I.V.SAVELYEV PHYSICS A GENERAL COURSE (Inthreevolumes) VOLUME II ELECTRICITY AND MAGNETISM WAVES OPTICS MIRPUBLISHERS MOSCOW TranslatedfromRussianbyG.Leib Firstpublished1980 Revisedfromthe1978Russianedition Secondprinting1985 Thirdprinting1989 PrintedintheUnionofSovietSocialistRepublics ISBN5-03-000902-7,1978 ISBN5-03-000900-0,1980 v PREFACE Themaincontentofthepresentvolumeisthescienceofelectromagnetismandthe scienceofwaves(elastic,electromagnetic,andlight). The International System of Units (SI) has been used throughout the book, although the reader is simultaneously acquainted with the Gaussian system. In additiontoalistofsymbols,theappendicesattheendofthebookgivetheunitsof electricalandmagneticquantitiesintheSIandintheGaussiansystemofunits,and alsocomparetheformofthebasicformulasofelectromagnetisminbothsystems. Thecourseistheresultoftwentyfiveyear’sworkintheDepartmentofGeneral PhysicsoftheMoscowInstituteofEngineeringPhysics. Iamgratefultomycol- leaguesandfriendsfortheirhelpfuldiscussions,criticismandadviceinthecourse ofthepreparationofthebook. Thepresentcourseisintendedaboveallforhighertechnicalschoolswithan extendedsyllabusinphysics.Thematerialhasbeenarranged,however,sothatthe bookcanbeusedasateachingaidforhighertechnicalschoolswithanordinary syllabussimplybyomittingsomesections. IgorSavelyev Moscow,November,1979 CONTENTS vii Contents Preface v I ELECTRICITYANDMAGNETISM 1 Chapter1. ELECTRICFIELDINAVACUUM 3 1.1 ElectricCharge 3 1.2 Coulomb’sLaw 4 1.3 SystemsofUnits 7 1.4 RationalizedFormofWritingFormulas 8 1.5 ElectricField.FieldStrength 9 1.6 Potential 12 1.7 InteractionEnergyofaSystemofCharges 16 1.8 RelationBetweenElectricFieldStrengthandPotential 17 1.9 Dipole 20 1.10 FieldofaSystemofChargesatGreatDistances 25 1.11 ADescriptionofthePropertiesofVectorFields 28 1.12 CirculationandCurlofanElectrostaticField 43 1.13 Gauss’sTheorem 45 1.14 CalculatingFieldswiththeAidofGauss’sTheorem 47 Chapter2. ELECTRICFIELDINDIELECTRICS 53 2.1 PolarandNon-PolarMolecules 53 2.2 PolarizationofDielectrics 55 2.3 TheFieldInsideaDielectric 56 2.4 SpaceandSurfaceBoundCharges 57 2.5 ElectricDisplacementVector 62 2.6 ExamplesofCalculatingtheFieldinDielectrics 65 2.7 ConditionsontheInterfaceBetweenTwoDielectrics 69 2.8 ForcesActingonaChargeinaDielectric 72 2.9 Ferroelectrics 74 Chapter3. CONDUCTORSINANELECTRICFIELD 77 3.1 EquilibriumofChargesonaConductor 77 3.2 AConductorinanExternalElectricField 80 viii CONTENTS 3.3 Capacitance 80 3.4 Capacitors 82 Chapter4. ENERGYOFANELECTRICFIELD 85 4.1 EnergyofaChargedConductor 85 4.2 EnergyofaChargedCapacitor 85 4.3 EnergyofanElectricField 88 Chapter5. STEADYELECTRICCURRENT 93 5.1 ElectricCurrent 93 5.2 ContinuityEquation 96 5.3 ElectromotiveForce 97 5.4 Ohm’sLaw.ResistanceofConductors 99 5.5 Ohm’sLawforanInhomogeneousCircuitSection 101 5.6 MultiloopCircuits.Kirchhoff’sRules 103 5.7 PowerofaCurrent 106 5.8 TheJoule-LenzLaw 107 Chapter6. MAGNETICFIELDINAVACUUM 109 6.1 InteractionofCurrents 109 6.2 MagneticField 112 6.3 FieldofaMovingCharge 113 6.4 TheBiot-SavartLaw 116 6.5 TheLorentzForce 119 6.6 Ampere’sLaw 122 6.7 MagnetismasaRelativisticEffect 124 6.8 CurrentLoopinaMagneticField 130 6.9 MagneticFieldofaCurrentLoop 135 6.10 WorkDoneWhenaCurrentMovesinaMagneticField 138 6.11 DivergenceandCurlofaMagneticField 142 6.12 FieldofaSolenoidandToroid 146 Chapter7. MAGNETICFIELDINASUBSTANCE 151 7.1 MagnetizationofaMagnetic 151 7.2 MagneticFieldStrength 152 7.3 CalculationoftheFieldinMagnetics 158 7.4 ConditionsattheInterfaceofTwoMagnetics 160 7.5 KindsofMagnetics 164 7.6 GyromagneticPhenomena 164 7.7 Diamagnetism 169 7.8 Paramagnetism 173 7.9 Ferromagnetism 175 Chapter8. ELECTROMAGNETICINDUCTION 181 8.1 ThePhenomenonofElectromagneticInduction 181 8.2 InducedE.M.F. 182 8.3 WaysofMeasuringtheMagneticInduction 186 8.4 EddyCurrents 187 8.5 Self-Induction 189 CONTENTS ix 8.6 CurrentWhenaCircuitIsOpenedorClosed 191 8.7 MutualInduction 194 8.8 EnergyofaMagneticField 196 8.9 WorkinMagneticReversalofaFerromagnetic 198 Chapter9. MAXWELL’SEQUATIONS 201 9.1 VortexElectricField 201 9.2 DisplacementCurrent 203 9.3 Maxwell’sEquations 207 Chapter10. MOTIONOFCHARGEDPARTICLESINELECTRIC ANDMAGNETICFIELDS 211 10.1 MotionofaChargedParticleinaHomogeneousMagneticField 211 10.2 DeflectionofMovingChargedParticlesbyanElectricandaMagneticField 213 10.3 DeterminationoftheChargeandMassofanElectron 216 10.4 DeterminationoftheSpecificChargeofIons.MassSpectrographs 221 10.5 ChargedParticleAccelerators 225 Chapter11. THECLASSICALTHEORYOFELECTRICALCONDUCTANCE OFMETALS 231 11.1 TheNatureofCurrentCarriersinMetals 231 11.2 TheElementaryClassicalTheoryofMetals 233 11.3 TheHallEffect 237 Chapter12. ELECTRICCURRENTINGASES 241 12.1 Semi-Self-SustainedandSelf-SustainedConduction 241 12.2 Semi-Self-SustainedGasDischarge 241 12.3 IonizationChambersandCounters 245 12.4 ProcessesLeadingtotheAppearanceofCurrentCarriers 250 12.5 Gas-DischargePlasma 254 12.6 GlowDischarge 256 12.7 ArcDischarge 259 12.8 SparkandCoronaDischarges 260 Chapter13. ELECTRICALOSCILLATIONS 265 13.1 QuasistationaryCurrents 265 13.2 FreeOscillationsinaCircuitWithoutaResistance 266 13.3 FreeDampedOscillations 269 13.4 ForcedElectricalOscillations 273 13.5 AlternatingCurrent 277 II WAVES 281 Chapter14.ELASTICWAVES 283 14.1 PropagationofWavesinanElasticMedium 283 14.2 EquationsofaPlaneandaSphericalWave 286 14.3 EquationofaPlaneWavePropagatinginanArbitraryDirection 289 x CONTENTS 14.4 TheWaveEquation 291 14.5 VelocityofElasticWavesinaSolidMedium 292 14.6 EnergyofanElasticWave 294 14.7 StandingWaves 299 14.8 OscillationsofaString 302 14.9 Sound 303 14.10 TheVelocityofSoundinGases 306 14.11 TheDopplerEffectforSoundWaves 311 Chapter15. ELECTROMAGNETICWAVES 313 15.1 TheWaveEquationforanElectromagneticField 313 15.2 PlaneElectromagneticWave 315 15.3 ExperimentalInvestigationofElectromagneticWaves 318 15.4 EnergyofElectromagneticWaves 319 15.5 MomentumofElectromagneticField 322 15.6 DipoleEmission 324 III OPTICS 329 Chapter16. OPTICS 331 16.1 TheLightWave 331 16.2 RepresentationofHarmonicFunctionsUsingExponents 334 16.3 ReflectionandRefractionofaPlaneWaveattheInterfaceBetweenTwo Dielectrics 336 16.4 LuminousFlux 342 16.5 PhotometricQuantitiesandUnits 343 16.6 GeometricalOptics 347 16.7 CenteredOpticalSystem 351 16.8 ThinLenses 358 16.9 Huygens’Principle 359 Chapter17. INTERFERENCEOFLIGHT 361 17.1 InterferenceofLightWaves 361 17.2 Coherence 366 17.3 WaysofObservingtheInterferenceofLight 374 17.4 InterferenceofLightReflectedfromThinPlates 376 17.5 TheMichelsonInterferometer 386 17.6 MultibeamInterference 389 Chapter18. DIFFRACTIONOFLIGHT 397 18.1 Introduction 397 18.2 Huygens-FresnelPrinciple 398 18.3 FresnelZones 401 18.4 FresnelDiffractionfromSimpleBarriers 406 18.5 FraunhoferDiffractionfromaSlit 417 18.6 DiffractionGrating 425 18.7 DiffractionofX-Rays 434