Lecture 4 Fundamental of EM filed theory .pdf

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1、Lecture4FundamentalofEMfieldtheoryReviewQ-4.1Whichofthefollowingbasevectorsareconstantunitvector?Explain.aˆaˆx(√)aˆRaˆaˆz(√)aˆrQ-4.2whataremetriccoefficient?Invectorcalculusweareoftenrequiredtoperformline,surface,andvolumeintegrals.Ineachcaseweneedtoexpressthe

2、differentiallength-changecorrespondingtoadifferentialchangeinoneofthecoordinates.However,someofthecoordinates,sayuii1,2,or3,maynotbealength;andaconversionfactorisneededtoconvertadifferentialchangeduiintoachangeinlengthdli.hhh1h11,h23rh,1h11,h23R,hRsi

3、n123Outline•ScalarfieldandVectorfield•GradientofaScalarField•DivergenceofaVectorField4.1ScalarfieldandVectorfield4.1.1definitionoffieldFieldisthepositionfunctionofascalarorvector.Whenwedefinethebehaviorofaquantityinagivenregionintermsofasetofvalues,oneforeachpo

4、intintheregion,werefertothisbehaviorofthequantityasafield5(x,yz,)2224[(x1)(yz2)]ScalarfieldSuchastemperature,electricpotential,elevationr22E(x,y,z)2axxyaayzxzxyzVectorfieldSuchaselectricfieldintensity,velocity.4.1.2FieldlineAfieldlineisalocusthatisdefi

5、nedbyavectorfield.Fieldlines,notphysicallines,areusefulforvisualizingfields,whichareotherwisehardtodepict.ØContour:Graphicalrepresentationofascalarfield,suchaselevation,temperature.Eachlinerepresentsallpointsofequalvaluehx,,yzconstElevation,ascalarfield,shown

6、ascontoursElevation,ascalarfield,shownascolors在某一高度上沿什么方向高度变化最快？Ødirectedfieldlines(fluxlinesorstreamlines)thedirectionistangentialtothepathateachpoint,themagnitudeisproportionaltothedensityoffieldlines(numberoffieldlinesperunitperpendiculararea)rrØGivenvectorfu

7、nctionFF(x,y,z)axFx(x,y,z)aayFy((x,y,z))zzFx,,yzranddifferentiallengthdlaxdxaayzdydzvvrAccordingtothedefinitionFFdl0PrdrrrrrrrdaxaayzrrdxdydzFdlFFF0OxyzFFFxyzdxdydzObtainthedifferentialequation’sgeneralsolutions,thendrawthevectorfiledlinese.g.apoi

8、ntchargeislocatedattheoriginofcoordinates.TheelectricfieldintensityatP(x,y,z)inspaceisrqrEr340rWhereqandeareconstant,r=ax+ay+azispositionvectorofP.findthe0xyzvecto