Introduction to Electromagnetic Waves with Maxwell's Equations

ISBN-13: 9781119626725 / Angielski / Twarda / 2021 / 592 str.

Ozgur Ergul

Spis treści

Preface 15Mathematical Notation 23List of Symbols 27Special Functions 31Frequently Used Identities 33Tools to Understand Maxwell's Equations 370 Preliminary 390.1 Scalar and Vector Fields 400.2 Cartesian Coordinate Systems 420.3 Basic Vector Operations 420.4 Orthogonal Coordinate Systems 430.4.1 Properties of a Cartesian Coordinate System 430.4.2 Cylindrical Coordinate System 440.4.3 Spherical Coordinate System 450.5 Electrostatics, Magnetostatics, and Electromagnetics 470.6 Time in Electromagnetics 490.7 Final Remarks 511 Gauss' Law 531.1 Integral Form of Gauss' Law 541.1.1 Differential Surface With Direction 551.1.2 Dot Product 561.1.3 Flux of Vector Fields 621.1.4 Meaning of Gauss' Law and Its Application 661.1.5 Examples 671.2 Using the Integral Form of Gauss' Law 691.2.1 Examples 711.3 Differential Form of Gauss' Law 731.3.1 Electric Charge Density 731.3.2 Divergence of Vector Fields 751.3.3 Divergence Theorem and the Differential Form of Gauss' Law 811.3.4 Examples 831.4 Using the Differential Form of Gauss' Law 851.4.1 Examples 881.5 Boundary Conditions for Normal Electric Fields 891.6 Static Cases and Coulomb's Law 921.6.1 Superposition Principle 931.6.2 Coulomb's Law and Electric Force 991.6.3 Examples 1011.7 Gauss' Law and Dielectrics 1061.7.1 Electric Dipole 1121.7.2 Polarization 1131.7.3 Equivalent Polarization Charges 1151.7.4 Examples 1201.8 Final Remarks 1231.9 Exercises 1241.10 Questions 1272 Ampere's Law 1332.1 Integral Form of Ampere's Law 1342.1.1 Differential Length With Direction 1352.1.2 Circulation of Vector Fields 1372.1.3 Meaning of Ampere's Law and Its Application 1402.1.4 Examples 1432.2 Using the Integral Form of Ampere's Law 1452.2.1 Examples 1472.3 Differential Form of Ampere's Law 1512.3.1 Electric Current Density 1522.3.2 Cross Product 1542.3.3 Curl of Vector Fields 1572.3.4 Stoke's Theorem and the Differential Form of Ampere's Law 1642.3.5 Examples 1652.4 Using the Differential Form of Ampere's Law 1692.4.1 Examples 1722.5 Boundary Conditions for Tangential Magnetic Fields 1732.6 Gauss' Law and Ampere's Law 1762.7 Static Cases, Biot-Savart Law, and Ampere's Force Law 1792.7.1 Superposition Principle 1802.7.2 Ampere's Force Law and Magnetic Force 1902.7.3 Examples 1942.8 Ampere's Law and Magnetic Materials 2002.8.1 Magnetic Dipole 2062.8.2 Magnetization 2082.8.3 Equivalent Magnetization Currents 2102.8.4 Examples 2172.9 Final Remarks 2182.10 Exercises 2192.11 Questions 2213 Faraday's Law 2253.1 Integral Form of Faraday's Law 2263.1.1 Meaning of Faraday's Law and Its Application 2273.1.2 Lorentz Force Law 2293.2 Using the Integral Form of Faraday's Law 2313.2.1 Examples 2363.3 Differential Form of Faraday's Law 2403.4 Boundary Conditions for Tangential Electric Fields 2423.5 Combining Faraday's Law with Gauss' and Ampere's Laws 2443.6 Static Cases and Electric Scalar Potential 2463.6.1 Gradient of Scalar Fields 2483.6.2 Examples 2523.6.3 Gradient Theorem 2533.6.4 Gradient in Gauss' Law, Ampere's Law, and Faraday's Law 2543.6.5 Electric Potential Energy 2573.6.5.1 Electric Potential Energy of Discrete Charge Distributions 2613.6.5.2 Stored Electric Potential Energy by an Electric Dipole 2633.6.5.3 Stored Electric Potential Energy in Charge Distributions 2653.6.5.4 Electric Potential Energy and Electric Force 2693.6.6 Examples 2723.6.7 Poisson's Equation and Laplace's Equation 2763.6.8 Examples 2833.6.9 Finding Electric Scalar Potential From Electric Field Intensity 2833.6.10 Examples 2863.6.11 Electrostatic Boundary Value Problems 2883.6.12 Examples 2913.7 Final Remarks 2943.8 Exercises 2943.9 Questions 2964 Gauss' Law for Magnetic Fields 2994.1 Integral and Differential Forms of Gauss' law for Magnetic Fields 3004.1.1 Meaning of Gauss' law for Magnetic Fields 3024.1.2 Examples 3044.2 Boundary Conditions for Normal Magnetic Fields 3064.2.1 Examples 3074.3 Static Cases and Magnetic Vector Potential 3084.3.1 Magnetic Vector Potential and Coulomb's Gauge 3094.3.2 Examples 3184.3.3 Magnetic Potential Energy 3214.3.3.1 Magnetic Potential Energy of Discrete Current Distributions 3234.3.3.2 Stored Magnetic Potential Energy by a Magnetic Dipole 3244.3.3.3 Stored Magnetic Potential Energy in Current Distributions 3264.3.3.4 Magnetic Potential Energy and Magnetic Force 3294.3.4 Examples 3324.4 Combining All Maxwell's Equations 3344.4.1 Wave Equations 3364.4.2 Wave Equations for Potentials 3434.4.3 Time-Harmonic Sources and Helmholtz Equations 3494.4.4 Examples 3544.5 Final Remarks 3594.6 Exercises 3604.7 Questions 3635 Basic Solutions of Maxwell's Equations 3655.1 Summary of Maxwell's Equations, Wave Equations, and Helmholtz Equations 3665.1.1 Examples 3755.2 Electromagnetic Propagation and Radiation 3775.2.1 Hertzian Dipole 3825.2.2 Examples 3855.3 Plane Waves 3895.3.1 Examples 4005.3.2 Polarization of Plane Waves 4015.3.3 Examples 4075.3.4 Power of Plane Waves 4095.3.5 Reflection and Refraction of Plane Waves 4125.3.6 General Case for Reflection and Refraction 4165.3.6.1 Perpendicular Polarization 4185.3.6.2 Parallel Polarization 4215.3.7 Examples 4235.3.8 Total Internal Reflection 4275.3.9 Total Transmission 4305.3.10 Examples 4345.3.11 Reflection and Transmission for Two Parallel Interfaces 4375.4 Final Remarks 4405.5 Exercises 4405.6 Questions 4436 Analyses of Conducting Objects 4476.1 Ohm's Law 4496.2 Joule's Law 4526.3 Relaxation Time 4536.4 Boundary Conditions for Conducting Media 4566.5 Analyses of Perfectly Conducting Objects 4576.5.1 Electric Scalar Potential for PECs 4586.5.2 Boundary Conditions for PECs 4586.5.3 Basic Responses of PECs 4606.5.4 Concerns in Geometric Representations of PECs 4626.5.5 Electrostatics for PECs 4646.5.6 Method of Images 4666.5.7 Examples 4706.6 Maxwell's Equations in Conducting Media 4746.6.1 Complex Permittivity 4766.6.2 Power and Energy in Conducting Media 4786.6.3 Plane Waves in Conducting Media 4796.6.4 Power of Plane Waves in Conducting Media 4836.6.5 Reflection from PECs 4846.6.6 Examples 4946.7 Capacitance 5036.7.1 Capacitance and Electric Potential Energy 5046.7.2 Parallel-Plate Capacitors 5056.7.3 Spherical Capacitors 5136.7.4 Cylindrical Capacitors 5186.7.5 Examples 5206.8 Resistance 5286.8.1 Examples 5356.9 Inductance 5446.9.1 Examples 5536.10 Final Remarks 5596.11 Exercises 5606.12 Questions 5657 Transmission of Electromagnetic Waves 5697.1 Antennas and Wireless Transmission 5707.1.1 Basic Properties of Antennas 5717.1.2 Antenna Design Parameters 5827.1.3 Antenna Types 5857.1.3.1 Antenna Arrays 5887.1.4 Friis Transmission Equation 6007.1.5 Examples 6037.2 Waveguides 6137.2.1 Transverse and Axial Fields 6147.2.2 Rectangular Waveguides 6177.2.2.1 Transverse Magnetic Modes 6187.2.2.2 Transverse Electric Modes 6207.2.2.3 Non-Existing Modes 6237.2.2.4 Important Properties of Modes 6247.2.3 Parallel-Plate Waveguides 6287.2.4 Examples 6307.3 Transmission Line Theory 6357.3.1 Telegrapher's Equations 6377.3.1.1 Transmission Line With a Load 6417.3.1.2 Special Cases 6437.3.1.3 Common Cases 6467.3.2 Voltage and Current Patterns 6477.3.3 Examples 6517.4 Concluding Remarks 6587.5 Exercises 6587.6 Questions 6638 Concluding Chapter 6698.1 Electromagnetic Spectrum 6708.1.1 Radio Waves (3 Hz to 300 GHz) 6718.1.2 Microwaves (300 MHz to 300 GHz) 6728.1.3 Infrared Radiation (300 GHz to 400 THz) 6738.1.4 Visible Range (400 THz to 800 THz) 6748.1.5 Ultraviolet Radiation (800 THz to 30 PHz) 6758.1.6 X-Rays (30 PHz to 30 EHz) 6768.1.7 Gamma Rays (Above 30 EHz) 6788.2 Brief History of Electromagnetism (Electricity, Magnetism, and a Little Optics) 6798.3 Electromagnetism in Action 6858.3.1 Snapshots From Nature 6868.3.1.1 Blue Sky, Bright Sun, Red Sunset 6868.3.1.2 Rainbow in Pocket 6878.3.1.3 Green Leaf, Red Apple, Blue Sea 6888.3.1.4 Electromagnetic Waves From Space 6898.3.1.5 Magnetic Earth 6908.3.2 Snapshots From Technology 6918.3.2.1 Telegraph to Cellular Phones 6918.3.2.2 Home: Where Electromagnetism Happens 6938.3.2.3 Looking Inside Body 6948.3.2.4 Seeing World with Sensors and Radars 6968.3.2.5 Atoms Under Microscope 6998.4 How to Solve Maxwell's Equations 7008.4.1 Full-Wave Methods 7058.4.1.1 Differential-Equation Solvers 7068.4.1.1.1 Finite-Difference Time-Domain Method (FDTD): 7068.4.1.1.2 Finite Element Method (FEM): 7078.4.1.2 Integral-Equation Solvers 7088.4.1.2.1 Method of Moments (MoM): 7098.4.1.2.2 Acceleration Algorithms: 7098.4.1.2.3 FMM and MLFMA: 7118.4.2 Asymptotic Techniques 7118.4.2.0.1 Quasistatic Approximations: 7128.4.2.0.2 Geometrical Optics: 7138.4.2.0.3 Uniform Geometrical Theory of Diffraction: 7138.4.2.0.4 Physical Optics: 714Bibliography 717Index 725

O autorze

Ozgur Ergul, PhD, is Professor at the Middle East Technical University in Ankara, Turkey. His research focus is on the development of fast and accurate algorithms for the solution of electromagnetics problems involving large and complicated structures, integral equations, iterative methods, parallel programming, and high-performance computing.