重邮大学物理英文 .pptx
2023/3/271(1)Thetangentdirectionateverypointonanelectricfieldlineisjustthedirectionofthefieldintensityatthatpointorthedirectionoftheforceonthepositivepointchargeatthatpoint.(2)Theelectricfieldlinesaredenserintheplacewherethefieldintensityisstronger,andtheelectricfieldlinesaresparserintheplacewherethefieldintensityisweaker.(3)Theelectricfieldlinesstartonpositivechargesandterminateonnegativecharges,andneverintersectedeachother.Itisneverinterruptedinregionwithoutcharge;thisiscalledthecontinuityofelectricfieldline.(4)Keepinmind:electricfieldlinesdonotactuallyexist.第1页/共57页2023/3/272+Forapositivepointcharge,thelinesaredirectedradiallyoutward.Foranegativepointcharge,thelinesaredirectedradiallyinward.第2页/共57页+Theelectricfieldlinesfortwochargesofequalmagnitudeandoppositesign(anelectricdipole)NOTE:thenumberoflinesleavingthepositivechargeequalsthenumberterminatingatthenegativecharge.第3页/共57页+Theelectricfieldlinesfortwopositivepointcharges.第4页/共57页2qq+Theelectricfieldlinesforapointcharge+2qandasecondpointchargeq.第5页/共57页+第6页/共57页Ring Amount2023/3/277Flux Amount2.ElectricFlux e第7页/共57页SS1.Uniformelectricfield2.Uniformelectricfield=S3.Nonuniformelectricfield,arbitrarysurfacedSUNIT：Vm第8页/共57页2023/3/279Where 第9页/共57页2023/3/2710Aclosedsurfaceisdefinedasonethatcompletelydividesspaceintoaninsideregionandoutsideregion,sothatmovementcannottakeplacefromoneregiontotheotherwithoutpenetratingthesurface.Foraclosedsurface,usuallydefinethenormallineateverypointonthesurfacepointsoutoftheclosedsurfaceAclosedsurfaceAopensurface第10页/共57页2023/3/2711 =0 0 0nn第11页/共57页AttentionMIfthesurfacesisclosed,Ifthesurfaceisunclosed,thepositivenormaldirectioncanbefreechosen.isascalar.ItsSIunit:Nm2/C.Accordingtotheconvention,outwardtheclosedsurface;,inwardtheclosedsurface.第12页/共57页2023/3/2713Thereisacubesurfaceofedgelengthaintheuniformelectricfield（isaconstant）asshowninfigure.Findtheelectricfluxofeveryplaneandthecubesurface.ExampleXYZ第13页/共57页2023/3/2714Gaussworkedinawidevarietyoffieldsinbothmathematicsandphysicsincludingnumbertheory,analysis,differentialgeometry,geodesy,magnetism,astronomyandoptics.Hisworkhashadanimmenseinfluenceinmanyareas.SometimesknownastheprinceofmathematiciansandgreatestmathematiciansinceantiquityJohannCarlFriedrichGauss1777-18553.GAUSSS LAW第14页/共57页2023/3/2715Thenetelectricfluxofanarbitraryclosedsurface inthevacuumisequaltothenetchargeinsidethesurfacedividedby.(1)GAUSSSLAW第15页/共57页2023/3/2716S：Theclosedsurface,i.e.gaussiansurface.Itisanimaginarysurfaceandneednotcoincidewithanyrealphysicalsurface.isthetotalelectricfieldatanypointonthesurfaceduetoallcharges.Surfaceelement.Itsorientationisperpendiculartothesurfaceandpointsoutwardfromtheinsideregion.Thealgebrasumofchargesintheclosedsurface.Theclosesurfaceintegralisoverallgaussiansurface.第16页/共57页2023/3/2717Itgiveasimplewaytocalculatethedistributionofelectricfieldforagivenchargedistributionwithsufficientsymmetry.第17页/共57页2023/3/2718r+q(2)ProvingAsphericalgaussiansurfaceofradiusrsurroundingapointchargeq whichisatthecentreofthesphere.Theelectricfieldisnormaltothesurfaceandconstantinmagnitudeeverywhereonthesurface.第18页/共57页2023/3/2719Asphericalgaussiansurfaceofradiusrsurroundingapointchargeq whichisnotatthecentreofthesphere.r+qO第19页/共57页2023/3/2720Anarbitrarygaussiansurfacesurroundingapointchargeq.+S1S2Thenetelectricfluxthrougheachsurfaceisthesame.第20页/共57页2023/3/2721+Sq1+q2+q3+Therearemanychargesinsidetheguassiansurface.第21页/共57页2023/3/2722+qApointchargelocatedoutsideaclosedsurface.Thenumberoflinesenteringthesurfaceequalsthenumberleavingthesurface.Thenetelectricfluxthroughaclosedsurfacethatsurroundsnonetchargeiszero.Zerofluxisnotzerofield.第22页/共57页2023/3/2723ConclusionThenetfluxthroughanyclosedsurfacesurroundingthepointchargeqisgivenbyAsystemofchargesContinuousdistributionofcharges第23页/共57页2023/3/2724(3)PhysicalMeaningThepositivechargeisthesourceoftheelectrostaticfield.Gaussslawisvalidfortheelectricfieldofanysystemofchargesorcontinuousdistributionofcharge.Guassslawcanbeusedtoevaluatetheelectricfieldforchargedistributionsthathavespherical,cylindrical,orplanesymmetry.Thetechniqueisusefulonlyinsituationswherethedegreeofsymmetryishigh.第24页/共57页2023/3/2725QuickQuizWhyaretheelectrostaticfieldlinesneverinterruptedinregionwithoutcharge?第25页/共57页2023/3/2726aQFindthefluxthroughthesquare.QuickQuiz第26页/共57页2023/3/2727Considerwhetherthefollowingstatementsaretruth.ElectricfluxoftheGausssurfaceisrelatedwithchargesinGausssurfaceandisnotrelatedwithchargesoutofGausssurface.ThefieldintensityatapointontheGausssurfaceisrelatedwithchargesintheGausssurfaceandisnotrelatedwithchargesoutoftheGausssurface.IftheelectricfluxofaGausssurfaceequalszero,theremustbenotchargeintheGausssurface.第27页/共57页2023/3/2728IftheelectricfluxofaGausssurfaceequalszero,thenfieldintensityateverypointontheGausssurfaceiszero.Gausstheoremistenableonlytotheelectrostaticfieldwhosedistributionissymmetricalinspace.第28页/共57页2023/3/2729(4)ApplicationofGausssLawtoSymmetricChargeDistributionThegaussiansurfaceshouldalwaysbechosentotakeadvantageofthesymmetryofthechargedistribution,sothatwecanremoveEfromtheintegralandsolveit.第29页/共57页2023/3/2730Thegaussiansurfacehadbettersatisfiesoneormoreofthefollowingconditions:Thevalueoftheelectricfieldisconstant.andareparallel.andareperpendicular.isequaltozeroeverywhereonthesurface.Note:ThesurfaceintegralinGuassslawistakenovertheentiregaussiansurface.第30页/共57页2023/3/2731PlanesymmetrySphericalsymmetryThethreesymmetries:Cylindricalsymmetry第31页/共57页2023/3/2732Problem-solvingstrategyAnalysisthesymmetryofthefieldintensitydistribution.Selectappropriategaussiansurface.Selectappropriatecoordinates,applyGaussslaw.第32页/共57页2023/3/2733Example1.ElectricquantityQdistributesuniformlyonasphericalsurfaceofcenterOandradiusR.Findthefieldintensity.(1)ASphericallySymmetricChargeDistributionAnalysisthesymmetryofthefieldintensitydistributionRPO第33页/共57页2023/3/2734RPOSphericalsymmetryThemagnitudeoftheelectricfieldisconstanteverywhereontheconcentricsphericalsurface,andthefieldisnormaltothesurfaceateachpoint.第34页/共57页35Selectappropriategaussiansurface.rO第35页/共57页2023/3/2736NoteForauniformlychargedsphericalsurface,thefieldintheregionexternaltothesphericalsurfaceisequivalenttothatofapointchargeatthecenterofthespheresurface.第36页/共57页2023/3/2737R1，Q1R2，Q2QuickQuizTherearetwoconcentricchargedsphericalshellsofradiusR1andR2.Chargequantitiesdistributeuniformly.第37页/共57页2023/3/2738Example2.AninsulatingsolidsphereofradiusrhasauniformvolumechargedensityandcarriesatotalpositivechargeQ.Calculatetheelectricfieldintensity.roSolutionBecausethechargedistributionissphericallysymmetric,weselectasphericalgaussiansurfaceofradiusr,concentricwiththesphere.第38页/共57页2023/3/2739RrR0E第39页/共57页2023/3/2740Theelectricfieldinsidethesphere()varieslinearlywithr.Theelectricfieldoutsidethesphere()isthesameasthatofapointchargeQlocatedatr=0.0ERTheexpressionsoffieldintensitymatchwhenr=a.第40页/共57页2023/3/2741(2)ACylindricallySymmetricChargeDistributionaninfiniteuniformchargedstraightlineaninfiniteuniformchargedcylinderExample1Asectionofaninfinitelylongcylindricalplasticrodwithauniform+.Letusfindanexpressionforthemagnitudeoftheatadistancerfromtheaxisoftherod.Infinitelength第41页/共57页2023/3/2742POAnalysisthesymmetryofthefieldintensitydistribution第42页/共57页2023/3/2743CylindricalSymmetryThemagnitudeoftheelectricfieldisconstanteverywhereonthecoaxialcylindricalsurface,andthefieldisnormaltothesurfaceateachpoint.第43页/共57页2023/3/27442.Selectappropriategaussiansurface:acylindricalgaussiansurfaceofradiusr andlengthlthatiscoaxialwiththelinecharge.第44页/共57页2023/3/2745？r0第45页/共57页2023/3/2746Thefieldintensityofaninfiniteuniformchargedstraightline:第46页/共57页2023/3/2747Example2ThechargedensityofaninfiniteuniformchargedcylindricalsurfaceofradiusR isalongthedirectionofaxis,findtheelectricfieldintensity.r第47页/共57页2023/3/2748QuickQuizThechargedensityofaninfiniteuniformsolidchargedcylinderofradiusR is,findtheelectricfieldintensity.第48页/共57页2023/3/2749第49页/共57页3.PlanarSymmetryInfinite Charged Plane or Sheet.2023/3/2750+PlanarSymmetry:forthosepointswhosedistancetotheplaneisidentical,thefieldintensityisequalinmagnitudeandperpendiculartotheplane.第50页/共57页2023/3/2751Example3ResearchintheSymmetry.SelectGaussiansurface.Findtheelectricfieldduetoanonconducting,infiniteplanewithuniformsurfacechargedensity.+第51页/共57页2023/3/2752+Curvedsurface,Eachendofthegaussiansurface,Selectacylindricalgaussiansurfacepenetratinganinfinitesheetofcharge.第52页/共57页2023/3/2753s+Conclusion:thefieldisuniformeverywhere.第53页/共57页2023/3/2754Example4+Asshowninfigure,therearetwosameparallelsheetseachwithsurfacechargedensityandrespectively.Thedistancebetweenplanesissmallerfarthanthesizeofthem.Findtheelectricfielddensityatpoints(a)totheleftofthetwosheets.(b)inthebetween,and(c)totherightofthetwosheets.第54页/共57页2023/3/2755ABC+Solution+第55页/共57页2023/3/2756when 1=-2ParallelPlateCapacitor+第56页/共57页感谢您的观看！第57页/共57页
