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1、 2 3ELECTRICFLUX GAUSS SLAW 2020 5 30 1 1 ElectricFieldLines Aconvenientspecializedpictorialrepresentationforvisualizingelectricfieldpatternsiscreatedbydrawinglineswhicharecalledelectricfieldlines Theelectricfieldlinesarerelatedtotheelectricfieldinanyregionofspaceinthefollowingmanner 2020 5 30 2 1 T
2、hetangentdirectionateverypointonanelectricfieldlineisjustthedirectionofthefieldintensityatthatpointorthedirectionoftheforceonthepositivepointchargeatthatpoint 2 Theelectricfieldlinesaredenserintheplacewherethefieldintensityisstronger andtheelectricfieldlinesaresparserintheplacewherethefieldintensity
3、isweaker 3 Theelectricfieldlinesstartonpositivechargesandterminateonnegativecharges andneverintersectedeachother Itisneverinterruptedinregionwithoutcharge thisiscalledthecontinuityofelectricfieldline 4 Keepinmind electricfieldlinesdonotactuallyexist 2020 5 30 3 Forapositivepointcharge thelinesaredir
4、ectedradiallyoutward Foranegativepointcharge thelinesaredirectedradiallyinward Theelectricfieldlinesfortwochargesofequalmagnitudeandoppositesign anelectricdipole NOTE thenumberoflinesleavingthepositivechargeequalsthenumberterminatingatthenegativecharge Theelectricfieldlinesfortwopositivepointcharges
5、 Theelectricfieldlinesforapointcharge 2qandasecondpointcharge q RingAmount 2020 5 30 8 FluxAmount 2 ElectricFlux e 1 Uniformelectricfield 2 Uniformelectricfield S 3 Nonuniformelectricfield arbitrarysurface UNIT Vm 2020 5 30 10 Where 2020 5 30 11 Aclosedsurfaceisdefinedasonethatcompletelydividesspace
6、intoaninsideregionandoutsideregion sothatmovementcannottakeplacefromoneregiontotheotherwithoutpenetratingthesurface Foraclosedsurface usuallydefinethenormallineateverypointonthesurfacepointsoutoftheclosedsurface Aclosedsurface Aopensurface 2020 5 30 12 0 0 0 n n Accordingtotheconvention outwardthecl
7、osedsurface inwardtheclosedsurface 2020 5 30 14 Thereisacubesurfaceofedgelengthaintheuniformelectricfield isaconstant asshowninfigure Findtheelectricfluxofeveryplaneandthecubesurface Example 2020 5 30 15 Gaussworkedinawidevarietyoffieldsinbothmathematicsandphysicsincludingnumbertheory analysis diffe
8、rentialgeometry geodesy magnetism astronomyandoptics Hisworkhashadanimmenseinfluenceinmanyareas Sometimesknownas theprinceofmathematicians and greatestmathematiciansinceantiquity JohannCarlFriedrichGauss1777 1855 3 GAUSS SLAW 2020 5 30 16 Thenetelectricfluxofanarbitraryclosedsurfaceinthevacuumisequa
9、ltothenetchargeinsidethesurfacedividedby 1 GAUSS SLAW 2020 5 30 17 S Theclosedsurface i e gaussiansurface Itisanimaginarysurfaceandneednotcoincidewithanyrealphysicalsurface isthetotalelectricfieldatanypointonthesurfaceduetoallcharges Surfaceelement Itsorientationisperpendiculartothesurfaceandpointso
10、utwardfromtheinsideregion Thealgebrasumofchargesintheclosedsurface Theclosesurfaceintegralisoverallgaussiansurface 2020 5 30 18 Itgiveasimplewaytocalculatethedistributionofelectricfieldforagivenchargedistributionwithsufficientsymmetry 2020 5 30 19 r 2 Proving Asphericalgaussiansurfaceofradiusrsurrou
11、ndingapointchargeqwhichisatthecentreofthesphere Theelectricfieldisnormaltothesurfaceandconstantinmagnitudeeverywhereonthesurface 2020 5 30 20 Asphericalgaussiansurfaceofradiusrsurroundingapointchargeqwhichisnotatthecentreofthesphere r q O 2020 5 30 21 Anarbitrarygaussiansurfacesurroundingapointcharg
12、eq Thenetelectricfluxthrougheachsurfaceisthesame 2020 5 30 22 S q1 q2 q3 Therearemanychargesinsidetheguassiansurface 2020 5 30 23 Apointchargelocatedoutsideaclosedsurface Thenumberoflinesenteringthesurfaceequalsthenumberleavingthesurface Thenetelectricfluxthroughaclosedsurfacethatsurroundsnonetcharg
13、eiszero Zerofluxisnotzerofield 2020 5 30 24 Conclusion Thenetfluxthroughanyclosedsurfacesurroundingthepointchargeqisgivenby Asystemofcharges Continuousdistributionofcharges 2020 5 30 25 3 PhysicalMeaning Thepositivechargeisthesourceoftheelectrostaticfield Gauss slawisvalidfortheelectricfieldofanysys
14、temofchargesorcontinuousdistributionofcharge Guass slawcanbeusedtoevaluatetheelectricfieldforchargedistributionsthathavespherical cylindrical orplanesymmetry Thetechniqueisusefulonlyinsituationswherethedegreeofsymmetryishigh 2020 5 30 26 QuickQuiz Whyaretheelectrostaticfieldlinesneverinterruptedinre
15、gionwithoutcharge 2020 5 30 27 Findthefluxthroughthesquare QuickQuiz 2020 5 30 28 Considerwhetherthefollowingstatementsaretruth ElectricfluxoftheGausssurfaceisrelatedwithchargesinGausssurfaceandisnotrelatedwithchargesoutofGausssurface ThefieldintensityatapointontheGausssurfaceisrelatedwithchargesint
16、heGausssurfaceandisnotrelatedwithchargesoutoftheGausssurface IftheelectricfluxofaGausssurfaceequalszero theremustbenotchargeintheGausssurface 2020 5 30 29 IftheelectricfluxofaGausssurfaceequalszero thenfieldintensityateverypointontheGausssurfaceiszero Gausstheoremistenableonlytotheelectrostaticfieldwhosedistributionissymmetricalinspace 2020 5 30 30 4 ApplicationofGauss sLawtoSymmetricChargeDistribution Thegaussiansurfaceshouldalwaysbechosentotakeadvantageofthesymmetryofthechargedistribution soth
