This book, suitable for use in a one-semester introduction to electrodynamics for advanced undergraduates, emphasizes relativity and symmetry in developing the theory. By focusing immediately on the Lorentz invariance of Maxwell's equations, the presentation makes many advanced topics readily accessible to the student. After a brief review of the history of electrodynamics, the book presents the experimental basis for the four Maxwell equations, both in vacuo and in dielectric and magnetic media. The principle of relativity is then used to unify the equations into a pair of covariant field equations, and steady-state solutions of these are treated both analytically and numerically. The final chapters discuss radiation in a vacuum and in dielectric media; the motion of charged particles in electromagnetic fields; radiation by moving changes; and, briefly, extensions to quantum theory. Mathematica scripts on the included diskette provide graphic solutions to many of the examples discussed in the text.
Inhaltsverzeichnis
1 Introduction to Electrodynamics. - 1-1 A Brief History of Electromagnetism. - 1-2 Vectors. - 1 -3 Vector Calculus. - 1-4 Curvilinear Coordinate Systems. - 1 -5 Integration of Vectors. - 1-6 Delta Functions. - 1-7 Selected Bibliography. - 1-8 Problems. - App. 1-1 Vector Operators. - App. 1-2 Curvilinear Coordinates. - 2 Experimental Foundation. - 2-1 Fields. - 2-2 Coulomb's Law. - 2-3 Ampè re's Laws for the Magnetic Field. - 2-4 Faraday's Induction Law. - 2-5 Maxwells Equations. - 2-6 A Mechanical Model of the Electromagnetic Field. - 2-7 The Michelson-Morley Experiment. - 2-8 Systems of Units. - 2-9 Selected Bibliography. - 2-10 Problems. - App. 2-1 Field Plotter in 2-D. - 3 Dielectric and Magnetic Materials and Boundary Conditions. - 3-1 Dielectric Materials. - 3-2 Currents. - 3-3 Magnetic Materials. - 3-4 Boundary Conditions. - 3-5 Some Mathematical Aspects of Boundary Conditions. - 3-6 Selected Bibliography. - 3-7 Problems. - 4 Electromagnetic Equations. - 4-1 Tensor Notation. - 4-2 Integral Theorems. - 4-3 Relativity: A New Kinematics. - 4-4 The Electromagnetic Field. - 4-5 Electromagnetic Potentials and Gauge Conditions. - 4-6 Lorentz Transformed Fields. - 4-7 The Lagrangian Method. - 4-8 Selected Bibliography. - 4-9 Problems. - App. 4-1 Lorentz Transformation of the Field Tensor. - 5 Electromagnetic Fields in Steady States. - 5-1 Steady-State Equations. - 5-2 Multipole Expansion. - 5-3 Laplace's Equation: Separation of Variables. - 5-4 The Cauchy-Riemann Equations and Conformal Mapping. - 5-5 Numerical Solutions by Finite-Element Analysis. - 5-6 Magnetic Fields. - 5-7 Selected Bibliography. - 5-8 Problems. - App. 5-1 Relaxation Solution of Laplaces Equation. - App. 5-2 Gram-Schmidt Orthogonalization. - App. 5-3 Schwartz Transformations. - App. 5-4 Fourier Series. - App. 5-5 Laplace Equation. - 6Radiation and Optics in Dielectric Media. - 6-1 Wave Equation in Uniform Media. - 6-2 Spherical Waves. - 6-3 Radiation in Conductive and Dispersive Media. - 6-4 Refraction and Reflection at a Dielectric Boundary. - 6-5 Momentum and Energy. - 6-6 Huygens' Principle and Diffraction. - 6-7 Selected Bibliography. - 6-8 Problems. - App. 6-1 Bessel and Legendre Functions. - App. 6-2 Multipole Radiation Patterns. - App. 6-3 Single Slit Diffraction by Helmholtz Integral. - App. 6-4 The Electromagnetic Stress Tensor. - 7 Particle Motion in Electromagnetic Fields. - 7-1 Uniform Fields. - 7-2 Numerical Solutions. - 7-3 An Example: Particle Optics. - 7-4 Velocity Field Model of Single Particle Kinematics. - 7-5 Cross Sections. - 7-6 Selected Bibliography. - 7 Problems. - App. 7-1 Finite-Element Solution of a Differential Equation Using a Spreadsheet. - App. 7-2 Taylor Series Solutions of Differential Equations. - 8 Radiation by Moving Charges. - 8-1 Multipole Expansion. - 8-2 A Physical Model. - 8-3 Frequency Analysis of Radiation. - 8-4 Calculating with Delta Functions. - 8-5 Radiation by Charged Particles. - 8-6 Selected Bibliography. - 7 Problems. - App. 8-1 Radiation by a Fast Charged Particle. - App. 8-2 Tensor Potentials. - 9 Beyond the Classical Theory. - 9-1 Radiation Reaction. - 9-2 Classical Models of the Electron. - 9-3 Quantization. - 9-4 Unification with Weak Interactions. - 9-5 Selected Bibliography.
