Modern electrodynamics

An engaging writing style and a strong focus on the physics make this comprehensive, graduate level textbook unique among existing classical electromagnetism textbooks. Charged particles in vacuum and the electrodynamics of continuous media are given equal attention in discussions of electrostatics, magnetostatics, quasistatics, conservation laws, wave propagation, radiation, scattering, special relativity, and field theory. Extensive use of qualitative arguments similar to those used by working physicists makes Modern Electrodynamics a must have for every student of this subject. In 24 chapters, the textbook covers many more topics than can be presented in a typical two semester course, making it easy for instructors to tailor courses to their specific needs. Close to 120 worked examples and 80 applications boxes help the reader build physical intuition and develop technical skill. Nearly 600 end of chapter homework problems encourage students to engage actively with the material. A solutions manual is available for instructors at (http://www.cambridge.org/Zangwill) www.cambridge.org/Zangwill . Contents......Page 7 List of Applications......Page 15 Preface......Page 20 1.2 Vectors......Page 24 1.3 Derivatives......Page 30 1.4 Integrals......Page 32 1.5 Generalized Functions......Page 34 1.6 Fourier Analysis......Page 38 1.7 Orthogonal Transformations......Page 41 1.8 Cartesian Tensors......Page 43 1.9 The Helmholtz Theorem......Page 45 Sources, References, and Additional Reading......Page 47 Problems......Page 48 2.1 Introduction......Page 52 2.2 The Maxwell Equations in Vacuum......Page 56 2.3 Microscopic vs. Macroscopic......Page 61 2.4 The Maxwell Equations in Matter......Page 66 2.5 Quantum Limits and New Physics......Page 69 2.6 SI Units......Page 73 2.7 A Heuristic Derivation......Page 74 Sources, References, and Additional Reading......Page 76 Problems......Page 78 3.1 Introduction......Page 81 3.2 Coulomb’s Law......Page 82 3.3 The Scalar Potential......Page 83 3.4 Gauss’ Law and Solid Angle......Page 91 3.5 Electrostatic Potential Energy......Page 97 3.6 Electrostatic Total Energy......Page 99 3.7 The Electric Stress Tensor......Page 104 Sources, References, and Additional Reading......Page 107 Problems......Page 108 4.1 Introduction......Page 113 4.2 The Electric Dipole......Page 115 4.3 Electric Dipole Layers......Page 121 4.4 The Electric Quadrupole......Page 125 4.5 Spherical Mathematics......Page 129 4.6 Spherical and Azimuthal Multipoles......Page 132 4.7 Primitive and Traceless Multipole Moments......Page 139 Sources, References, and Additional Reading......Page 142 Problems......Page 144 5.2 Electrostatic Induction......Page 149 5.3 Screening and Shielding......Page 156 5.4 Capacitance......Page 157 5.5 The Energy of a System of Conductors......Page 165 5.6 Forces on Conductors......Page 166 5.7 Real Conductors......Page 172 Sources, References, and Additional Reading......Page 174 Problems......Page 175 6.2 Polarization......Page 181 6.3 The Field Produced by Polarized Matter......Page 185 6.4 The Total Electric Field......Page 188 6.5 Simple Dielectric Matter......Page 190 6.6 The Physics of the Dielectric Constant......Page 198 6.7 The Energy of Dielectric Matter......Page 201 6.8 Forces on Dielectric Matter......Page 207 Sources, References, and Additional Reading......Page 214 Problems......Page 216 7.1 Introduction......Page 220 7.2 Potential Theory......Page 221 7.3 Uniqueness......Page 222 7.4 Separation of Variables......Page 224 7.5 Cartesian Symmetry......Page 226 7.6 Azimuthal Symmetry......Page 232 7.7 Spherical Symmetry......Page 235 7.8 Cylindrical Symmetry......Page 238 7.9 Polar Coordinates......Page 241 7.10 The Complex Potential......Page 244 7.11 A Variational Principle......Page 249 Sources, References, and Additional Reading......Page 251 Problems......Page 252 8.2 The Key Idea: Superposition......Page 259 8.3 The Method of Images......Page 260 8.4 The Green Function Method......Page 273 8.5 The Dirichlet Green Function......Page 275 8.6 The Complex Logarithm Potential......Page 283 8.7 The Poisson-Boltzmann Equation......Page 285 Sources, References, and Additional Reading......Page 287 Problems......Page 288 9.1 Introduction......Page 295 9.2 Current in Vacuum......Page 296 9.3 Current in Matter......Page 298 9.4 Potential Theory for Ohmic Matter......Page 299 9.5 Electrical Resistance......Page 300 9.6 Joule Heating......Page 303 9.7 Electromotive Force......Page 305 9.8 Current Sources......Page 310 9.9 Diffusion Current: Fick’s Law......Page 314 Sources, References, and Additional Reading......Page 316 Problems......Page 317 10.1 Introduction......Page 324 10.2 The Law of Biot and Savart......Page 327 10.3 Amp` ere’s Law......Page 330 10.4 The Magnetic Scalar Potential......Page 335 10.5 The Vector Potential......Page 343 10.6 The Topology of Magnetic Field Lines......Page 348 Sources, References, and Additional Reading......Page 351 Problems......Page 352 11.1 Introduction......Page 359 11.2 The Magnetic Dipole......Page 360 11.3 Magnetic Dipole Layers......Page 368 11.4 Exterior Multipoles......Page 369 11.5 Interior Multipoles......Page 376 11.6 Axially Symmetric Magnetic Fields......Page 380 Sources, References, and Additional Reading......Page 382 Problems......Page 384 12.1 Introduction......Page 388 12.2 Charged Particle Motion......Page 389 12.3 The Force between Steady Currents......Page 391 12.4 The Magnetic Dipole......Page 395 12.5 The Magnetic Stress Tensor......Page 404 12.6 Magnetostatic Total Energy......Page 407 12.7 Magnetostatic Potential Energy......Page 412 12.8 Inductance......Page 417 Sources, References, and Additional Reading......Page 422 Problems......Page 424 13.2 Magnetization......Page 430 13.3 The Field Produced by Magnetized Matter......Page 435 13.4 Fictitious Magnetic Charge......Page 438 13.5 The Total Magnetic Field......Page 442 13.6 Simple Magnetic Matter......Page 444 13.7 The Energy of Magnetic Matter......Page 456 13.8 Forces on Magnetic Matter......Page 458 13.9 Permanent Magnetic Matter......Page 466 Sources, References, and Additional Reading......Page 470 Problems......Page 471 14.1 Introduction......Page 478 14.2 The Amp` ere-Maxwell Law......Page 479 14.3 Faraday’s Law......Page 483 14.4 Electromagnetic Induction......Page 485 14.5 Slowly Time-Varying Charge in Vacuum......Page 490 14.6 Slowly Time-Varying Current in Vacuum......Page 493 14.7 Quasistatic Fields in Matter......Page 495 14.8 Poor Conductors: Quasi-Electrostatics......Page 496 14.9 Good Conductors: Quasi-Magnetostatics......Page 498 14.10 The Skin Effect......Page 500 14.11 Magnetic Diffusion......Page 504 14.12 Eddy-Current Phenomena......Page 506 14.13 AC Circuit Theory......Page 509 Sources, References, and Additional Reading......Page 516 Problems......Page 517 15.2 Symmetry......Page 524 15.3 Electromagnetic Potentials......Page 526 15.4 Conservation of Energy......Page 530 15.5 Conservation of Linear Momentum......Page 534 15.6 Conservation of Angular Momentum......Page 539 15.7 The Center of Energy......Page 542 15.8 Conservation Laws in Matter......Page 545 15.9 The Force on Isolated Matter......Page 549 Sources, References, and Additional Reading......Page 552 Problems......Page 554 16.1 Introduction......Page 559 16.2 The Wave Equation......Page 560 16.3 Plane Waves......Page 562 16.4 Polarization......Page 568 16.5 Wave Packets......Page 575 16.6 The Helmholtz Equation......Page 580 16.7 Beam-Like Waves......Page 581 16.8 Spherical Waves......Page 588 16.9 Hertz Vectors......Page 592 16.10 Forces on Particles in Free Fields......Page 594 Sources, References, and Additional Reading......Page 598 Problems......Page 600 17.2 Plane Waves......Page 607 17.3 Reflection and Refraction......Page 611 17.4 Radiation Pressure......Page 622 17.5 Layered Matter......Page 625 17.6 Simple Conducting Matter......Page 630 17.7 Anisotropic Matter......Page 636 Sources, References, and Additional Reading......Page 639 Problems......Page 640 18.2 Frequency Dispersion......Page 647 18.3 Energy in Dispersive Matter......Page 650 18.4 Transverse and Longitudinal Waves......Page 652 18.5 Classical Models for Frequency Dispersion......Page 653 18.6 Wave Packets in Dispersive Matter......Page 664 18.7 The Consequences of Causality......Page 672 18.8 Spatial Dispersion......Page 679 Sources, References, and Additional Reading......Page 680 Problems......Page 682 19.1 Introduction......Page 689 19.2 Transmission Lines......Page 690 19.3 Planar Conductors......Page 695 19.4 Conducting Tubes......Page 698 19.5 Dielectric Waveguides......Page 710 19.6 Conducting Cavities......Page 716 19.7 Dielectric Resonators......Page 727 Sources, References, and Additional Reading......Page 729 Problems......Page 730 20.1 Introduction......Page 737 20.2 Inhomogeneous Wave Equations......Page 738 20.3 Retardation......Page 742 20.4 The Time-Dependent Electric Dipole......Page 750 20.5 Radiation......Page 753 20.6 Thin-Wire Antennas......Page 760 20.7 Cartesian Multipole Radiation......Page 766 20.8 Spherical Multipole Radiation......Page 778 20.9 Radiation in Matter......Page 785 Sources, References, and Additional Reading......Page 788 Problems......Page 790 21.1 Introduction......Page 798 21.2 The Scattering Cross Section......Page 799 21.3 Thomson Scattering......Page 800 21.4 Rayleigh Scattering......Page 805 21.5 Two Exactly Solvable Problems......Page 806 21.6 Two Approximation Schemes......Page 813 21.7 The Total Cross Section......Page 816 21.8 Diffraction by a Planar Aperture......Page 820 21.9 Generalized Optical Principles......Page 830 Sources, References, and Additional Reading......Page 835 Problems......Page 837 22.1 Introduction......Page 845 22.2 Galileo’s Relativity......Page 846 22.3 Einstein’s Relativity......Page 848 22.4 The Lorentz Transformation......Page 849 22.5 Four-Vectors......Page 857 22.6 Electromagnetic Quantities......Page 862 22.7 Covariant Electrodynamics......Page 871 22.8 Matter in Uniform Motion......Page 881 Sources, References, and Additional Reading......Page 886 Problems......Page 888 23.2 The Li ́ enard-Wiechert Problem......Page 893 23.3 Radiation in the Time Domain......Page 903 23.4 Radiation in the Frequency Domain......Page 909 23.5 Synchrotron Radiation......Page 914 23.6 Radiation Reaction......Page 922 23.7 Cherenkov Radiation......Page 929 Sources, References, and Additional Reading......Page 933 Problems......Page 935 24.2 Hamilton’s Principle......Page 939 24.3 Lagrangian Description......Page 941 24.4 Invariance and Conservation Laws......Page 950 24.5 Hamiltonian Description......Page 954 Sources, References, and Additional Reading......Page 963 Problems......Page 964 Appendix A List of Important Symbols......Page 968 Appendix B Gaussian Units......Page 972 Appendix C Special Functions......Page 976 Appendix D Managing Minus Signs in Special Relativity......Page 982 Index......Page 987 An Engaging Writing Style And A Strong Focus On The Physics Make This Comprehensive, Graduate-level Textbook Unique Among Existing Classical Electromagnetism Textbooks. Charged Particles In Vacuum And The Electrodynamics Of Continuous Media Are Given Equal Attention In Discussions Of Electrostatics, Magnetostatics, Quasistatics, Conservation Laws, Wave Propagation, Radiation, Scattering, Special Relativity, And Field Theory. Extensive Use Of Qualitative Arguments Similar To Those Used By Working Physicists Makes Modern Electrodynamics A Must-have For Every Student Of This Subject. In 24 Chapters, The Textbook Covers Many More Topics Than Can Be Presented In A Typical Two-semester Course, Making It Easy For Instructors To Tailor Courses To Their Specific Needs. Close To 120 Worked Examples And 60 Applications Boxes Help The Reader Build Physical Intuition And Develop Technical Skill. Nearly 600 End-of-chapter Homework Problems Encourage Students To Engage Actively With The Material. A Solutions Manual Is Available For Instructors At Www.cambridge.org/zangwill-- Machine Generated Contents Note: 1. Mathematical Preliminaries; 2. The Maxwell Equations; 3. Electrostatics; 4. Electric Multipoles; 5. Conducting Matter; 6. Dielectric Matter; 7. Laplace's Equation; 8. Poisson's Equation; 9. Steady Current; 10. Magnetostatics; 11. Magnetic Multipoles; 12. Magnetic Force And Energy; 13. Magnetic Matter; 14. Dynamic And Quasistatic Fields; 15. General Electromagnetic Fields; 16. Waves In Vacuum; 17. Waves In Simple Matter; 18. Waves In Dispersive Matter; 19. Guided And Confined Waves; 20. Retardation And Radiation; 21. Scattering And Diffraction; 22. Special Relativity; 23. Fields From Moving Charges; 24. Lagrangian And Hamiltonian Methods; Appendixes; Index. Andrew Zangwill. Includes Bibliographical References And Index. "An engaging writing style and a strong focus on the physics make this comprehensive, graduate-level textbook unique among existing classical electromagnetism textbooks. Charged particles in vacuum and the electrodynamics of continuous media are given equal attention in discussions of electrostatics, magnetostatics, quasistatics, conservation laws, wave propagation, radiation, scattering, special relativity, and field theory. Extensive use of qualitative arguments similar to those used by working physicists makes Modern Electrodynamics a must-have for every student of this subject. In 24 chapters, the textbook covers many more topics than can be presented in a typical two-semester course, making it easy for instructors to tailor courses to their specific needs. Close to 120 worked examples and 60 applications boxes help the reader build physical intuition and develop technical skill. Nearly 600 end-of-chapter homework problems encourage students to engage actively with the material. A solutions manual is available for instructors at www.cambridge.org/Zangwill"-- Provided by publisher An engaging writing style and a strong focus on the physics make this comprehensive, graduate-level textbook unique among existing classical electromagnetism textbooks. It features close to 120 worked examples, 80 applications boxes and nearly 600 end-of-chapter homework problems, with a solutions manual available to instructors at www.cambridge.org/Zangwill.