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Nathan Ida Engineering Electromagnetics With 821 Illustrations Springer Contents Preface Vector Algebra 1.1 Introduction 1.2 Scalars and Vectors 1.3 Products of Vectors 1.4 Definition of Fields 1.5 Systems of Coordinates 1.6 Position Vectors vu 1 1 2 13 25 29 47 Vector Calculus 2.1 Introduction 2.2 Integration of Scalar and Vector Functions 2.3 Differentiation of Scalar and Vector Functions 2.4 Conservative and Nonconservative Fields 2.5 Null Vector Identities and Classification of Vector Fields 57 57 58 73 106 108 Coulomb's Law and the Electric Field 3.1 Introduction 3.2 Charge and Charge Density 3.3 Coulomb's Law 3.4 The Electric Field Intensity 3.5 The Electric Flux Density: An Initial Definition 3.6 Applications 3.7 Experiments 121 121 122 126 132 155 158 163 Gauss's Law and the Electric Potential 4.1 Introduction 4.2 The Electrostatic Field: Postulates 4.3 Gauss's Law 4.4 The Electric Potential 173 173 173 178 190 xiii XIV CONTENTS 4.5 4.6 4.7 4.8 4.9 4.10 Materials in the Electric Field Interface Conditions Capacitance Energy in the Electrostatic Field: Point and Distributed Charges Applications Experiments 206 223 231 245 260 265 5 Boundary Value Problems: Analytic Methods of Solution 5.1 Introduction 5.2 Poisson's Equation for the Electrostatic Field 5.3 Laplace's Equation for the Electrostatic Field 5.4 Solution Methods 5.5 Experiments: The Method of Images 283 283 284 285 286 340 6 Boundary Value Problems: Numerical (Approximate) Methods 6.1 Introduction 6.2 The General Idea of Numerical Solutions 6.3 The Finite Difference Method: Solution to the Laplace and Poisson Equations 6.4 The Method of Moments: An Intuitive Approach 6.5 The Finite-Element Method: Introduction 353 353 355 7 The 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 417 417 418 419 428 433 437 443 449 454 459 Steady Electric Current Introduction Conservation of Charge Conductors, Dielectrics, and Lossy Dielectrics Ohm's Law Power Dissipation and Joule's Law The Continuity Equation and Kirchhoffs Current Law Current Density as a Field Interface Conditions for Current Density Applications Experiments 8 The Static Magnetic Field 8.1 Introduction 8.2 The Magnetic Field, Magnetic Field Intensity, and Magnetic Flux Density 8.3 The Biot-Savart Law 8.4 Ampere's Law 8.5 Magnetic Flux Density and Magnetic Flux 8.6 Postulates of the Static Magnetic Field 8.7 Potential Functions 8.8 Applications 8.9 Experiments 356 373 389 471 471 472 476 486 493 496 499 511 512 CONTENTS XV 9 Magnetic Materials and Properties 9.1 Introduction 9.2 Magnetic Properties of Materials 9.3 Magnetic Interface Conditions 9.4 Inductance and Inductors 9.5 Energy Stored in the Magnetic Field 9.6 Magnetic Circuits 9.7 Forces in the Magnetic Field 9.8 Torque 9.9 Applications 9.10 Experiments 525 525 528 553 559 573 586 592 606 609 612 10 Faraday's Law and Induction 10.1 Introduction 10.2 Faraday's Law 10.3 Lenz'sLaw 10.4 Motional Electromotive Force: The dc Generator 10.5 Induced emf due to Transformer Action ...... 10.6 Combined Motional and Transformer Action Electromotive Force . . . . . 10.7 The Transformer 10.8 Eddy Currents 10.9 Applications 10.10 Experiments 629 629 631 633 634 641 643 652 661 666 673 11 Maxwell's Equations 11.1 Introduction: The Electromagnetic Field 11.2 Maxwell's Equations 11.3 Time-Dependent Potential Functions 11.4 Interface Conditions for the Electromagnetic Field 11.5 Particular Forms of Maxwell's Equations 687 687 689 697 703 711 12 Electromagnetic Waves and Propagation 12.1 Introduction 12.2 The Wave 12.3 The Electromagnetic Wave Equation and Its Solution 12.4 The Electromagnetic Spectrum 12.5 The Poynting Theorem and Electromagnetic Power Density 12.6 The Complex Poynting Vector 12.7 Propagation of Waves in Materials 12.8 Polarization of Plane Waves 12.9 Applications 12.10 Experiments 725 725 725 731 748 750 760 764 786 793 795 13 Reflection and Transmission of Plane Waves 13.1 Introduction 13.2 Reflection and Transmission at a General Dielectric Interface: Normal Incidence 807 807 809 XVI CONTENTS 13.3 Reflection and Transmission at an Interface: Oblique Incidence on a Conductor 13.4 Oblique Incidence on Dielectric Interfaces 13.5 Reflection and Transmission for Layered Materials at Normal Incidence . . 13.6 Applications 13.7 Experiments 831 839 856 863 866 14 Theory of Transmission Lines 14.1 Introduction 14.2 The Transmission Line 14.3 Transmission Line Parameters 14.4 The Transmission Line Equations 14.5 Types of Transmission Lines 14.6 The Field Approach to Transmission Lines 14.7 Finite Transmission Lines 14.8 Power Relations on a General Transmission Line 14.9 Resonant Transmission Line Circuits 14.10 Applications 14.11 Experiment 877 877 881 882 890 895 904 909 928 931 936 939 15 The 15.1 15.2 15.3 15.4 15.5 15.6 953 953 954 964 967 984 988 Smith Chart, Impedance Matching, and Transmission Line Circuits Introduction The Smith Chart The Smith Chart as an Admittance Chart Impedance Matching and the Smith Chart Quarter-Wavelength Transformer Matching Experiments 16 Transients on Transmission Lines 16.1 Introduction 16.2 Propagation of Narrow Pulses on Finite, Lossless Transmission Lines . . . . 16.3 Propagation of Narrow Pulses on Finite, Distortionless Transmission Lines 16.4 Transients on Transmission Lines: Long Pulses 16.5 Transients on Transmission Lines: Finite-Length Pulses 16.6 Reflections from Discontinuities 16.7 Transients on Lines with Reactive Loading 16.8 Initial Condition on Line 16.9 Experiments 17 Waveguides 17.1 Introduction 17.2 The Concept of a Waveguide 17.3 Transverse Electromagnetic, Transverse Electric, and Transverse Magnetic Waves 17.4 TE Propagation in Parallel Plate Waveguides 17.5 TM Propagation in Parallel Plate Waveguides 997 997 998 1002 1007 1015 1018 1023 1029 1033 1041 1041 1042 1043 1055 1066 CONTENTS 17.6 17.7 17.8 17.9 17.10 17.11 17.12 TEM Waves in Parallel Plate Waveguides Rectangular Waveguides Other Waveguides Cavity Resonators Energy Relations in a Cavity Resonator Quality Factor of a Cavity Resonator Applications XVII 1072 1073 1097 1097 1105 1106 1106 18 Antennas and Electromagnetic Radiation 18.1 Introduction 18.2 Electromagnetic Radiation and Radiation Safety 18.3 Antennas 18.4 The Electric Dipole 18.5 Properties of Antennas 18.6 The Magnetic Dipole 18.7 Practical Antennas 18.8 Antenna Arrays 18.9 Reciprocity and Receiving Antennas 18.10 Effective Aperture 18.11 The Radar 18.12 OtherAntennas 18.13 Applications 1119 1119 1120 1121 1122 1133 1143 1150 1165 1180 1182 1188 1193 1193 Answers 1203 Index 1215