmission-Line Equations	338	(3)
Transmission-Line Parameters	341	(6)
Microstrip Lines	346	(1)
Wave Characteristics on an Infinite Transmission Line	347	(6)
Attenuation Constant from Power Relations	351	(2)
Wave Characteristics on Finite Transmission Lines	353	(13)
Open-Circuited and Short-Circuited Lines	356	(1)
Characteristic Impedance and Propagation Constant from Input Measurements	357	(9)
Reflection Coefficient and Standing-Wave Ratio	366	(1)
The Smith Chart	366	(11)
Admittances on Smith Chart	374	(3)
Transmission-Line Impedance Matching	377	(9)
Summary	381	(1)
Problems	382	(4)
Waveguides and Cavity Resonators	386	(40)
Overview	386	(1)
General Wave Behaviors along Uniform Guiding Structures	387	(13)
Transverse Electromagnetic Waves	390	(1)
Transverse Magnetic Waves	391	(3)
Transverse Electric Waves	394	(6)
Rectangular Waveguides	400	(13)
TM Waves in Rectangular Waveguides	400	(4)
TE Waves in Rectangular Waveguides	404	(5)
Attenuation in Rectangular Waveguides	409	(4)
Other Waveguide Types	413	(1)
Cavity Resonators	414	(12)
Rectangular Cavity Resonators	415	(4)
Quality Factor of Cavity Resonators	419	(3)
Summary	422	(1)
Problems	423	(3)
Antennas and Antenna Arrays	426	(1)
Overview	426	(2)
The Elemental Electric Dipole	428	(2)
Antenna Patterns and Directivity	430	(6)
Thin Linear Antennas	436	(3)
The Half-Wave Dipole	439	(3)
Antenna Arrays	442	(1)
Two-Element Arrays	442	(4)
General Uniform Linear Arrays	446	(5)
Effective Area and Backscatter Cross Section	451	(1)
Effective Area	452	(2)
Backscatter Cross Section	454	(1)
Friis Transmission Formula and Radar Equation	455	(5)
Summary	460	(1)
Problems	460	(1)
APPENDIXES A Symbols and Units
A-1 Fundamental SI (Rationalized MKSA) Units	465
A-2 Derived Quantities	446	(22)
A-3 Multiples and Submultiples of Units	468	(1)
B Some Useful Material Constants
B-1 Constants of Free Space	469	(1)
B-2 Physical Constants of Electron and Proton	469	(1)
B-3 Relative Permittivities (Dielectric Constants)	470	(1)
B-4 Conductivities	470	(1)
B-5 Relative Permeabilities	471
Bibliography
Answers to Odd-Numbered Problems
Index

Excerpts

This book is designed for use as an undergraduate text on engineering electromagnetics. Electromagnetics is one of the most fundamental subjects in an electrical engineering curriculum. Knowledge of the laws governing electric and magnetic fields is essential to the understanding of the principle of operation of electric and magnetic instruments and machines, and mastery of the basic theory of electromagnetic waves is indispensable to explaining action-at-a-distance electromagnetic phenomena and systems. Because most electromagnetic variables are functions of three-dimensional space coordinates as well as of time, the subject matter is inherently more involved than electric circuit theory, and an adequate coverage normally requires a sequence of two semester-courses, or three courses in a quarter system. However, some electrical engineering curricula do not schedule that much time for electromagnetics. The purpose of this book is to meet the demand for a textbook that not only presents the fundamentals of electromagnetism in a concise and logical manner, but also includes important engineering application topics such as electric motors, transmission lines, waveguides, antennas, antenna arrays, and radar systems. I feel that one of the basic difficulties that students have in learning electromagenetics is their failure to grasp the concept of an electromagnetic model. The traditional inductive approach of starting with experimental laws and gradually synthesizing them into Maxwell's equations tends to be fragmented and incohesive; and the introduction of gradient, divergence e, and curl operations appears to be ad hoc and arbitrary. On the other hand, the extreme of starting with the entire set of Maxwell's equations, which are of considerable complexity, as fundamental postulates is likely to cause consternation and resistance in students at the outset. The question of the necessity and sufficiency of these general equations is not addressed, and the concept of the electromagnetic model is left vague. This book builds the electromagnetic model using an axiomatic approach in steps--first for static electric fields, then for static magnetic fields, and finally for time-varying fields leading to Maxwell's equations. The mathematical basis for each step is Helmholtz's theorem, which states that a vector field is determined to within an additive constant if both its divergence and its curl are specified everywhere. A physical justification of this theorem may be based on the fact that the divergence of a vector field is a measure of the strength of its flow source and the curl of the field is a measure of strength of its vortex source. When the strengths of both the flow source and the vortex source are specified, the vector field is determined. For the development of the electrostatic model in free space, it is only necessary to define a single vector (namely, the electric field intensity E) by specifying its divergence and its curl as postulates. All other relations in electrostatics for free space, including Coulomb's law and Gauss's law, can be derived from the two rather simple postulates. Relations in material media can be developed through the concept of equivalent charge distributions of polarized dielectrics. Similarly, for the magnetostatic model in free space it is necessary to define only a single magnetic flux density vector B by specifying its divergence and its curl as postulates; all other formulas can be derived from these two postulates. Relations in material media can be developed through the concept of equivalent current densities. Of course, the validity of the postulates lies in their ability to yield results that conform with experimental evidence. For time-varying fields, the electric and magnetic field intensities are coupled. The curl E postulate for the electrostatic model must be modified to