CLASSICAL ELECTRICITY

Transcription

1 CLASSICAL ELECTRICITY AND MAGNETISM by WOLFGANG K. H. PANOFSKY Stanford University and MELBA PHILLIPS Washington University SECOND EDITION ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo Park, California London Sydney Manila

2 CHAPTER 1. THE ELECTROSTATIC FIELD IN VACUUM Vector fields The electric field Coulomb's law The electrostatic potential The potential in terms of charge distribution Field singularities Clusters of point charges Dipole interactions Surface singularities Volume distributions of dipole moment 23 CHAPTER 2. BOUNDARY CONDITIONS AND RELATION OF MICROSCOPIC TO MACROSCOPIC FIELDS The displacement vector Boundary conditions The electric field in a material medium Polarizability 38 CHAPTER 3. GENERAL METHODS FOR THE SOLUTION OF POTENTIAL PROBLEMS Uniqueness theorem Green's reciprocation theorem Solution by Green's function Solution by inversion Solution by electrical images Solution of Laplace's equation by the separation of variables 53 CHAPTER 4. TWO-DIMENSIONAL POTENTIAL PROBLEMS Conjugate complex functions Capacity and field strength The potential of a uniform field The potential of a line charge Complex transformations General Schwarz transformation Single-angle transformations Multiple-angle transformations Direct solution of Laplace's equation by the method of harmonics Illustration: Line charge and dielectric cylinder Line charge in an angle between two conductors 77 ix

3 X CHAPTER 5. THREE-DIMENSIONAL POTENTIAL PROBLEMS The solution of Laplace's equation in spherical coordinates The potential of a point charge The potential of a dielectric sphere and a point charge The potential of a dielectric sphere in a uniform field The potential of an arbitrary axially-symmetric spherical potential distribution The potential of a charged ring Problems not having axial symmetry The solution of Laplace's equation in cylindrical coordinates Application of cylindrical solutions to potential problems.. 91 CHAPTER 6. ENERGY RELATIONS AND FORCES IN THE ELECTRO STATIC FIELD Field energy in free space Energy density within a dielectric Thermodynamic interpretation of U Thomson's theorem Maxwell stress tensor Volume forces in the electrostatic field in the presence of dielectrics The behavior of dielectric liquids in an electrostatic field.. Ill CHAPTER 7. STEADY CURRENTS AND THEIR INTERACTION Ohm's law Electromotive force The solution of stationary current problems Time of relaxation in a homogeneous medium The magnetic interaction of steady line currents The magnetic induction field The magnetic scalar potential The magnetic vector potential Types of currents Polarization currents Magnetic moments Magnetization and magnetization currents Vacuum displacement current 135 CHAPTER 8. MAGNETIC MATERIALS AND BOUNDARY VALUE PROBLEMS Magnetic field intensity Magnetic sources Permeable media: magnetic susceptibility and boundary conditions Magnetic circuits 145

4 XI 8-5 Solution of boundary value problems by magnetic scalar potentials Uniqueness theorem for the vector potential The use of the vector potential in the solution of problems The vector potential in two dimensions The vector potential in cylindrical coordinates 153 CHAPTER 9. MAXWELL'S EQUATIONS Faraday's law of induction Maxwell's equations for stationary media Faraday's law for moving media Maxwell's equations for moving media Motion of a conductor in a magnetic field 165 CHAPTER 10. ENERGY, FORCE, AND MOMENTUM RELATIONS IN THE ELECTROMAGNETIC FIELD Energy relations in quasi-stationary current systems Forces on current systems Inductance Magnetic volume force General expressions for electromagnetic energy Momentum balance 181 CHAPTER 11. THE WAVE EQUATION AND PLANE WAVES The wave equation Plane waves Radiation pressure Plane waves in a moving medium Reflection and refraction at a plane boundary Waves in conducting media and metallic reflection Group velocity 202 CHAPTER 12. CONDUCTING FLUIDS IN A MAGNETIC FIELD (MAGNETOHYDRODYNAMICS) "Frozen-in" lines of force Magnetohydrodynamic waves 207 CHAPTER 13. WAVES IN THE PRESENCE OF METALLIC BOUNDARIES The nature of metallic boundary conditions Eigenfunctions and eigenvalues of the wave equation Cavities with rectangular boundaries Cylindrical cavities Circular cylindrical cavities Waveguides Scattering by a circular cylinder 226

5 xii 13-8 Spherical waves Scattering by a sphere 233 CHAPTER 14. THE INHOMOGENEOUS WAVE EQUATION The wave equation for the potentials Solution by Fourier analysis The radiation fields Radiated energy The Hertz potential Computation of radiation fields by the Hertz method Electric dipole radiation Multipole radiation Derivation of multipole radiation from scalar superpotentials Energy and angular momentum radiated by multipoles CHAPTER 15. THE EXPERIMENTAL BASIS FOR THE THEORY OF SPECIAL RELATIVITY Galilean relativity and electrodynamics The search for an absolute ether frame The Lorentz-Fitzgerald contraction hypothesis "Ether drag" Emission theories Summary 283 CHAPTER 16. RELATIVISTIC KINEMATICS AND THE LORENTZ TRANSFORMATION The velocity of light and simultaneity Kinematic relations in special relativity The Lorentz transformation Geometric interpretations of the Lorentz transformation Transformation equations for velocity 301 CHAPTER 17. COVARIANCE AND RELATIVISTIC MECHANICS The Lorentz transformation of a four-vector Some tensor relations useful in special relativity The conservation of momentum Relation of energy to momentum and to mass The Minkowski force The collision of two similar particles The use of four-vectors in calculating kinematic relations for collisions 320 CHAPTER 18. COVARIANT FORMULATION OF ELECTRODYNAMICS The four-vector potential The electromagnetic field tensor The Lorentz force in vacuum 331

6 Xlll 18-4 Covariant description of sources in material media The field equations in a material medium Transformation properties of the partial fields 336 CHAPTER 19. THE LIENARD-WIECHERT POTENTIALS AND THE FIELD OF A UNIFORMLY MOVING ELECTRON The Lienard-Wiechert potentials The fields of a charge in uniform motion Direct solution of the wave equation The "convection potential" The virtual photon concept 350 CHAPTER 20. RADIATION FROM AN ACCELERATED CHARGE Fields of an accelerated charge Radiation at low velocity The case of ü parallel to u Radiation when the acceleration is perpendicular to the velocity (radiation from circular orbits) Radiation with no restrictions on the acceleration or velocity Classical cross section for bremsstrahlung in a Coulomb field Cerenkov radiation 373 CHAPTER 21. RADIATION REACTION AND COVARIANT FORMULATION OF THE CONSERVATION LAWS OF ELECTRODYNAMICS Covariant formulation of the conservation laws of vacuum electrodynamics Transformation properties of the "free" radiation field The electromagnetic energy momentum tensor in material media Electromagnetic mass Electromagnetic mass qualitative considerations The reaction necessary to conserve radiated energy Direct computation of the radiation reaction from the retarded fields Properties of the equation of motion Covariant description of the mechanical properties of the electromagnetic field of a charge The relativistic equations of motion The integration of the relativistic equation of motion Modification of the theory of radiation to eliminate divergent mass integrals. Advanced potentials Direct calculation of the relativistic radiation reaction CHAPTER 22. RADIATION, SCATTERING, AND DISPERSION Radiative damping of a charged harmonic oscillator Forced vibrations Scattering by an individual free electron 404

7 XIV 22-4 Scattering by a bound electron Absorption of radiation by an oscillator Equilibrium between an oscillator and a radiation field Effect of a volume distribution x>f scatterers Scattering from a volume distribution. Rayleigh scattering The dispersion relation A general theorem on scattering and absorption 419 CHAPTER 23. THE MOTION OF CHARGED PARTICLES IN ELECTRO MAGNETIC FIELDS ' World-line description Hamiltonian formulation and the transition to threedimensional formalism Equations for the trajectories Applications The motion of a particle with magnetic moment in an electromagnetic field 437 CHAPTER 24. HAMILTONIAN FORMULATION OF MAXWELL'S EQUATIONS Transition to a one-dimensional continuous system Generalization to a three-dimensional continuum The electromagnetic field Periodic solutions in a box. Plane wave representation APPENDIX I. UNITS AND DIMENSIONS IN ELECTROMAGNETIC THEORY. 459 Tables: 1-1. Conversion Factors Fundamental Electromagnetic Relations Valid in vacuo as They Appear in the Various Systems of Units Definition of Fields from Sources (mks system) Useful Numerical Relations 469 APPENDIX II. USEFUL VECTOR RELATIONS 470 Table II-l. Vector Formulas 470 APPENDIX III. VECTOR RELATIONS IN CURVILINEAR COORDINATES Table III 1. Coordinate Systems 475 BIBLIOGRAPHY 479 INDEX 485