工程电磁场第二章

2-1EngineeringElectromagneticsW.H.Hayt,Jr.andJ.A.BuckChapter2Coulomb’sLawandElectricFieldIntensity2-2Coulomb’sExperimentalLaw++Q1Q2RFForceofrepulsion,F,occurswhenchargeshavethesamesign.Chargesattractwhenofoppositesignwhere2-3FreeSpacePermittivitywithwhichtheCoulombforcebecomes:2-4CoulombForcewithChargesOff-Origin2-5ElectricFieldIntensityConsidertheforceactingonatestcharge,Qt,arisingfromchargeQ1:wherea1tistheunitvectordirectedfromQ1toQtTheelectricfieldintensityisdefinedastheforceperunittestcharge,orN/CAmoreconvenientunitforelectricfieldisV/m,aswillbeshown.t2-6ElectricFieldofaChargeOff-Origin2-7SuperpositionofFieldsFromTwoPointChargesForncharges:2-8ExampleFindEatP,usingFirst,findthevectors:Then:2-9Example(continued)FindEatP,usingNow:sothat:where2-10VolumeChargeDensityGivenachargeQwithinavolume,thevolumechargedensityisdefinedas:….sothatthechargecontainedwithinavolumeis2-11ExampleFindthechargecontainedwithina2-cmlengthoftheelectronbeamshownbelow,inwhichthechargedensityis32-12Example(continued)Q2-13ElectricFieldfromVolumeChargeDistributionsNext,sumallcontributionsthroughoutavolumeandtakethelimitasapproacheszero,toobtaintheintegral:2-14LineChargeElectricFieldLinechargeofconstantdensityLCoul/mliesalongtheentirezaxis.AtpointP,theelectricfieldarisingfromchargedQonthezaxisis:wheresothatThereforeand2-15LineChargeField(continued)Wehave:Bysymmetry,onlyaradialcomponentispresent:2-16LineChargeFieldResults2-17Example:Off-AxisLineChargeWiththelinedisplacedto(6,8),thefieldbecomes:whereFinally:2-18SheetChargeFieldUniformsurfacechargeofdensityscoverstheentirey-zplane.Webeginbywritingdownthelinechargefieldonthexaxisforastripofdifferentialwidthdy´,whereweconsiderthexcomponentofthatfield:Thetotalfieldonthexaxisis:or2-19TypesofStreamlineSketchesofFields:2-20MethodologyofStreamlineConstructionTheratiooftheyandxfieldcomponentsgivestheslopeofthefieldplotinthex-yplane2-21Example:LineChargeFieldBeginwiththenormalizedlinechargefieldincylindricalcoordinates:Converttorectangularcomponents:ThenwhosesolutionisFinally