重邮大学物理英文 .pptx

《重邮大学物理英文 .pptx》由会员分享，可在线阅读，更多相关《重邮大学物理英文 .pptx（57页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、2023/3/271(1)Thetangentdirectionateverypointonanelectricfieldlineisjustthedirectionofthefieldintensityatthatpointorthedirectionoftheforceonthepositivepointchargeatthatpoint.(2)Theelectricfieldlinesaredenserintheplacewherethefieldintensityisstronger,andtheelectricfieldlinesaresparserintheplacewhereth

2、efieldintensityisweaker.(3)Theelectricfieldlinesstartonpositivechargesandterminateonnegativecharges,andneverintersectedeachother.Itisneverinterruptedinregionwithoutcharge;thisiscalledthecontinuityofelectricfieldline.(4)Keepinmind:electricfieldlinesdonotactuallyexist.第1页/共57页2023/3/272+Forapositivepo

3、intcharge,thelinesaredirectedradiallyoutward.Foranegativepointcharge,thelinesaredirectedradiallyinward.第2页/共57页+Theelectricfieldlinesfortwochargesofequalmagnitudeandoppositesign(anelectricdipole)NOTE:thenumberoflinesleavingthepositivechargeequalsthenumberterminatingatthenegativecharge.第3页/共57页+Theel

4、ectricfieldlinesfortwopositivepointcharges.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202

5、3/3/279Where 第9页/共57页2023/3/2710Aclosedsurfaceisdefinedasonethatcompletelydividesspaceintoaninsideregionandoutsideregion,sothatmovementcannottakeplacefromoneregiontotheotherwithoutpenetratingthesurface.Foraclosedsurface,usuallydefinethenormallineateverypointonthesurfacepointsoutoftheclosedsurfaceAcl

6、osedsurfaceAopensurface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2023/3/2713Thereisacubesurfaceofed

7、gelengthaintheuniformelectricfield（isaconstant）asshowninfigure.Findtheelectricfluxofeveryplaneandthecubesurface.ExampleXYZ第13页/共57页2023/3/2714Gaussworkedinawidevarietyoffieldsinbothmathematicsandphysicsincludingnumbertheory,analysis,differentialgeometry,geodesy,magnetism,astronomyandoptics.Hisworkha

8、shadanimmenseinfluenceinmanyareas.SometimesknownastheprinceofmathematiciansandgreatestmathematiciansinceantiquityJohannCarlFriedrichGauss1777-18553.GAUSSS LAW第14页/共57页2023/3/2715Thenetelectricfluxofanarbitraryclosedsurface inthevacuumisequaltothenetchargeinsidethesurfacedividedby.(1)GAUSSSLAW第15页/共5

9、7页2023/3/2716S：Theclosedsurface,i.e.gaussiansurface.Itisanimaginarysurfaceandneednotcoincidewithanyrealphysicalsurface.isthetotalelectricfieldatanypointonthesurfaceduetoallcharges.Surfaceelement.Itsorientationisperpendiculartothesurfaceandpointsoutwardfromtheinsideregion.Thealgebrasumofchargesinthec

10、losedsurface.Theclosesurfaceintegralisoverallgaussiansurface.第16页/共57页2023/3/2717Itgiveasimplewaytocalculatethedistributionofelectricfieldforagivenchargedistributionwithsufficientsymmetry.第17页/共57页2023/3/2718r+q(2)ProvingAsphericalgaussiansurfaceofradiusrsurroundingapointchargeq whichisatthecentreof

11、thesphere.Theelectricfieldisnormaltothesurfaceandconstantinmagnitudeeverywhereonthesurface.第18页/共57页2023/3/2719Asphericalgaussiansurfaceofradiusrsurroundingapointchargeq whichisnotatthecentreofthesphere.r+qO第19页/共57页2023/3/2720Anarbitrarygaussiansurfacesurroundingapointchargeq.+S1S2Thenetelectricflu

12、xthrougheachsurfaceisthesame.第20页/共57页2023/3/2721+Sq1+q2+q3+Therearemanychargesinsidetheguassiansurface.第21页/共57页2023/3/2722+qApointchargelocatedoutsideaclosedsurface.Thenumberoflinesenteringthesurfaceequalsthenumberleavingthesurface.Thenetelectricfluxthroughaclosedsurfacethatsurroundsnonetchargeisz

13、ero.Zerofluxisnotzerofield.第22页/共57页2023/3/2723ConclusionThenetfluxthroughanyclosedsurfacesurroundingthepointchargeqisgivenbyAsystemofchargesContinuousdistributionofcharges第23页/共57页2023/3/2724(3)PhysicalMeaningThepositivechargeisthesourceoftheelectrostaticfield.Gaussslawisvalidfortheelectricfieldofa

14、nysystemofchargesorcontinuousdistributionofcharge.Guassslawcanbeusedtoevaluatetheelectricfieldforchargedistributionsthathavespherical,cylindrical,orplanesymmetry.Thetechniqueisusefulonlyinsituationswherethedegreeofsymmetryishigh.第24页/共57页2023/3/2725QuickQuizWhyaretheelectrostaticfieldlinesneverinter

15、ruptedinregionwithoutcharge?第25页/共57页2023/3/2726aQFindthefluxthroughthesquare.QuickQuiz第26页/共57页2023/3/2727Considerwhetherthefollowingstatementsaretruth.ElectricfluxoftheGausssurfaceisrelatedwithchargesinGausssurfaceandisnotrelatedwithchargesoutofGausssurface.ThefieldintensityatapointontheGausssurfa

16、ceisrelatedwithchargesintheGausssurfaceandisnotrelatedwithchargesoutoftheGausssurface.IftheelectricfluxofaGausssurfaceequalszero,theremustbenotchargeintheGausssurface.第27页/共57页2023/3/2728IftheelectricfluxofaGausssurfaceequalszero,thenfieldintensityateverypointontheGausssurfaceiszero.Gausstheoremiste

17、nableonlytotheelectrostaticfieldwhosedistributionissymmetricalinspace.第28页/共57页2023/3/2729(4)ApplicationofGausssLawtoSymmetricChargeDistributionThegaussiansurfaceshouldalwaysbechosentotakeadvantageofthesymmetryofthechargedistribution,sothatwecanremoveEfromtheintegralandsolveit.第29页/共57页2023/3/2730Th

18、egaussiansurfacehadbettersatisfiesoneormoreofthefollowingconditions:Thevalueoftheelectricfieldisconstant.andareparallel.andareperpendicular.isequaltozeroeverywhereonthesurface.Note:ThesurfaceintegralinGuassslawistakenovertheentiregaussiansurface.第30页/共57页2023/3/2731PlanesymmetrySphericalsymmetryThet

19、hreesymmetries:Cylindricalsymmetry第31页/共57页2023/3/2732Problem-solvingstrategyAnalysisthesymmetryofthefieldintensitydistribution.Selectappropriategaussiansurface.Selectappropriatecoordinates,applyGaussslaw.第32页/共57页2023/3/2733Example1.ElectricquantityQdistributesuniformlyonasphericalsurfaceofcenterOa

20、ndradiusR.Findthefieldintensity.(1)ASphericallySymmetricChargeDistributionAnalysisthesymmetryofthefieldintensitydistributionRPO第33页/共57页2023/3/2734RPOSphericalsymmetryThemagnitudeoftheelectricfieldisconstanteverywhereontheconcentricsphericalsurface,andthefieldisnormaltothesurfaceateachpoint.第34页/共57

21、页35Selectappropriategaussiansurface.rO第35页/共57页2023/3/2736NoteForauniformlychargedsphericalsurface,thefieldintheregionexternaltothesphericalsurfaceisequivalenttothatofapointchargeatthecenterofthespheresurface.第36页/共57页2023/3/2737R1，Q1R2，Q2QuickQuizTherearetwoconcentricchargedsphericalshellsofradiusR

22、1andR2.Chargequantitiesdistributeuniformly.第37页/共57页2023/3/2738Example2.AninsulatingsolidsphereofradiusrhasauniformvolumechargedensityandcarriesatotalpositivechargeQ.Calculatetheelectricfieldintensity.roSolutionBecausethechargedistributionissphericallysymmetric,weselectasphericalgaussiansurfaceofrad

23、iusr,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)ACylindricallySymmetricChar

24、geDistributionaninfiniteuniformchargedstraightlineaninfiniteuniformchargedcylinderExample1Asectionofaninfinitelylongcylindricalplasticrodwithauniform+.Letusfindanexpressionforthemagnitudeoftheatadistancerfromtheaxisoftherod.Infinitelength第41页/共57页2023/3/2742POAnalysisthesymmetryofthefieldintensitydi

25、stribution第42页/共57页2023/3/2743CylindricalSymmetryThemagnitudeoftheelectricfieldisconstanteverywhereonthecoaxialcylindricalsurface,andthefieldisnormaltothesurfaceateachpoint.第43页/共57页2023/3/27442.Selectappropriategaussiansurface:acylindricalgaussiansurfaceofradiusr andlengthlthatiscoaxialwiththelinec

26、harge.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2023/3/2748QuickQuizThechargede

27、nsityofaninfiniteuniformsolidchargedcylinderofradiusR 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,thefieldintensityisequalinmagnitudeandperpendiculartotheplan

28、e.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

29、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