《物理雙語(yǔ)教學(xué)課件》Chapter-15-Electric-Fields-電場(chǎng)

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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,theinformationaboutthemovebyq1travelsoutwardfromq1aselectromagneticwaveatthe

SomeElectricFieldlines

Theelectricfieldlinesofaspherewithuniformchargeasshownintherightfigure.

Rightfiguregivestheelectricfieldlinesofaninfinitelylarge,non-conductingsheet(orplane)withauniformdistributionofpositivechargeononeside.

Thefigureshowsthefieldlinesfortwoequalpositivepointcharges.

Thefigureshowsthepatternfortwochargesthatareequalinmagnitudebutoppositesign.

Fromabovefigures,wecancometotheconclusion:Electricfieldlinesextendawayfrompositivechargeandtowardnegativecharge.

15.3TheElectricFieldsforsomecases

Theelectricfieldduetoapointchargeq

Ifweputapositivetestchargeq0atanypointadistancerfromthepointcharge,themagnitudeoftheelectrostaticforceactingonq0,fromCoulomb’slaw,is.Themagnitudeoftheelectricfieldvectoris.Thedirectionofisthesameasthatoftheforceonthepositivetestcharge:directlyawayfromthepointcharge,asshowninrightfigure,ifqispositive,andtowarditifqisnegative.

Wecanfindthenet,orresultant,electricfieldduetomorethanonepointchargeswiththeaidoftheprincipleofsuperposition.Ifweplaceapositivetestchargeq0nearnpointchargesq1,q2,…,qn,thenthenetforcefromthenpointchargesactingonthetestchargeis.Sothenetelectricfieldatthepositionofthetestchargeis.Hereistheelectricfieldthatwouldbesetupbypointchargeiactingalone.

Theelectricfieldduetoanelectricdipole:Figure(a)showstwochargesofmagnitudeqbutofoppositesign,separatedbyadistanced.Wecallthisconfigurationanelectricdipole.LetusfindtheelectricfieldduetothedipoleatapointP,adistancezfromthemidpointofthedipoleandonitscentralaxis,asshowninthefigure.(1)Themagnitudeoftheelectricfieldis,inwhichtheproductqdisthemagnitudepofavectorquantityknownastheelectricdipolemomentofthedipole.

Theelectricfieldduetoalineofcharge

Sofarwehaveconsideredtheelectricfieldthatisproducedbyoneor,atmost,afewpointcharges.Wenowconsiderchargedistributionsthatconsistofgreatmanyclosedspacedpointcharges(perhapsbillions)thatarespreadalongaline,overasurface,orwithinavolume.Suchdistributionsaresaidtobecontinuousratherthandiscrete.Whenwedealwithcontinuouschargedistributions,itismostconvenienttoexpressthechargeonanobjectasachargedensityratherthanasatotalcharge.Foralineofcharge,forexample,wewouldreportthelinearchargedensity(orchargeperlength),whoseSIunitisthecoulombpermeter.

ThefigureshowsathinringofradiusRwithauniformpositivelinearchargedensityarounditscircumference.WhatistheelectricfieldatpointP,adistancezfromtheplaneoftheringalongitscentralaxis?

Wecangetthemagnitudeoftheelectricfieldas.

Theelectricfieldduetoachargeddisk

ThefigureshowsacircularplasticdiskofradiusRthathasapositivesurfacechargeuniformdensityonitsuppersurface.WhatistheelectricfieldatpointP,adistancezfromthediskalongitscentralaxis?

OurplanistodividethediskintoconcentricflatringsandthentocalculatetheelectricfieldatpointPbyaddingupthecontributionsofallrings.Themagnitudeoftheelectricfieldis.

15.4Apointchargeinanelectricfield

Wenowwanttodeterminewhathappenstoachargedparticlethatisinanelectricfieldthatproducedbyotherstationaryorslowlymovingcharges.Thisforceisgivenby,inwhichqisthechargeoftheparticleandistheelectricfieldthatotherchargeshaveproducedatthelocationoftheparticle.

Measuringtheelementarycharge:FigureshowstheMillikanoil-dropapparatusformeasuringtheelementarychargee.

Ink-jetprinting:Figureshowstheessentialfeaturesofanink-jetprinter.

15.5ADipoleinanElectricField

Thefigureshowswhythemoleculeofwater(H2O)isanelectricdipole.Ifthewatermoleculeisplacedinanexternalelectricfield,itbehavesaswouldbeexpectedofthemoreabstractelectricdipole.

Thetorquecanbewrittenas.

Po