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CHAPTER1 Vector Analysis 1

1.1 Scalars and Vectors 1

1.2 Vector Algebra 2

1.3 The Rectangular Coordinate System 4

1.4 Vector Components and Unit Vectors 5

1.5 The Vector Field 8

1.6 The Dot Product 9

1.7 The Cross Product 12

1.8 Other Coordinate Systems：Circular Cylindrical Coordinates 14

1.9 The Spherical Coordinate System 19

References 22

CHAPTER1 Problems 23

CHAPTER2 Coulomb’s Law and Electric Field Intensity 26

2.1 The Experimental Law of Coulomb 27

2.2 Electric Field Intensity 30

2.3 Field Due to a Continuous Volume Charge Distribution 34

2.4 Field of a Line Charge 37

2.5 Field of a Sheet of Charge 43

2.6 Streamlines and Sketches of Fields 45

References 48

CHAPTER2 Problems 48

CHAPTER3 Electric Flux Density，Gauss’s Law，and Divergence 51

3.1 Electric Flux Density 51

3.2 Gauss’s Law 55

3.3 Application of Gauss’s Law：Some Symmetrical Charge Distributions 59

3.4 Application of Gauss’s Law：Differential Volume Element 64

3.5 Divergence 67

3.6 Maxwell’s First Equation（Electrostatics） 70

3.7 The Vector Operator ？ and the Divergence Theorem 72

References 75

CHAPTER3 Problems 76

CHAPTER4 Energy and Potential 80

4.1 Energy Expended in Moving a Point Charge in an Electric Field 81

4.2 The Line Integral 82

4.3 Definition of Potential Difference and Potential 87

4.4 The Potential Field of a Point Charge 89

4.5 The Potential Field of a System of Charges：Conservative Property 91

4.6 Potential Gradient 95

4.7 The Dipole 101

4.8 Energy Density in the Electrostatic Field 106

References 110

CHAPTER4 Problems 110

CHAPTER5 Current and Conductors 114

5.1 Current and Current Density 114

5.2 Continuity of Current 116

5.3 Metallic Conductors 118

5.4 Conductor Properties and Boundary Conditions 123

5.5 The Method of Images 128

5.6 Semiconductors 130

References 132

CHAPTER5 Problems 132

CHAPTER6 Dielectrics and Capacitance 136

6.1 The Nature of Dielectric Materials 137

6.2 Boundary Conditions for Perfect Dielectric Materials 143

6.3 Capacitance 149

6.4 Several Capacitance Examples 152

6.5 Capacitance of a Two-Wire Line 155

6.6 Using Field Sketches to Estimate Capacitance in Two-Dimensional Problems 160

6.7 Current Analogies 165

References 167

CHAPTER6 Problems 167

CHAPTER7 Poisson’s and Laplace’s Equations 172

7.1 Derivation of Poisson’s and Laplace’s Equations 173

7.2 Uniqueness Theorem 175

7.3 Examples of the Solution of Laplace’s Equation 177

7.4 Example of the Solution of Poisson’s Equation 184

7.5 Product Solution of Laplace’s Equation 188

7.6 Solving Laplace’s Equation Through Numerical Iteration 196

References 202

CHAPTER7 Problems 203

CHAPTER8 The Steady Magnetic Field 210

8.1 Biot-Savart Law 210

8.2 Ampère’s Circuital Law 218

8.3 Curl 225

8.4 Stokes’Theorem 232

8.5 Magnetic Flux and Magnetic Flux Density 237

8.6 The Scalar and Vector Magnetic Potentials 240

8.7 Derivation of the Steady-Magnetic-Field Laws 247

References 253

CHAPTER8 Problems 253

CHAPTER9 Magnetic Forces，Materials，and Inductance 259

9.1 Force on a Moving Charge 260

9.2 Force on a Differential Current Element 261

9.3 Force Between Differential Current Elements 265

9.4 Force and Torque on a Closed Circuit 267

9.5 The Nature of Magnetic Materials 273

9.6 Magnetization and Permeability 276

9.7 Magnetic Boundary Conditions 281

9.8 The Magnetic Circuit 284

9.9 Potential Energy and Forces on Magnetic Materials 290

9.10 Inductance and Mutual Inductance 292

References 299

CHAPTER9 Problems 299

CHAPTER10 Time-Varying Fields and Maxwell’s Equations 306

10.1 Faraday’s Law 306

10.2 Displacement Current 313

10.3 Maxwell’s Equations in Point Form 317

10.4 Maxwell’s Equations in Integral Form 319

10.5 The Retarded Potentials 321

References 325

CHAPTER10 Problems 325

CHAPTER12 The Uniform Plane Wave 332

12.1 Wave Propagation in Free Space 332

12.2 Wave Propagation in Dielectrics 340

12.3 Poynting’s Theorem and Wave Power 349

12.4 Propagation in Good Conductors：Skin Effect 352

12.5 Wave Polarization 359

References 366

CHAPTER12 Problems 366

CHAPTER13 Plane Wave Reflection and Dispersion 370

13.1 Reflection of Uniform Plane Waves at Normal Incidence 370

13.2 Standing Wave Ratio 377

13.3 Wave Reflection from Multiple Interfaces 381

13.4 Plane Wave Propagation in General Directions 389

13.5 Plane Wave Reflection at Oblique Incidence Angles 392

13.6 Total Reflection and Total Transmission of Obliquely Incident Waves 398

13.7 Wave Propagation in Dispersive Media 401

13.8 Pulse Broadening in Dispersive Media 407

References 411

CHAPTER13 Problems 412

CHAPTER14 Guided Waves and Radiation 416

14.1 Transmission Line Fields and Primary Constants 417

14.2 Basic Waveguide Operation 426

14.3 Plane Wave Analysis of the Parallel-Plate Waveguide 430

14.4 Parallel-Plate Guide Analysis Using the Wave Equation 439

14.5 Rectangular Waveguides 442

14.6 Planar Dielectric Waveguides 447

14.7 Optical Fiber 453

14.8 Basic Antenna Principles 463

References 473

CHAPTER14 Problems 473

Appendix A Vector Analysis 478

A.1 General Curvilinear Coordinates 478

A.2 Divergence，Gradient，and Curl in General Curvilinear Coordinates 479

A.3 Vector Identities 481

Appendix B Units 482

Appendix C Material Constants 487

Appendix D Origins of the Complex Permittivity 490

Appendix E Answers to Odd-Numbered Problems 497