Contents Preface to the Second Edition Preface to the First Edition Main Character, Parameters and The Expressions of Gradient, Divergence, Rotation Chapter 1 Vector Analysis 1 1.1 Scalar and Vector Fields 1 1.2 Operation of Vector 2 1.3 Flux and Divergence of Vector 7 1.4 Gauss’s Theorem 9 1.5 Vector Circulation and Rotation 10 1.6 Stockes’ Theorem 12 1.7 Gradient of a Scalar Field 14 Exercises 16 Chapter 2 Electrostatic Fields 19 2.1 Electrostatic Field’s Divergence Equation and Rotation Equation 19 2.2 Electric Potential and Electric Potential Gradient 29 2.3 Laplace’s equation and Poisson’s equation 32 2.4 Electric Dipole 33 2.5 Conductors in the Electrostatic Field 36 2.6 Dielectrics in the Electrostatic Field 37 2.7 The Boundary Conditions of the Electrostatic Field 42 2.8 Capacitance of Conductor System 46 2.9 Energy of Electrostatic Field and Electrostatic Force 51 2.10 5 Function and Its Related Properties 59 Exercises 61 Chapter 3 Constant Magnetic Field 65 3.1 The Curl Equation and Divergence Equation of Constant Magnetic Field 65 3.2 Magnetic Vector Potential A and Scalar Magnetic Potential 73 3.3 Magnetic Dipole 76 3.4 Medium in Constant Magnetic Field 78 3.5 Boundary Condition of Constant Magnetic Field 81 3.6 Self Inductance and Mutual Inductance 83 3.7 Magnetic Energy and Magnetic Force 89 Exercises 95 Chapter 4 Steady Electric Field 99 4.1 Current Density 99 4.2 Current Continuity Equation 101 4.3 Steady Electric Fields are Irrotational Fields 101 4.4 Loss of Energy in A Conducting Medium 104 4.5 Boundary Condition of the Steady Electric Field 105 4.6 Analogy of the Steady Electric Field and the Electrostatic Field 106 4.7 Capacitor Considering the Loss of Medium 110 Exercises 111 Chapter 5 Solutions of Electrostatic Field Boundary Value Problem 115 5.1 Electrostatic Field Boundary Value Problems 115 5.2 Uniqueness Theorem 116 5.3 Solving the One-Dimension Field by Integral 119 5.4 Using Separation of Variables to Solve Two-Dimension and Three-Dimension Laplace’s Equation 122 5.5 Image Method 146 5.6 Conformal Transformation, or Called Conformal Mapping 162 5.7 Finite-Difference Method—Numerical Computation Methods 170 5.8 Green’s Function and Green’s First, Second Identities 174 Exercises 176 Chapter 6 Alternating Electromagnetic Fields 181 6.1 Maxwell’s Equations 181 6.2 Law of Induction and Maxwell’s Second Equation 182 6.3 Ampere’s Circuital Law and Maxwell’s First Equation 184 6.4 Gauss’s Law and Maxwell’s Third Equation 188 6.5 Maxwell’s Fourth Equation 188 6.6 Maxwell’s Equations and Auxiliary Equations 190 6.7 Complex Format of Maxwell’s Equations 191 6.8 Boundary Conditions for Alternating Fields 194 6.9 Poynting’s Theorem and Poynting Vector 199 6.10 Potentials and Fields for Alternating Fields 207 6.11 On Lorentz Gauge 210 Exercises 212 Chapter 7 Propagation of Plane Wave in Infinite Medium 215 7.1 Wave Equations and Solutions 215 7.2 Plane Wave in Perfect Dielectric 219 7.3 Polarization of Electromagnetic Wave 227 7.4 Plane Wave in A Conducting Medium 232 7.5 Loss Tangent tan 5 and Medium Category 236 7.6 Plane Wave in A Good Dielectric 237 7.7 Plane Wave in A Good Conductor 239 7.8 Skin Effect 241 7.9 Surface Impedance Zs of A Good Conductor 243 7.10 Power Loss in A Conducting Medium 247 7.11 Dispersive Medium, Dispersive Distortion and Normal Dispersion, Anomalous Dispersion 248 7.12 Electromagnetic Waves in Ferrite Medium 252 Exercises 259 Chapter 8 Reflection and Refraction of Electromagnetic Waves 263 8.1 Plane Wave Normally Incident on the Surface of Perfect Conductor 263 8.2 Plane Wave Normally Incident on the Interface between Perfect Dielectrics 266 8.3 Plane Waves Obliquely Incident upon the Surface of Perfect Conductor 272 8.4 Plane Wave Obliquely Incident upon the Interface between Perfect Dielectrics 278 8.5 Reflection and Refraction of Waves on the Interface between Conductive Media 299 8.6 Plane Waves Normally Incident upon the Interfaces among Multi-layered Media 301 8.7 On the Multiformity of the Definitions of Fresnel Equations (R, T) 303 Exercises 308 Chapter 9 Two-Conductor Transmission Lines——Transverse Electromagnetic Wave Guiding System 313 9.1 Introduction 313 9.2 Properties of Wave Equations for TEM Waves 314 9.3 Parallel-Plate Transmission System 315 9.4 Two-Wire Transmission Lines 320 9.5 Coaxial Cable 338 9.6 Quasi-TEM Waves in Lossy Transmission Lines 342 Exercises 344 Chapter 10 TE and TM Modes Transmission System——Waveguide 347 10.1 Rectangular Waveguide 347 10.2 Circular Waveguide 368 10.3 Higher Modes in Coaxial Line 378 Exercises 380 Chapter 11 Electromagnetic Radiation 383 11.1 Lag Potential of Alternating Field 383 11.2 Electric Dipole 389 11.3 The Magnetic Dipole 396 11.4 Dipole Antenna and the Concept of Antenna Array 400 11.5 Duality Theory 408 Exercises 411 References 414 Appendix Common Formula 415 Answer 419
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