文字版 2013 Primary Theory of Electromagnetics by Hyo J. Eom

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文字版 Primary Theory of Electromagnetics by Hyo J. Eom
2013
ISBN-10: 9400771428 |



This is a textbook on electromagnetics for undergraduate students in electrical engineering, information, and communications. The book contents are very compact and brief compared to other commonly known electromagnetic books for undergraduate students and emphasizes mathematical aspects of basic electromagnetic theory. The book presents basic electromagnetic theory starting from static fields to time-varying fields. Topics are divided into static electric fields, static magnetic fields, time-varying fields, and electromagnetic waves. The goal of this textbook is to lead students away from memorization, but towards a deeper understanding of formulas that are used in electromagnetic theory. Many formulas commonly used for electromagnetic analysis are mathematically derived from a few empirical laws. Physical interpretations of formulas are de-emphasized. Each important formula is framed to indicate its significance. Primary Theory of Electromagnetics shows a clear and rigorous account of formulas in a consistent manner, thus letting students understand how electromagnetic formulas are related to each other.

Contents
1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Vector Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Vector Addition and Scalar Multiplication . . . . . . . . . . . 1
1.1.2 Vector Multiplications . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Orthogonal Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Rectangular (Cartesian) Coordinates . . . . . . . . . . . . . . . 3
1.2.2 Cylindrical Coordinates . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Spherical Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Operator Del, Divergence Theorem, and Stokes’s Theorem . . . . 12
1.3.1 Gradient, Divergence, Curl, and Laplacian . . . . . . . . . . . 12
1.3.2 Divergence Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.3 Stokes’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4 Problems for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1 Fundamentals of Electric Fields . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.1 Coulomb’s Law and Electric Fields. . . . . . . . . . . . . . . . 21
2.1.2 Electric Scalar Potential. . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.3 Gauss’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Dielectrics and Boundary Conditions . . . . . . . . . . . . . . . . . . . . 32
2.2.1 Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.3 Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4 Electrostatic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5 Poisson’s Equation for Electric Fields . . . . . . . . . . . . . . . . . . . 46
2.6 Image Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.7 Problems for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Magnetostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1 Conduction Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1.1 Steady Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1.2 Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1.3 Joule Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2 Fundamentals of Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . 65
3.2.1 Ampère’s Law of Force and Magnetic Flux Density . . . . 65
3.2.2 Magnetic Vector Potential . . . . . . . . . . . . . . . . . . . . . . 69
3.2.3 Ampère’s Circuital Law. . . . . . . . . . . . . . . . . . . . . . . . 74
3.3 Magnetic Forces and Torques . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4 Magnetic Materials and Boundary Conditions . . . . . . . . . . . . . . 82
3.4.1 Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.4.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.5 Poisson’s Equation for Magnetic Fields . . . . . . . . . . . . . . . . . . 88
3.6 Problems for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4 Faraday’s Law of Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.1 Faraday’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3 Magnetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4 Problems for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.1 Continuity Equation and Ampère’s Law. . . . . . . . . . . . . . . . . . 113
5.1.1 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.1.2 Ampère’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.2.1 Time-Varying Forms . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.2.3 Static Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.3 Poynting’s Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.4 Phasors for Time-Harmonic Fields. . . . . . . . . . . . . . . . . . . . . . 122
5.4.1 Maxwell’s Equations in Phasor Form . . . . . . . . . . . . . . 122
5.4.2 Poynting’s Theorem in Phasor Form . . . . . . . . . . . . . . . 123
5.5 Scalar and Vector Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.6 Problems for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6 Uniform Plane Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.1 Waves in Lossless Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.2 Waves in Conductive Media . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.3 Polarization of Plane Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.4 Reflection and Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.4.1 Perpendicular Polarization . . . . . . . . . . . . . . . . . . . . . . 139
6.4.2 Parallel Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.5 Problems for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7 Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.1 Fundamentals of Transmission Lines: Field Approach . . . . . . . . 147
7.2 Fundamentals of Transmission Lines: Circuit Approach . . . . . . . 150
7.3 Terminated Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . 154
7.4 Smith Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.5 Transient Waves on Transmission Lines. . . . . . . . . . . . . . . . . . 160
7.6 Problems for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8 Waveguides and Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.1 Fundamentals of Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.2 Rectangular Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
8.2.1 TM Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
8.2.2 TE Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
8.3 Fundamentals of Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.3.1 Free-Space Solution . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.3.2 Far Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
8.4 Wire Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
8.4.1 Hertzian Dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
8.4.2 Circular Loop Antennas . . . . . . . . . . . . . . . . . . . . . . . . 183
8.5 Problems for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Appendix A: Symbols, Notations, and Acronyms . . . . . . . . . . . . . . . . 189
Appendix B: Vector Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Appendix C: Gradients, Divergences, Curls, and Laplacians . . . . . . . . 195
Appendix D: Dirac Delta Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Appendix E: Answers to Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

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