《物理双语教学课件》Chapter15ElectricFields电场Word文件下载.docx
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Anotheraction-at-a-distanceproblemarisesifwemoveq1,say,towardq2.Coulomb’slawtellsusthatwhenq1isclosertoq2,therepulsiveelectrostaticforceactingonq2mustbegreater,anditis.Doestheelectricfieldatq2,andthustheforceactingonq2,changeimmediately?
Theanswerisno.Instead,theinformationaboutthemovebyq1travelsoutwardfromq1aselectromagneticwaveatthespeedoflightc.Thechangeintheelectricfieldatq2,andthusthechangeintheforceactingonq2,occurswhenthewavefinallyreachq2.
15.1TheElectricField
1.Thetemperatureateverypointinaroomhasadefinitevalue.Wecalltheresultingdistributionoftemperatureastemperaturefield.Inmuchthesameway,youcanimagineapressurefieldintheatmosphere:
itconsistsofthedistributionofairpressurevalues,oneforeachpointintheatmosphere.Thesestwoexamplesareofscalarfield,becausetemperatureandair-pressurearescalarquantities.
2.Theelectricfieldisavectorfield
(1)Itconsistsofadistributionofvectors,oneforeachpointintheregionaroundachargedobject.
(2)Inprinciple,wecandefinetheelectricfieldatsomepointnearthechargedobjectbyplacingapositivechargeq0,calledatestcharge,atthepoint.
(3)Wethenmeasuretheelectrostaticforce
thatactsonthetestcharge.Theelectricfield
atpointPduetothechargedobjectisdefinedas
.
(4)WerepresenttheelectricfieldatpointPwithavectorwhosetailisatP,asshowninthefigure.
(5)
TheSIunitfortheelectricfieldisthenewtonpercoulomb(N/C).
15.2ElectricFieldLines
1.MichaelFraday,whointroducedtheideaofelectricfieldsinthe19thcentury,thoughtofthespacearoundachargedbodyasfilledwithlinesofforce.Althoughwenolongerattachmuchrealitytotheselines,nowusuallycalledelectricfieldlines,theystillprovideanicewaytovisualizepattersinelectricfields.
2.Therelationbetweenthefieldlinesandelectricfieldvectors
(1)Atanypoint,thedirectionofastraightfieldlineorthedirectionofthetangenttoacurvefieldlinegivesthedirectionof
atthatpoint.
(2)Thefieldlinesaredrawnsothatthenumberoflinesperunitarea,measuredinaplanethatisperpendiculartothelines,isproportionaltothemagnitudeof
.Thissecondrelationmeansthatwherethefieldlinesareclosetogether,Eislarge;
andwheretheyarefarapart,Eissmall.
3.
SomeElectricFieldlines
(1)Theelectricfieldlinesofaspherewithuniformchargeasshownintherightfigure.
(2)
Rightfiguregivestheelectricfieldlinesofaninfinitelylarge,non-conductingsheet(orplane)withauniformdistributionofpositivechargeononeside.
(3)Thefigureshowsthefieldlinesfortwoequalpositivepointcharges.
(4)Thefigureshowsthepatternfortwochargesthatareequalinmagnitudebutoppositesign.
(5)Fromabovefigures,wecancometotheconclusion:
Electricfieldlinesextendawayfrompositivechargeandtowardnegativecharge.
15.3TheElectricFieldsforsomecases
1.Theelectricfieldduetoapointchargeq
(1)
Ifweputapositivetestchargeq0atanypointadistancerfromthepointcharge,themagnitudeoftheelectrostaticforceactingonq0,fromCoulomb’slaw,is
.Themagnitudeoftheelectricfieldvectoris
.Thedirectionof
isthesameasthatoftheforceonthepositivetestcharge:
directlyawayfromthepointcharge,asshowninrightfigure,ifqispositive,andtowarditifqisnegative.
(2)Wecanfindthenet,orresultant,electricfieldduetomorethanonepointchargeswiththeaidoftheprincipleofsuperposition.Ifweplaceapositivetestchargeq0nearnpointchargesq1,q2,…,qn,thenthenetforce
fromthenpointchargesactingonthetestchargeis
.Sothenetelectricfieldatthepositionofthetestchargeis
.Here
istheelectricfieldthatwouldbesetupbypointchargeiactingalone.
2.
Theelectricfieldduetoanelectricdipole:
Figure(a)showstwochargesofmagnitudeqbutofoppositesign,separatedbyadistanced.Wecallthisconfigurationanelectricdipole.LetusfindtheelectricfieldduetothedipoleatapointP,adistancezfromthemidpointofthedipoleandonitscentralaxis,asshowninthefigure.
(1)Themagnitudeoftheelectricfieldis
inwhichtheproductqdisthemagnitudepofavectorquantityknownastheelectricdipolemoment
ofthedipole.
3.Theelectricfieldduetoalineofcharge
(1)Sofarwehaveconsideredtheelectricfieldthatisproducedbyoneor,atmost,afewpointcharges.Wenowconsiderchargedistributionsthatconsistofgreatmanyclosedspacedpointcharges(perhapsbillions)thatarespreadalongaline,overasurface,orwithinavolume.Suchdistributionsaresaidtobecontinuousratherthandiscrete.Whenwedealwithcontinuouschargedistributions,itismostconvenienttoexpressthechargeonanobjectasachargedensityratherthanasatotalcharge.Foralineofcharge,forexample,wewouldreportthelinearchargedensity(orchargeperlength)
whoseSIunitisthecoulombpermeter.
ThefigureshowsathinringofradiusRwithauniformpositivelinearchargedensity
arounditscircumference.WhatistheelectricfieldatpointP,adistancezfromtheplaneoftheringalongitscentralaxis?
(3)Wecangetthemagnitudeoftheelectricfieldas
4.
Theelectricfieldduetoachargeddisk
(1)ThefigureshowsacircularplasticdiskofradiusRthathasapositivesurfacechargeuniformdensity
onitsuppersurface.WhatistheelectricfieldatpointP,adistancezfromthediskalongitscentralaxis?
(2)OurplanistodividethediskintoconcentricflatringsandthentocalculatetheelectricfieldatpointPbyaddingupthecontributionsofallrings.Themagnitudeoftheelectricfieldis
15.4Apointchargeinanelectricfield
1.Wenowwanttodeterminewhathappenstoachargedparticlethatisinanelectricfieldthatproducedbyotherstationaryorslowlymovingcharges.Thisforceisgivenby
inwhichqisthechargeoftheparticleand
istheelectricfieldthatotherchargeshaveproducedatthelocationoftheparticle.
Measuringtheelementarycharge:
FigureshowstheMillikanoil-dropapparatusformeasuringtheelementarychargee.
Ink-jetprinting:
Figureshowstheessentialfeaturesofanink-jetprinter.
15.5ADipoleinanElectricField
1.
Thefigureshowswhythemoleculeofwater(H2O)isanelectricdipole.Ifthewatermoleculeisplacedinanexternalelectricfield,itbehavesaswouldbeexpectedofthemoreabstractelectricdipole.
2.Thetorquecanbewrittenas
.
Potentialenergyofanelectricdipole:
Theexpressionforthepotentialenergyofanelectricdipoleinanexternalelectricfieldissimplestifwechoosethepotentialenergytobezerowhentheangle
inthefigureis
.Itcanbewrittenas
Microwavecooking:
theexplanationit.