《物理双语教学课件》Chapter15ElectricFields电场.docx

《物理双语教学课件》Chapter15ElectricFields电场.docx

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《物理双语教学课件》Chapter15ElectricFields电场

《物理双语教学课件》Chapter-15-Electric-Fields-电场

Chapter15ElectricFields

Supposewefixapositivelychargedparticleq1inplaceandthenputasecondpositivelychargedparticleq2nearit.FromCoulomb'slawweknowthatq1exertsarepulsiveelectrostaticforceonq2.Thenyoumayaskhowq1"know"ofthepresenceofq2?

Thatis,sincethechargesdonottouch,howcanq1exertaforceonq2?

Thisquestionaboutactionatadistancecanbeansweredbysayingthatq1setupanelectricfieldinthespacesurroundingit.AtanygivenpointPinthatspace,thefieldhasbothmagnitudeanddirection.Thuswhenweplaceq2atP,q1interactswithq2throughtheelectricfieldatP.Themagnitudeanddirectionofthatelectricfielddeterminethemagnitudeanddirectionoftheforceactingonq2.

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.

（2）

ThefigureshowsathinringofradiusRwithauniformpositivelinearchargedensity

arounditscircumference.WhatistheelectricfieldatpointP,adistancezfromtheplaneoftheringalongitscentralaxis?

（3）Wecangetthemagnitudeoftheelectricfieldas

.

4.

Theelectricfieldduetoachargeddisk

（1）ThefigureshowsacircularplasticdiskofradiusRthathasapositivesurfacechargeuniformdensity

onitsuppersurface.WhatistheelectricfieldatpointP,adistancezfromthediskalongitscentralaxis?

（2）OurplanistodividethediskintoconcentricflatringsandthentocalculatetheelectricfieldatpointPbyaddingupthecontributionsofallrings.Themagnitudeoftheelectricfieldis

.

15.4Apointchargeinanelectricfield

1.Wenowwanttodeterminewhathappenstoachargedparticlethatisinanelectricfieldthatproducedbyotherstationaryorslowlymovingcharges.Thisforceisgivenby

inwhichqisthechargeoftheparticleand

istheelectricfieldthatotherchargeshaveproducedatthelocationoftheparticle.

2.

Measuringtheelementarycharge:

FigureshowstheMillikanoil-dropapparatusformeasuringtheelementarychargee.

3.

Ink-jetprinting:

Figureshowstheessentialfeaturesofanink-jetprinter.

15.5ADipoleinanElectricField

1.

Thefigureshowswhythemoleculeofwater（H2O）isanelectricdipole.Ifthewatermoleculeisplacedinanexternalelectricfield,itbehavesaswouldbeexpectedofthemoreabstractelectricdipole.

2.Thetorquecanbewrittenas

.

3.

Potentialenergyofanelectricdipole:

Theexpressionforthepotentialenergyofanelectricdipoleinanexternalelectricfieldissimplestifwechoosethepotentialenergytobezerowhentheangle

inthefigureis

.Itcanbewrittenas

.

Microwavecooking:

theexplanationit.