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1、CHAPTER26TheElectricFieldRecommendedclassdays:3minimum,4preferredBackgroundInformationChapter25introducedthefieldmodel,andChapter26willnowdevelopthequantitativeanalysisofelectricfieldsandofthemotionofchargedparticlesinthefield.Thegoalisnotforstudentstobecomeexp
2、ertsatcalculatingfields,althoughtheyshouldbeabletodocalculationsforsimplechargedistributions,butforthemtorecognizestandardelectricfieldssuchasthoseofdipolesandoflinesandplanesofcharge.Fieldcalculationsarebaseddirectlyupontheprincipleofsuperposition.Superpositio
3、nisastraightforwardandreadilyunderstoodprocedure,whereas,aswillbediscussedmoreinChapter27,researchhasfoundthatonlyaverysmallfractionofstudentsareabletounderstandGauss’slaw.Further,superpositionhelpsstudentswiththeirconceptualdifficultiesbyexplicitlylinkingfield
4、calculationstoCoulomb’slaw.Withoneexception,allthestandardfieldscaneasilybefoundusingsuperposition.Theexceptionisthefieldofasphereofcharge,forwhichtheintegrations—althoughdoable—aretoocomplexforanintroductoryclass.However,itisquitebelievable,withoutarigorouspro
5、of,thattheexteriorfieldofasphereofchargeisthesameasthatofapointcharge.Weroutinelymakethissameassertion,withoutproof,forNewton’slawofgravity.Atthispointinthecourse,studentshavebeendoingcalculuslongenoughthatnearlyallcancarryoutanintegration.However,studentsarest
6、illveryinexperiencedatusingcalculustoanalyzeaproblem.Theirdifficultywiththischapter—anditisamajordifficultyformost—isnotwithdoingintegralsbutwithknowingwhattointegrate.Studentsareunfamiliarwiththeprocedureofdividingachargedistributionintosmallpieces,writingthes
7、uperpositionoffieldsasasum,andthenconvertingthesumtoanintegralbyusingthechargedensity.Theemphasisinthischapterneedstobeontheanalysisandtheproceduresthatleadtoanintegration.Studentsalsohaveahardtimevisualizingfieldsinthreedimensions.Thefieldsofinterestinthiscour
8、seusuallyhaveanaxisofsymmetry,soyouneedtoencouragestudentstoimaginethe26-1two-dimensionaldrawingsofthetextbook,orthatyoudrawontheboard,asbeingrotatedaboutthataxis.Severalsof
