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1、Chapter4ElectrostaticFieldsinMatterProblem4.1EV/x500/10-35x105.Table4.1:a/47r00.66x10-30soa47r8.85x10-120.66x10-307.34X10-41.paEeddaE/e7.34x10-415x105/1.6x10-192.29X10-16m.d/R2.29x10-16/0.5x10-1014.6x10-6.1ToionizesaydR.ThenRaE/eaV/exVRex/a.0.5x10-101.6x10-1910-3/7.34x10-411108v.1Problem4.2Firstfind
2、thefieldatradiusrusingGausslaw:JE.daEQencorE4lt0Qenc.lr47rqlr-4qa-a2lrQencpdT-e-2r/ar2dr-e-2r/ar2ar-07ra30a32202qa2a2rr2-a2e-2r/ar2arquot2-quot2q1-e-2r/a122a2.Note:Qencr-00q.SothefieldoftheelectroncloudisEe4lt01-e-2r/a122.Theprotonwillbeshiftedfromr0tothepointdwhereEeEtheexternalfield:1q2d/adE-1-e-1
3、2-2-.47r0d2aa2Expandinginpowersofd/a:e-2d/a1-2d2d2-.2d3.1-222-3.a2a3aaa3a1-1-22r-r.-122dcP.dcP.d3cP.d34r-r-2t-2:2t4:4:-2:-4:-.ad2ad2d3d2d33a34d33higherorderterms.dd21-e-2d/a12-2-aa27374CHAPTER4.ELECTROSTATICFIELDSINMATTER1q4d3141.I3IE-qd-poa311quot:oa.471quot0dl-3a3471quot03a3371quotoa3Notsodifferen
4、tfromtheuniformspheremodelofEx.4.1seeEq.4.2.Notethatthisresultpredicts4EOaa30.5X10-1030.09X10-30m3comparedwithanexperimentalvalueTable4.1of0.66x10-30m3.IronicallythequotclassicalquotformulaEq.4.2isslightlyclosertotheempiricalvalue.Problem4.3perAr.ElectricfieldbyGausssLaw:E.daE471quotr2-oQencEloJAr47
5、1quotr2drorE471quotAr4Ar2.ThisquotinternalquotfieldbalancestheexternalfieldEwhennucleusisquotoff-centerquotanamount471quotro440d:ad2/40EdV4oE/A.Sotheinduceddipolemomentisped2ev0/AVE.EvidentlyIpisproportionaltoEl/2.1ForEq.4.1toholdintheweak-fieldlimitEmustbeproportionaltorforsmallrwhichmeansthatpmust
6、gotoaconstantnotzeroattheorigin:IpO:/0Inorinfinite.Problem4.4rFieldofq:f.Induceddipolemomentofatom:PaE.0QA1IquotEOrq411quotE:r2r.Fieldofthisdipoleatlocationofq071quotinEq.3.103:E_41132aq2totheright.7Iquot0r471quotorForceonqduetothisfield:IF2a-4q213Iattractive.7Iquot0rProblem4.5FieldofPIatP2071quot/2
7、inEq.3.103:E14PI39pointsdown.7IquotorFieldofP2atPI071quotinEq.3.103:E24P23-2fpointstotheright.7IquotorI2PIP2I.TorqueonPI:N1PIXE2-43pomtsmtothepage.7IquotorProblem4.6aUseimagedipoleasshowninFig.a.RedrawplacingPiattheoriginFig.b.E-P.-471quot02z32cosOfsinO9PpcosOfpsinO9.10oPif/Z2NPXEi471quot:2Z3cos0fsi
8、n09x2cos0fsin09p2AA4r.02z3cosOsinO4J2sinOcosO-4Jp2sin0cos0A471quot02z3-4Joutofthepage.b75.p2sin20Butsin0cos01/2sm20soIN4m:o16z3outofthepage.For0lt0ltr/2Ntendstorotatepcounterclockwiseforr/2lt0ltrNrotatespclockwise.Thusthestableorientationisperpendiculartothesurface-eithertor.t.Problem47Saythefieldis
9、uniformandpointsintheydirection.Firstslidepinfrominfinityalongthexaxis-thistakesnoworksinceFisJ.dl.IfEisnotuniformslidepinalongatrajectoryJ.thefield.Nowrotatecounterclockwiseintofinalposition.ThetorqueexertedbyEisNpxEpEsinOz.ThetorqueweexertisNpEsinOxclockwiseanddOiscounterclockwisesothenetworkdoneb
10、yusisnegative:UJ:/2pEsinOdOpE-cosO1/2-pEcosO-cos-pEcos0-pE.QedProblem48U-pIE2butE2-:r3p2ff-P2.SOU-:rPIP2-3pIfp2f.QedProblem491qqxxyyzzaFp.VEEq.4.5E_4r_42223/2rEOrrEOxyzytEO.Pp888qxFxPx-P-pz-.8xY8y8z4rEOX2y2Z23/2q132x32y-4rEOPxx2y2Z23/2-2xX2y2Z25/2py-2xX2y2Z25/232zqPx3xqp3rp.rpz-2xX2y2Z25/24rEOr3-:sP
11、xxPyypzz4rEOr3-r5x.FI_41p-3p.ff.rEorbE_41-.3p.-f-f-p_41133p.ff-p.ThisisfromEq.3.104theminussignsrEOrrEOrarebecauserpointstowardpinthisproblem.FqE1-41q33p.ff-prEOrNotethattheforcesareequalandoppositeasyouwouldexpectfromNewtonsthirdlaw.Problem41018212aUbPnkRPb-V.p-3quot-8rkr-3krrrrbForrltRE3oprfProb.2
12、.12soEI-k/EOr.1ForrgtRsameasifallchargeatcenterbutQtotkR4rR2-3ktrR30soIE0.176CHAPTER4.ELECTROSTATICFIELDSINMATTERProblem4.11Pb0abP.il:Pplussignatoneend-theonePpointstowardminussignattheother-theonePpointsawayfrom.iL?a.ThentheendslooklikepointchargesandthewholethingislikeaphysicaldipoleQflengthLandch
13、argeP-rra2.SeeFig.a.iiL?a.Thenitslikeacircularparallel-platecapacitor.Fieldisnearlyuniforminsidenonuniformquotfringingfieldquotattheedges.SeeFig.b.iiiLa.SeeFig.c.pppaLikeadipolebLikeaparallel-platecapacitorcProblem4.12v4EOJIjdTp.4EOJdT.Butthetermincurlybracketsispreciselythefieldofauniformlychargeds
14、pheredividedbyp.TheintegralwasdoneexplicitlyinProb.2.7and2.8:IR3AIR3PcosBIgtRI4/3R3PfrgtR3or2P.r3or2r1.t.1411quot0rSoVrBdT-4WltO.-p4/3wRprrltR.I.P.rIquotowoo1rltR.411quot0R330Problem4.13Thinkofitastwocylindersofoppositeuniformchargedensity:p.Insidethefieldatadistancesfromtheaxisofauniformlychargecyl
15、inderisgivenbyGaussslaw:E211quotse-:OP1lquotS2e:Ep/20s.FortwosuchcylindersoneplusandoneminusthenetfieldinsideisEEE-p/2fOs-s_.Buts-s-dsoEl-pd/20Iwheredisthevectorfromthenegativeaxistopositiveaxis.InthiscasethetotaldipolemomentofachunkoflengtheisP1Iquota2ep7ra2ed.SopdPandIE-P/20Iforslta.77OutsideGauss
16、slawgivesE27r8?.1.p7ra2?:E1?.2a2foronecylinder.ForthecombinationElt0lt0sEE-1?.2a2:t.-iLwherelt0ss-ds:ST-j2d12-1-1S:i:2a-1ds.d1ds.d-ST-8-Ts.d-ST-IT-ST-1:f:-8t2482282822821s.dd.82S:f:S-2Tquot2keepmgonly1stordertermsind.8-Lss-s-s2SS.d-d.s8-828228228282a21Es-2P.8-P2fO82for8gta.Problem4.14TotalchargeonthedielectricisQtotisOquotbdaIvPbdrisP.da-IvV.pdr.Butthedivergencetheoremsaysisp.daIvV.pdrsoQencO.qedProblem4.15aPb-vp-
