Modern Problems in Classical Electrodynamics by Charles A. Brau

Modern Problems in Classical Electrodynamics

byCharles A. Brau

Hardcover | September 17, 2003

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Designed as an upper-level undergraduate/beginning graduate text and as a reference for research scientists, Modern Problems in Classical Electrodynamics addresses a wide range of topics in modern physics--including lasers and nonlinear optics--that are not found in other texts. The bookbegins with relativistic mechanics and field theory, partly because they lend unity and beauty to electrodynamics, and also because relativistic concepts appear frequently throughout the book. Electrostatics and magnetostatics, waves, continuous media, nonlinear optics, diffraction, and radiation bymoving particles are then covered in depth. The book concludes by returning to basics, discussing the fundamental problems inherent in the classical theory of electrons. Modern Problems in Classical Electrodynamics features examples and homework exercises drawn from condensed-matter physics, particle physics, optics, and atomic physics. Many of these are experimentally oriented and help to make the book interesting and relevant to a broad audience. An instructor'smanual including answers to the homework exercises is available to adopters. An accompanying website,, contains errata and additional homework exercises that instructors can use to supplement the exercises in the text.

About The Author

Charles A. Brau received his B.A. in Engineering from Cornell University and his M.A. (in Engineering) and Ph.D. in Applied Physics from Harvard University. In the course of his career, he has been a theorist, an experimenter, a manager, and currently a professor of physics at the Vanderbilt University in Nashville, Tennessee. He focu...

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Title:Modern Problems in Classical ElectrodynamicsFormat:HardcoverDimensions:608 pages, 7.72 × 9.41 × 1.3 inPublished:September 17, 2003Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195146654

ISBN - 13:9780195146653

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Table of Contents

Preface0 Prologue0.1. Introduction0.2. Electrostatics0.2.1. Charges0.2.2. Forces and Electric Fields0.3. Magnetostatics0.3.1. Currents0.3.2. Forces and Fields0.3.3. Vector Potential0.4. Electrodynamics0.4.1. Conservation of Charge0.4.2. Faraday's Law0.4.3. Energy in the Magnetic Field0.5. The Maxwell Equations and Electromagnetic Waves0.5.1. The Maxwell--Ampere Law0.5.2. Electromagnetic Waves0.5.3. Potentials and Gauges0.6. Conservation Laws0.6.1. Poynting's Theorem0.6.2. Conservation of Momentum1. Relativistic Kinematics1.1. The Principles of Special Relativity1.1.1. Historical Overview1.1.2. Einstein's Postulate1.1.3. Intervals1.1.4. Proper Time1.2. The Lorentz Transformation1.2.1. Rotation in 4-Spave1.2.2. Time Dilation and Length Contraction1.2.3. Velocity Transformation1.3. 4-Vectors and 4-Tensors1.3.1. Cartesian Tensors1.3.2. Relativistic Metric and Lorentz Transformation1.3.3. 4-Vector Calculus1.4. Electromagnetic Fields1.4.1. The 4-Tensor Electromagnetic Field1.4.2. Transformation of Electromagnetic Fields2. Relativistic Mechanics and Field Theory2.1. Relativistic Free Particle2.1.1. Hamilton's Principle and the Calculus of Variations2.1.2. Langrangian for a Free Particle2.1.3. Energy and Momentum2.1.4. de Broglie Waves2.1.5. Rotational Invariance and Angular Momentum2.2. Charged Particle in a Vector Potential2.2.1. Langrangian Mechanics2.2.2. Canonical Momentum2.2.3. Canonical Equations of Motion2.3. The Maxwell Equations2.3.1. Equations of Motion of a Vector Field2.3.2. Proca Mass Term2.4. Invariance and Conservation Laws2.4.1. Gauge Transformations2.4.2. Symmetric Stress Tensor for the Electromagnetic Field3. Time-Independent Electromagnetic Fields3.1. Electrostatics3.1.1. Coulomb's Law3.1.2. Energy in Electrostatic Fields3.1.3. Multipole Moments3.2. Boundary-Value Problems with Conductors3.2.1. Boundary Conditions and Uniqueness Theorems3.2.2. Energy and Capacitance3.2.3. Method of Images3.2.4. Separation of Variables3.2.5. Spheroidal Coordinates3.2.6. Spherical Harmonics3.2.7. Variational Methods3.2.8. Numerical Methods3.2.9. Green Functions3.3. Magnetostatics3.3.1. Biot-Savart Law3.3.2. Forces and Energy3.3.3. Multipole Moments3.3.4. Magnetic Scalar Potential4. Electromagnetic Waves4.1. Plane Waves4.1.1. Electric and Magnetic Fields in Plane Waves4.1.2. Charged Particle in a Plane Wave4.2. Canonical Equations of an Electromagnetic Field4.2.1. Fourier Decomposition of the Field4.2.2. Spontaneous Emission by a Harmonic Oscillator4.2.3. Canonical Equations of the Electromagnetic Field4.2.4. Blackbody Radiation and the Einstein Coefficients4.3. Waves in Plasmas4.3.1. Transverse Electromagnetic Waves4.3.2. Longitudinal Electrostatic Waves5. Fourier Techniques and Virtual Quanta5.1. Fourier Transformation5.1.1. Fourier's Theorem5.1.2. Asymptotic Behavior of Fourier Transforms5.1.3. -Functions5.1.4. Autocorrelation Functions and the Wiener-Khintchine Theorem5.1.5. Pulse Compression5.2. Method of Virtual Quanta5.2.1. Fourier Decomposition of the Field of a Relativistic Charge5.2.2. Bremsstrahlung5.2.3. Excitation by a Fast Charged Particle5.2.4. Transition Radiation6. Macroscopic Materials6.1. Polarization and Magnetization6.1.1. The Macroscopic Form of the Maxwell Equations6.1.2. The Constitutive Relations6.1.3. Boundary Conditions6.1.4. Magnetic Scalar Potentia6.1.5. Conservation of Energy, and Poynting's Theorem6.2. Properties of Dielectric and Magnetic Materials6.2.1. Dielectric Materials6.2.2. Magnetic Materials7. Linear, Dispersive Media7.1. Linear Media7.1.1. Waves in a Nondispersive Medium7.1.2. Constitutive Relations in Dispersive Media7.1.3. Kramers-Kronig Relations7.1.4. Plane Waves in Dispersive Media7.1.5. Phase Velocity and Group Velocity7.1.6. Conservation of Energy in Dispersive Media7.1.7. Lorentz-Drude Model7.2. Reflection and Refraction at Surfaces7.2.1. Boundary Conditions7.2.2. Dielectric Reflection7.2.3. Metallic Reflection7.2.4. Surface Waves7.3. Energy Loss by Fast Particles Traveling Through Matter7.3.1. Ionization and Excitation7.3.2. Relativistic Limit and the Density Effect8. Nonlinear Optics8.1. Nonlinear Susceptibility8.1.1. Nonlinear Polarization8.1.2. Anisotropic Materials8.2. Multiphoton Processes8.2.1. Coupled-Wave Equation8.2.2. Second-Harmonic Generation8.2.3. Sum-Frequency Generation8.3. Nonlinear Index of Refraction8.3.1. Third-Order Susceptibility8.3.2. Wave Equation with a Nonlinear Index of Refraction8.3.3. Phase-Conjugate Reflection8.4. Raman Processes8.4.1. Raman Scattering8.4.2. Coherent Raman Amplification9. Diffraction9.1. Geometrical Optics9.1.1. Eikonal Approximation9.1.2. Rays in Geometrical Optics9.1.3. Integral Theorems9.2. Gaussian Optics and Laser Resonators9.2.1. Paraxial Approximation9.2.2. Laser Resonators and Mode Spacing9.2.3. Transverse Modes and Resonator Stability9.3. Diffraction9.3.1. Scalar Diffraction Theory9.3.2. Fraunhofer Diffraction (Far Field)9.3.3. Fresnel Diffraction (Near Field)10. Radiation by Relativistic Particles10.1. Angular and Spectral Distribution of Radiation10.1.1. Fourier Decomposition of the Fields10.1.2. Retarded Fields and Lienard-Wiechert Fields10.1.3. Multipole Radiation10.1.4. Spectral Distribution of Radiation from a Point Charge10.1.5. Angular Distribution of Radiation from a Point Charge10.1.6. Total Power Radiated by a Point Charge10.2. Bremsstrahlung and Transition Radiation10.2.1. Bremsstrahlung10.2.2. Transition Raidiation10.3. Thomson Scattering10.3.1. Linear Thomson Scattering10.3.2. Nonlinear Thomson Scattering10.4. Synchrotron Radiation and Undulator Radiation10.4.1. Synchrotron Radiation10.4.2. Undulator Radiation10.5. Coherent Emission from Multiple Particles10.5.1. Coherence and Form Factor10.5.2. Coherent Radiative Processes10.6. Radiation from Relativistic Particles Traveling Through Matter10.6.1. Angular Spectral Fluence10.6.2. Cherenkov Radiation11. Fundamental Particles in Classical Electrodynamics11.1. Electromagnetic Mass and the Radiation Reaction11.1.1. Difficulties in the Classical Theory11.1.2. The 4/3 Problem and Poincare Stresses11.1.3. Point Particles and the Radiation Reaction11.1.4. Extended Particles11.2. Magnetic Monopoles11.2.1. The Maxwell Equations11.2.2. Magnetic Monopoles and Charge Quantization11.3. Spin11.3.1. Relativistic Equations of Motion11.3.2. Thomas Precession and Spin-Orbit CouplingAppendix: Units and DimensionsA.1. ArbitrarinessA.2. SI UnitsA.3. Gaussian UnitsA.4. Conversion of Formulas Between SI and Gaussian UnitsIndex