EELECTROMAGNETICFIELDTHEORYrBo ThideMEUPSNDIAIL00由
“main” 2000/11/13 page 1 ELECTRO MAGNETIC FIELD THEORY Υ Bo Thidé U P S I L O N M E D I A
ELECTROMAGNETICFIELD THEORYBo ThideSwedishInstituteof SpacePhysicsandDepartment of Astronomy and Space PhysicsUppsala University, SwedenrUPSILONMEDIAUPPSALASWEDEN④①
“main” 2000/11/13 page 1 ELECTROMAGNETIC FIELD THEORY Bo Thidé Swedish Institute of Space Physics and Department of Astronomy and Space Physics Uppsala University, Sweden Υ U P S I L O N M E D I A · U P P S A L A · S W E D E N
EContentsPrefacexi11ClassicalElectrodynamics11.1Electrostatics11.1.1Coulomb'slaw21.1.2The electrostaticfield41.2MagnetostaticsX1.2.1Ampere'slaw1.2.26The magnetostatic field81.3Electrodynamics91.3.1Equation of continuity91.3.2Maxwell'sdisplacementcurrent1.3.310Electromotiveforce111.3.4Faraday's law of induction141.3.5Maxwell'smicroscopicequations141.3.6Maxwell'smacroscopicequations151.4ElectromagneticDualityExample 1.1Duality of the electromagnetodynamic equations 16Example 1.2 Maxwell from Dirac-Maxwell equations for a17fixed mixing angle...18Example 1.3 The complex field six-vector19Example 1.4 Duality expressed in the complex field six-vector20Bibliography232Electromagnetic Waves242.1Thewaveequation242.1.1The wave equation for E2.1.224The wave equation for B252.1.3The time-independent wave equation for E2.226Planewaves272.2.1Telegrapher's equationi①由D
“main” 2000/11/13 page i Contents Preface xi 1 Classical Electrodynamics 1 1.1 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Coulomb’s law . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 The electrostatic field . . . . . . . . . . . . . . . . . . 2 1.2 Magnetostatics . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Ampère’s law . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 The magnetostatic field . . . . . . . . . . . . . . . . . 6 1.3 Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Equation of continuity . . . . . . . . . . . . . . . . . 9 1.3.2 Maxwell’s displacement current . . . . . . . . . . . . 9 1.3.3 Electromotive force . . . . . . . . . . . . . . . . . . . 10 1.3.4 Faraday’s law of induction . . . . . . . . . . . . . . . 11 1.3.5 Maxwell’s microscopic equations . . . . . . . . . . . 14 1.3.6 Maxwell’s macroscopic equations . . . . . . . . . . . 14 1.4 Electromagnetic Duality . . . . . . . . . . . . . . . . . . . . 15 Example 1.1 Duality of the electromagnetodynamic equations 16 Example 1.2 Maxwell from Dirac-Maxwell equations for a fixed mixing angle . . . . . . . . . . . . . . . 17 Example 1.3 The complex field six-vector . . . . . . . . 18 Example 1.4 Duality expressed in the complex field six-vector 19 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 Electromagnetic Waves 23 2.1 The wave equation . . . . . . . . . . . . . . . . . . . . . . . 24 2.1.1 The wave equation for E . . . . . . . . . . . . . . . . 24 2.1.2 The wave equation for B . . . . . . . . . . . . . . . . 24 2.1.3 The time-independent wave equation for E . . . . . . 25 2.2 Plane waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.1 Telegrapher’s equation . . . . . . . . . . . . . . . . . 27 i
EiiCONTENTS292.2.2Waves in conductive media302.3Observablesandaverages31Bibliography333ElectromagneticPotentials333.1The electrostatic scalar potential343.2The magnetostatic vector potential343.3The electromagnetic scalar and vector potentials363.3.1Electromagneticgauges36Lorentzequationsfortheelectromagneticpotentials36Gaugetransformations3.3.2Solution of the Lorentz equations for the electromag-38neticpotentials41The retarded potentials41Bibliography434TheElectromagnetic Fields454.1The magnetic field474.2Theelectricfield49Bibliography515.Relativistic Electrodynamics515.1The special theoryofrelativity525.1.1The Lorentz transformation535.1.2Lorentz space54Metrictensor54Radius four-vector in contravariant and covariant form55Scalarproductand norm56Invariantlineelementandpropertime57Four-vectorfields57TheLorentz transformation matrix58TheLorentzgroup585.1.3Minkowskispace615.2Covariant classical mechanics625.3Covariantclassicalelectrodynamics625.3.1The four-potential5.3.263The Lienard-Wiechert potentials655.3.3The electromagnetic field tensor67BibliographyDraftverssion released 13th November 2000 at 22:01.Downloadedfrorse/CED/Bookmhttp://①由由
“main” 2000/11/13 page ii ii CONTENTS 2.2.2 Waves in conductive media . . . . . . . . . . . . . . . 29 2.3 Observables and averages . . . . . . . . . . . . . . . . . . . . 30 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3 Electromagnetic Potentials 33 3.1 The electrostatic scalar potential . . . . . . . . . . . . . . . . 33 3.2 The magnetostatic vector potential . . . . . . . . . . . . . . . 34 3.3 The electromagnetic scalar and vector potentials . . . . . . . . 34 3.3.1 Electromagnetic gauges . . . . . . . . . . . . . . . . 36 Lorentz equations for the electromagnetic potentials . 36 Gauge transformations . . . . . . . . . . . . . . . . . 36 3.3.2 Solution of the Lorentz equations for the electromagnetic potentials . . . . . . . . . . . . . . . . . . . . . 38 The retarded potentials . . . . . . . . . . . . . . . . . 41 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4 The Electromagnetic Fields 43 4.1 The magnetic field . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 The electric field . . . . . . . . . . . . . . . . . . . . . . . . 47 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5 Relativistic Electrodynamics 51 5.1 The special theory of relativity . . . . . . . . . . . . . . . . . 51 5.1.1 The Lorentz transformation . . . . . . . . . . . . . . 52 5.1.2 Lorentz space . . . . . . . . . . . . . . . . . . . . . . 53 Metric tensor . . . . . . . . . . . . . . . . . . . . . . 54 Radius four-vector in contravariant and covariant form 54 Scalar product and norm . . . . . . . . . . . . . . . . 55 Invariant line element and proper time . . . . . . . . . 56 Four-vector fields . . . . . . . . . . . . . . . . . . . . 57 The Lorentz transformation matrix . . . . . . . . . . . 57 The Lorentz group . . . . . . . . . . . . . . . . . . . 58 5.1.3 Minkowski space . . . . . . . . . . . . . . . . . . . . 58 5.2 Covariant classical mechanics . . . . . . . . . . . . . . . . . 61 5.3 Covariant classical electrodynamics . . . . . . . . . . . . . . 62 5.3.1 The four-potential . . . . . . . . . . . . . . . . . . . 62 5.3.2 The Liénard-Wiechert potentials . . . . . . . . . . . . 63 5.3.3 The electromagnetic field tensor . . . . . . . . . . . . 65 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Downloaded from http://www.plasma.uu.se/CED/Book Draft version released 13th November 2000 at 22:01
Eili69Interactions of Fields and Particles6696.1ChargedParticlesinanElectromagneticField696.1.1Covariant equations of motion69Lagrangeformalism72Hamiltonianformalism766.2CovariantFieldTheoryLagrange-Hamilton formalism for fields and interactions 776.2.180TheelectromagneticfieldExample 6.1 Field energy difference expressed in the field81tensor84Otherfields85Bibliography877InteractionsofFieldsandMatter877.1Electricpolarisationandtheelectricdisplacementvector877.1.1Electricmultipolemoments907.2Magnetisation and the magnetising field917.3Energy and momentum927.3.1The energy theorem inMaxwell's theory937.3.2Themomentumtheorem inMaxwell'stheory95Bibliography978Electromagnetic Radiation978.1Theradiationfields998.2Radiatedenergy1008.2.1Monochromatic signals8.2.2100Finitebandwidth signals8.3102Radiationfromextendedsources8.3.1102Linearantenna1048.4Multipoleradiation8.4.1104The Hertz potential8.4.2108Electricdipoleradiation8.4.3109Magnetic dipole radiation1108.4.4Electric quadrupole radiation8.5111Radiation froma localised charge inarbitrarymotion1128.5.1TheLienard-Wiechert potentials8.5.2114Radiationfromanacceleratedpointcharge121Example 8.1 The fields from a uniformly moving chargeExample8.2Theconvectionpotential and theconvection123forceDraft vered13thNoyber2000at 22:01.Downloadedfromhttp://ww.plase/CED/Book①由④
“main” 2000/11/13 page iii iii 6 Interactions of Fields and Particles 69 6.1 Charged Particles in an Electromagnetic Field . . . . . . . . . 69 6.1.1 Covariant equations of motion . . . . . . . . . . . . . 69 Lagrange formalism . . . . . . . . . . . . . . . . . . 69 Hamiltonian formalism . . . . . . . . . . . . . . . . . 72 6.2 Covariant Field Theory . . . . . . . . . . . . . . . . . . . . . 76 6.2.1 Lagrange-Hamilton formalism for fields and interactions 77 The electromagnetic field . . . . . . . . . . . . . . . . 80 Example 6.1 Field energy difference expressed in the field tensor . . . . . . . . . . . . . . . . . . . . . 81 Other fields . . . . . . . . . . . . . . . . . . . . . . . 84 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7 Interactions of Fields and Matter 87 7.1 Electric polarisation and the electric displacement vector . . . 87 7.1.1 Electric multipole moments . . . . . . . . . . . . . . 87 7.2 Magnetisation and the magnetising field . . . . . . . . . . . . 90 7.3 Energy and momentum . . . . . . . . . . . . . . . . . . . . . 91 7.3.1 The energy theorem in Maxwell’s theory . . . . . . . 92 7.3.2 The momentum theorem in Maxwell’s theory . . . . . 93 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 8 Electromagnetic Radiation 97 8.1 The radiation fields . . . . . . . . . . . . . . . . . . . . . . . 97 8.2 Radiated energy . . . . . . . . . . . . . . . . . . . . . . . . . 99 8.2.1 Monochromatic signals . . . . . . . . . . . . . . . . . 100 8.2.2 Finite bandwidth signals . . . . . . . . . . . . . . . . 100 8.3 Radiation from extended sources . . . . . . . . . . . . . . . . 102 8.3.1 Linear antenna . . . . . . . . . . . . . . . . . . . . . 102 8.4 Multipole radiation . . . . . . . . . . . . . . . . . . . . . . . 104 8.4.1 The Hertz potential . . . . . . . . . . . . . . . . . . . 104 8.4.2 Electric dipole radiation . . . . . . . . . . . . . . . . 108 8.4.3 Magnetic dipole radiation . . . . . . . . . . . . . . . 109 8.4.4 Electric quadrupole radiation . . . . . . . . . . . . . . 110 8.5 Radiation from a localised charge in arbitrary motion . . . . . 111 8.5.1 The Liénard-Wiechert potentials . . . . . . . . . . . . 112 8.5.2 Radiation from an accelerated point charge . . . . . . 114 Example 8.1 The fields from a uniformly moving charge . 121 Example 8.2 The convection potential and the convection force . . . . . . . . . . . . . . . . . . . . . 123 Draft version released 13th November 2000 at 22:01. Downloaded from http://www.plasma.uu.se/CED/Book