第1章静止电荷电场(之一)

Chapter1 ElectricFieldsofStaticCharges ElectricChargesCoulomb sLawTheElectricFieldElectricFieldofaPointChargeElectricFieldofaBunchofChargesElectricFieldofaContinuousChargeDistribution Today sAgenda ElectricCharges Arosinrodrubbedwithfurissuspendedbyathread Aglassrodrubbedwithsilkisbroughtneartherosinrod Therosinrodisattractedtowardtheglassrod Iftwochargedrosinrods ortwochargedglassrods arebroughtneareachother therosinrod orglassrod isrepelledbytheotherrosinrod orglassrod ElectricCharges DuFay sexplanation 法国科学家杜菲的解释 Thereexisttwokindsofchargesinnature Oneisvitreous 玻璃型 theotherisresinous 松脂型 Unlikechargesattract likechargesrepel 异种电荷相吸 同种电荷相斥 PropertiesofElectricCharges Thisisanimportantpropertyofelectriccharges PropertiesofElectricCharges ConventionssuggestedbyB Franklin 1706 1790 美国独立宣言的起草人之一 避雷针的发明人 Theelectricchargeontheglassrodiscalledpositive Theelectricchargeontherosinrodiscallednegative Franklin sfamouskiteexperiment PropertiesofElectricCharges Chargeisconserved 电荷守恒 Foranisolatedsystem 孤立系统 thealgebraicsumofthequantityofthepositiveandnegativechargeskeepsconstantatanytime Animportantpropertyofelectriccharges PropertiesofElectricCharges Chargeisquantized 电荷的量子性 Electricchargealwaysoccursassomeintegralmultipleofsomefundamentalunitofcharge e 1 602 10 19C Thusq Ne AnimportantpropertyofelectricchargesdiscoveredbyRobertMillikanin1909 PropertiesofElectricCharges Atomismadeupofthreeelementaryparticles Protonhasoneunitofpositivecharge e Electronhasoneunitofnegativecharge e Neutronhasnonetcharge QuarkModel Viewedmacroscopically Neutronisneutral PropertiesofElectricCharges Relativisticinvarianceofelectriccharge 电荷的相对论不变性 Theelectricquantityofanelectricchargeisindependentofthestateofmotion Animportantpropertyofelectriccharges PointCharge orParticleCharge 点电荷 It sanidealizedmodel It samathematicalpoint nosizeandnoshape Ithaschargeandmass Dealwithitregardlessofthedistributionofcharge Isitlikeparticle 质点 whichwementionedinMechanics Coulomb sLaw Inverse squareforcelawforelectricity Inaninertialframeofreference theforcebetweentwosmallstationarypointchargesinvacuumisintheinverseratioofthesquaresofthedistancebetweenthetwoparticlesandisproportionaltotheproductofthechargesq1andq2 It sattractiveifq1andq2areofoppositesignandrepulsiveifsamesign Coulomb sLaw SIUnits rinmeters m qincoulombs C inNewtons N isaunitvectorpointingfromq2toq1 CommentsonCoulomb sLaw Thisforcehassamespatialdependenceasthegravitationalforce Thestrengthoftheforcebetweentwoparticlechargesisdeterminedbythechargeandtheseparationbetweenthem TheCoulomb sLawappliesexactlyonlytopointchargesinvacuum TheCoulomb sforceisacentralforce 有心力 CommentsonCoulomb sLaw Theexponent 2 inCoulomb sLawhasbeenshowntobeaccurateto1partin1016 thatis TheCoulomb sforceisvalidwhiletheorderofmagnitudeofrisbetweenand Gravitationalvs ElectricalForce Whathappenswhenyouconsidermorethantwoparticlecharges Whatistheforceonqwhenbothq1andq2arepresent Ifq1weretheonlyothercharge wewouldknowtheforceonqduetoq1 Ifq2weretheonlyothercharge wewouldknowtheforceonqduetoq2 Morethantwoparticlecharges Justasinmechanics wehavetheSuperpositionprincipleofCoulomb sforce it sanexperimentallyobservedfact TheTOTALFORCEonaparticlechargeisjusttheVECTORSUMoftheindividualforcesduetootherparticlecharges Parallelogramruleofvectoraddition Example q0 q1 andq2areallpointchargeswhereq0 1mC q1 3mC andq2 4mC Theirlocationsareshowninthediagram Whatistheforceactingonq0 Example Example Example Let sputinthenumbers q0 1mC q1 3mC q2 4mCx0 1cm x2 5cm y0 3cm y2 0r01 3cm r02 5cm AnotherExample Supposeyourfriendcanpushhisarmsapartwithaforceof100lbf 磅力 Howmuchchargecanheholdoutstretched Electricfield Whatistheelectricforcetransferredby AFIELDissomethingthatcanbedefinedanywhereinspace WhatIsField Afieldrepresentssomephysicalquantity e g temperature windspeed force Itcanbeascalarfield e g Temperaturefield Itcanbeavectorfield e g Electricfield Itcanbeatensor 张量 field e g Space timecurvatureGac AScalarField Theseisolatedtemperaturessamplethescalarfield youonlylearnthetemperatureatthepointyouchoose butTisdefinedeverywhere x y AVectorField Itmaybemoreinterestingtoknowwhichwaythewindisblowing Thatwouldrequireavectorfield youlearnbothwindspeedanddirection ElectricFieldofaPointCharge Asimple yetprofoundobservation TheCoulombforceonagivenchargeq0isalwaysproportionaltothestrengthofchargeq0 qisthesourcecharge q0isthetestcharge isaunitvectordirectedfromqtoq0 ElectricFieldofaPointCharge Wecannowdefineaquantity theelectricfield whichisindependentofthetestcharge q0 anddependsonlyonpositioninspace Asimple yetprofoundobservation ElectricField Applyingthesuperpositionprinciple wecan map theelectricfieldanywhereinspaceproducedbyanyarbitrary BunchofCharges Whereriisthedistancefromtheithchargeqi tothepointPandisaunitvectordirectedfromqitowardP ElectricField Applyingthesuperpositionprinciple wecan map theelectricfieldanywhereinspaceproducedbyanyarbitrary ContinuousChargeDistribution Whereristhedistancefromtheinfinitesimalchargeelementdq tothepointPandisaunitvectordirectedfromdqtowardP Anelectricdipole 电偶极子 isformedbyequalandoppositepointchargesseparatedbyadistancel 2a l r ElectricFieldofDipole ElectricFieldofDipole Calculateforapointalongy axis 0 y ElectricFieldofDipole NO Youmusttaketheorderofmagnitudeintoaccount Itdoesn tlookliketheresultantfieldofpointcharges qand qatorigin ElectricDipoleMoment ElectricFieldofDipole CalculatetheE fieldforapointalongx axis x 0 Examples lineofchargechargedplatesringofcharge ElectricFieldsfromContinuousChargeDistributions Approach FindtheE fieldduetopersegmentofchargedq Adduptheelectricfieldcontributionfromeachsegmentofcharge usingsuperpositionoftheresultstogetthefinalfield Howdowerepresentthecharge q onanextendedobject ChargeDensities Electricfieldfromaninfinitelinecharge Inpractice FindtheE fieldpersegmentofcharge Plantointegratealongtheline x from to q from p 2to p 2 Anysymmetries Thismayhelpforeasycancellations InfiniteLineofCharge TofindthetotalfieldE wemustintegrateoverallchargesalongtheline Ifweintegrateoverq wemustwriter anddqintermsofqanddq Theelectricfieldduetodqis Wemustwritetheintegralintermsofq InfiniteLineofCharge InfiniteLineofCharge ycomponents Integrate InfiniteLineofCharge Conclusion Theelectricfieldproducedbyaninfinitelineofchargeis everywhereperpendiculartothelineisproportionaltothechargedensitydecreasesasnextlecture Gauss Lawmakesthistrivial OtherExamples Example1 5 1 6onpage20 21 WaystoVisualizetheE Field ConsidertheE fieldofapositivepointchargeattheorigin RulesforVectorMaps Directionofarrowindicatesdirectionof Lengthofarrows localmagnitudeo