ELEMENTARY ELECTROMAGNETIC THEORY: STEADY ELECTRIC FIELDS AND CURRENTS

By S. HIMAA

1 1 STATIC CHARGES 1 1 1 THE ELECTROSTATIC FORCE 1 1 3 GAUSS’LAW 1 1 4 THE ELECTRIC POTENTIAL 1 2 MOVING CHARGES 1 2 1 THE CONTINUITY EQUATION 1 2 2 MAGNETIC FORCES 1 2 4 AMP`ERE’S LAW 1 2 6 THE MAGNETIC SCALAR POTENTIAL EXERCISES AND PROBLEMS 2 1 MULTIPOLE MOMENTS 2 1 1 THE CARTESIAN MULTIPOLE EXPANSION 2 2 INTERACTIONS WITH THE FIELD 2 2 2 MAGNETIC DIPOLES 2 3 POTENTIAL ENERGY EXERCISES AND PROBLEMS CHAPTER 3—SLOWLY VARYING FIELDS IN VACUUM 3 1 MAGNETIC INDUCTION 3 1 3 TIME-DEPENDENT MAGNETIC FIELDS 3 1 4 FARADAY’S LAW 3 2 DISPLACEMENT CURRENT 3 3 MAXWELL’S EQUATIONS 3 4 THE POTENTIALS 3 4 1 THE LORENTZ FORCE AND CANONICAL MOMENTUM 3 4 2 GAUGE TRANSFORMATIONS 3 5 1 PLANE WAVES 3 5 2 SPHERICAL WAVES 4 1 1 STATIONARY CHARGES 4 1 3 FORCES ON CHARGE DISTRIBUTIONS 4 3 MOMENTUM OF THE FIELDS 4 3 1 THE CARTESIAN MAXWELL STRESS TENSOR 4 3 2 THE MAXWELL STRESS TENSOR AND MOMENTUM 4 4 MAGNETIC MONOPOLES CHAPTER 5—STATIC POTENTIALS IN VACUUM – LAPLACE’S EQUATION 5 1 2 ?2V = 0 IN ONE DIMENSION 5 2 ?2V = 0 IN TWO DIMENSIONS 5 2 1 CARTESIAN COORDINATES IN TWO DIMENSIONS 5 2 2 PLANE POLAR COORDINATES 5 2 3 SPHERICAL POLAR COORDINATES WITH AXIAL SYMMETRY 5 2 6 CAPACITANCE 5 2 7 NUMERICAL SOLUTION 5 3 ?2V = 0 IN THREE DIMENSIONS CHAPTER 6—STATIC POTENTIALS WITH SOURCES–POISSON’S EQUATION 6 1 POISSON’S EQUATION 6 2 IMAGE CHARGES 6 2 1 THE IN?NITE CONDUCTING PLANE 6 3 GREEN’S FUNCTIONS 6 3 1 GREEN’S THEOREM 6 3 2 POISSON’S EQUATION AND GREEN’S THEOREM 6 3 3 EXPANSION OF THE DIRICHLET GREEN’S FUNCTION IN SPHERICAL HARMONICS 6 3 4 DIRICHLET GREEN’S FUNCTION FROM DI?ERENTIAL EQUATION CHAPTER 7—STATIC ELECTROMAGNETIC FIELDS IN MATTER 7 1 THE ELECTRIC FIELD DUE TO A POLARIZED DIELECTRIC 7 1 1 EMPIRICAL DESCRIPTION OF DIELECTRICS 7 1 2 ELECTRIC DISPLACEMENT FIELD 7 2 MAGNETIC INDUCTION FIELD DUE TO A MAGNETIZED MATERIAL 7 2 1 MAGNETIC FIELD INTENSITY 7 3 MICROSCOPIC PROPERTIES OF MATTER 7 3 1 POLAR MOLECULES (LANGEVIN-DEBYE FORMULA) 7 3 2 NONPOLAR MOLECULES 7 3 3 DENSE MEDIA—THE CLAUSIUS-MOSOTTI EQUATION 7 3 4 CRYSTALLINE SOLIDS 7 3 5 SIMPLE MODEL OF PARAMAGNETICS AND DIAMAGNETICS 7 3 6 CONDUCTION 7 4 BOUNDARY CONDITIONS FOR THE STATIC FIELDS 7 5 3 MAGNETOSTATICS AND MAGNETIC POLES 7 7 MAGNETIC CIRCUITS 7 7 1 MAGNETIC CIRCUITS CONTAINING A PERMANENT MAGNET 7 7 2 THE HYSTERESIS CURVE OF A FERROMAGNET CHAPTER 8—TIME DEPENDENT ELECTRIC FIELDS IN MATTER 8 1 MAXWELL’S EQUATIONS 8 2 ENERGY AND MOMENTUM IN THE FIELDS 8 2 1 ENERGY OF ELECTRIC AND MAGNETIC FIELDS 8 2 2 MOMENTUM AND THE MAXWELL STRESS TENSOR 8 2 3 BLACKBODY RADIATION PRESSURE 8 3 THE ELECTROMAGNETIC POTENTIALS 8 4 PLANE WAVES IN MATERIAL MEDIA 8 4 1 PLANE WAVES IN LINEAR, ISOTROPIC DIELECTRICS 8 4 2 RE?ECTION AND REFRACTION—SNELL’S LAW 8 4 3 FRESNEL’S EQUATIONS 8 4 4 THE EVANESCENT WAVE 8 4 8 SIMPLE MODEL FOR THE FREQUENCY DEPENDENCE OF DIELECTRIC SUSCEPTIBILITY 8 4 9 SIMPLE MODEL OF A CONDUCTOR IN AN OSCILLATING FIELD CHAPTER 9—WAVEGUIDE PROPAGATION – BOUNDED WAVES 9 1 BOUNDED WAVES 9 1 1 TE MODES IN A RECTANGULAR WAVEGUIDE 9 2 1 CIRCULAR CYLINDRICAL WAVEGUIDES 9 2 2 RESONANT CAVITIES 9 3 DIELECTRIC WAVEGUIDES (OPTICAL FIBERS) 9 3 1 HE MODES 10 1 THE INHOMOGENEOUS WAVE EQUATION 10 1 1 SOLUTION BY FOURIER ANALYSIS 10 1 2 GREEN’S FUNCTION FOR THE INHOMOGENEOUS WAVE EQUATION 10 2 RADIATION FROM A LOCALIZED OSCILLATING SOURCE 10 2 1 ELECTRIC DIPOLE RADIATION 10 2 2 MAGNETIC DIPOLE AND ELECTRIC QUADRUPOLE RADIATION 10 2 3 RADIATION BY HIGHER ORDER MOMENTS 10 2 4 ENERGY AND ANGULAR MOMENTUM OF THE MULTIPOLE FIELDS 10 3 THE LI´ENARD-WIECHERT POTENTIALS 10 3 3 RADIATION FROM SLOWLY MOVING CHARGES 10 3 4 THOMPSON SCATTERING 10 3 7 BREMSTRAHLUNG AND CHERENKOV RADIATION CHAPTER 11—THE COVARIANT FORMULATION 11 1 THE FOUR-POTENTIAL AND COULOMB’S LAW 11 2 1 MAGNETIZATION AND POLARIZATION 11 4 THE STRESS-ENERGY-MOMENTUM TENSOR 11 5 RADIATION FROM RELATIVISTIC PARTICLES 12 1 ELECTROMAGNETIC INERTIA 12 2 THE REACTION FORCE NEEDED TO CONSERVE ENERGY 12 3 DIRECT CALCULATION OF RADIATION REACTION – THE ABRAHAM-LORENTZ MODEL 12 4 THE EQUATION OF MOTION