PHYSICS OF CLASSICAL ELECTROMAGNETISM
CONTENTS 1 STEADY ELECTRIC CURRENTS 1 1 INTRODUCTION 1 2 STANDARDS FOR ELECTRIC VOLTAGES AND CURRENT 1 3 OHM LAW’S AND HEAT ENERGY 1 4 THE KIRCHHOFF THEOREM PART 1 ELECTROSTATICS 2 ELECTROSTATIC FIELDS 2 1 STATIC CHARGES AND THEIR INTERACTIONS 2 2 A TRANSIENT CURRENT AND STATIC CHARGES 2 3 UNIFORM ELECTRIC FIELD IN A PARALLEL-PLATE CONDENSER 2 3 1 THE ELECTRIC FIELD VECTOR 2 3 2 THE FLUX DENSITY VECTOR 2 4 PARALLEL AND SERIES CONNECTIONS OF CAPACITORS 2 5 INSULATING MATERIALS 3 THE GAUSS THEOREM 3 1 A SPHERICAL CAPACITOR 3 2 A CYLINDRICAL CAPACITOR 3 3 THE GAUSS THEOREM 3 4 BOUNDARY CONDITIONS 3 4 1 A CONDUCTING BOUNDARY 3 4 2 A DIELECTRIC BOUNDARY 4 THE LAPLACE–POISSON EQUATIONS 4 1 THE ELECTROSTATIC POTENTIAL 4 2 THE GAUSS THEOREM IN DIFFERENTIAL FORM 4 3 CURVILINEAR COORDINATES (1) 4 4 THE LAPLACE–POISSON EQUATIONS 4 4 1 BOUNDARY CONDITIONS 4 4 2 UNIQUENESS THEOREM 4 4 3 GREEN’S FUNCTION METHOD 4 5 SIMPLE EXAMPLES 4 6 THE COULOMB POTENTIAL 4 7 POINT CHARGES AND THE SUPERPOSITION PRINCIPLE 4 7 1 AN ELECTRIC IMAGE 4 7 2 ELECTRIC DIPOLE MOMENT 4 7 3 THE DIPOLE-DIPOLE INTERACTION 5 THE LEGENDRE EXPANSION OF POTENTIALS 5 1 THE LAPLACE EQUATION IN SPHERICAL COORDINATES 5 2 SERIES EXPANSION OF THE COULOMB POTENTIAL 5 3 LEGENDRE’S POLYNOMIALS 5 4 A CONDUCTING SPHERE IN A UNIFORM FIELD 5 5 A DIELECTRIC SPHERE IN A UNIFORM FIELD 5 6 A POINT CHARGE NEAR A GROUNDED CONDUCTING SPHERE 5 7 A SIMPLE QUADRUPOLE 5 8 ASSOCIATED LEGENDRE POLYNOMIALS 5 9 MULTIPOLE POTENTIALS PART 2 ELECTROMAGNETISM 6 THE AMP`ERE LAW 6 1 INTRODUCTION 6 2 THE AMP`ERE LAW 6 3 A LONG SOLENOID 6 4 STOKES’ THEOREM 6 5 CURVILINEAR COORDINATES (2) 6 6 THE AMP`ERE LAW IN DIFFERENTIAL FORM 6 7 THE ROWLAND EXPERIMENT 7 MAGNETIC INDUCTION 7 1 LAWS OF MAGNETIC INDUCTION 7 1 1 THE FARADAY LAW 7 1 2 THE LENZ LAW 7 1 3 MAGNETIC FIELD VECTORS 7 2 DIFFERENTIAL LAW OF INDUCTION AND THE DYNAMIC ELECTRIC FIELD 7 3 MAGNETIC MOMENTS 8 SCALAR AND VECTOR POTENTIALS 8 1 MAGNETS 8 2 POHL’S MAGNETIC POTENTIOMETER 8 3 SCALAR POTENTIALS OF MAGNETS 8 3 1 A LABORATORY MAGNET 8 3 2 A UNIFORMLY MAGNETIZED SPHERE 8 4 VECTOR POTENTIALS 8 5 EXAMPLES OF STEADY MAGNETIC FIELDS 8 6 VECTOR AND SCALAR POTENTIALS OF A MAGNETIC MOMENT 8 7 MAGNETISM OF A BOHR’S ATOM 9 INDUCTANCES AND MAGNETIC ENERGIES 9 1 INDUCTANCES 9 2 SELF- AND MUTUAL INDUCTANCES 9 3 MUTUAL INTERACTION FORCE BETWEEN CURRENTS 9 4 EXAMPLES OF MUTUAL INDUCTION 9 4 1 PARALLEL CURRENTS 9 4 2 TWO RING CURRENTS 10 TIME-DEPENDENT CURRENTS 10 1 CONTINUITY OF CHARGE AND CURRENT 10 2 ALTERNATING CURRENTS 10 3 IMPEDANCES 10 4 COMPLEX VECTOR DIAGRAMS 10 5 RESONANCES 10 5 1 A FREE LC OSCILLATION 10 5 2 SERIES RESONANCE 10 5 3 PARALLEL RESONANCE 10 6 FOUR-TERMINAL NETWORKS 10 6 1 RC NETWORK 10 6 2 LOADED TRANSFORMER 10 6 3 AN INPUT-OUTPUT RELATION IN A SERIES RCL CIRCUIT 10 6 4 FREE OSCILLATION IN AN RCL CIRCUIT PART 3 ELECTROMAGNETIC WAVES 11 TRANSMISSION LINES 11 1 SELF-SUSTAINED OSCILLATORS 11 2 TRANSMISSION LINES 11 3 FOURIER TRANSFORMS 11 4 RE?ECTION AND STANDING WAVES 11 5 THE SMITH CHART 12 THE MAXWELL EQUATIONS 12 1 THE MAXWELL EQUATIONS 12 2 ELECTROMAGNETIC ENERGY AND THE POYNTING THEOREM 12 3 VECTOR AND SCALAR POTENTIALS 12 4 RETARDED POTENTIALS 12 5 MULTIPOLE EXPANSION 13 ELECTROMAGNETIC RADIATION 13 1 DIPOLE ANTENNA 13 2 ELECTRIC DIPOLE RADIATION 13 3 THE HERTZ VECTOR 13 4 A HALF-WAVE ANTENNA 13 5 A LOOP ANTENNA 13 6 PLANE WAVES IN FREE SPACE 14 THE SPECIAL THEORY OF RELATIVITY 14 1 NEWTON’S LAWS OF MECHANICS 14 2 THE MICHELSON–MORLEY EXPERIMENT 14 3 THE LORENTZ TRANSFORMATION 14 4 VELOCITY AND ACCELERATION IN FOUR-DIMENSIONAL SPACE 14 5 RELATIVISTIC EQUATION OF MOTION 14 6 THE ELECTROMAGNETIC FIELD IN FOUR-DIMENSIONAL SPACE 15 WAVES AND BOUNDARY PROBLEMS 15 1 SKIN DEPTHS 15 2 PLANE ELECTROMAGNETIC WAVES IN A CONDUCTING MEDIUM 15 3 BOUNDARY CONDITIONS FOR PROPAGATING WAVES 15 4 RE?ECTION FROM A CONDUCTING BOUNDARY 15 5 DIELECTRIC BOUNDARIES 15 6 THE FRESNEL FORMULA 16 GUIDED WAVES 16 1 PROPAGATION BETWEEN PARALLEL CONDUCTING PLATES 16 2 UNIFORM WAVEGUIDES 16 2 1 TRANSVERSAL MODES OF PROPAGATION (TE AND TM MODES) 16 2 2 TRANSVERSAL ELECTRIC-MAGNETIC MODES (TEM) 16 3 EXAMPLES OF WAVEGUIDES PART 4 COHERENT WAVES AND RADIATION QUANTA 17 WAVEGUIDE TRANSMISSION 17 1 ORTHOGONALITY RELATIONS OF WAVEGUIDE MODES 17 2 IMPEDANCES 17 3 POWER TRANSMISSION THROUGH A WAVEGUIDE 17 4 MULTIPLE RE?ECTIONS IN A WAVEGUIDE 18 RESONANT CAVITIES 18 1 SLATER’S THEORY OF NORMAL MODES 18 2 THE MAXWELL EQUATIONS IN A CAVITY 18 3 FREE AND DAMPED OSCILLATIONS 18 4 INPUT IMPEDANCE OF A CAVITY 18 5 EXAMPLE OF A RESONANT CAVITY 18 6 MEASUREMENTS OF A CAVITY RESONANCE 19 ELECTRONIC EXCITATION OF CAVITY OSCILLATIONS 19 1 ELECTRONIC ADMITTANCE 19 2 A KLYSTRON CAVITY 19 3 VELOCITY MODULATION 19 4 A RE?EX OSCILLATOR 20 DIELECTRIC AND MAGNETIC RESPONSES IN RESONANT ELECTROMAGNETIC FIELDS 20 1 INTRODUCTION 20 2 THE KRAMERS–KR¨ONIG FORMULA 20 3 DIELECTRIC RELAXATION 20 4 MAGNETIC RESONANCE 20 5 THE BLOCH THEORY 20 6 MAGNETIC SUSCEPTIBILITY MEASURED BY RESONANCE EXPERIMENTS 21 LASER OSCILLATIONS, PHASE COHERENCE, AND PHOTONS 21 1 OPTICAL RESONATORS 21 2 QUANTUM TRANSITIONS 21 3 INVERTED POPULATION AND THE NEGATIVE TEMPERATURE 21 4 AMMONIUM MASER 21 5 COHERENT LIGHT EMISSION FROM A GAS LASER 21 6 PHASE COHERENCE AND RADIATION QUANTA