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CollegeMajorandclassNo.Name---○---○------○---○---Sealedupline…………UniversityPhysicsTestpaperofCSU(2010~2010)NoOnetwothreefourfivesixtotalScoreReaderRe-checkerScoreReaderOne:Selecttherightanswerinthebrackets(ineachproblem):title12345678910answers1.Asolidnon-conductingsphereofradiusRhasanon-uniformchargedistributionofvolumedensity,whereisaconstantandisthedistancefromthecenterofthesphere.Sothetotalchargeonthesphereis(A);(B)(C);(D).RCLLII2.ThewireshowninfigurecarriescurrentI.SothemagneticfieldBisproducedatthecenterCofthesemicirclebythetotalwireis(A)0;(B);(C);(D).3.Twoconcentricthinmetalshells,radiiareandrespectively.Ifthetwoshellschargedandandtheirpotentialsareandrespectively.Nowifweconnectthetwoshellswithconductingwire,theirpotentialis:(A)(B)(C)(D)Rrp4.Asshowninfigure,uniformmagneticfieldisconfinedinlongcylindricalspace.If,sothemagnitudeoftheinducedelectricfieldofpointpoutsidethecylinderis:(A)(B)(C)二、选择题(本题10分，每小题2分)三、四、 5.TheMaxwellequationwhichdescribesthevariableelectricfieldwillproducemagneticfieldis(A)(B)(C)(D)a6．Asshowninrightfigure,themagneticfieldisplacedinthedirectionofnegativedirectionofy-axis,ifweknowthattheelectricpotentialdifferencebetweenaandb,sothematerialis(A)Ntype(B)Ptype(C)metal(D)notcertain.7.Whichofthefollowingdescriptionsofwavefunctionisright?(A)istheprobabilityoffindingtheparticleatpositionr;(B)isprobabilitydensityoffindingtheparticleatpositionrattimet;(C)isprobabilitydensityoffindingtheparticlesatpositionrattimet;(D)isprobabilityoffindingtheparticlesatpositionrattimet.8.Ifthequantumnumbern=1,whichofthefollowingquantumstateispossible：(A)(1,1,0,1/2)(B)(1,1,0,0)(C)(1,0,0,-1/2)(D)(1,0,0,0)ScorereaderTwo(ineachproblem):Writetherightanswerinblanks1.Themaximumkineticenergyofanelectronejectedfromasodiumsurfacewhoseworkfunctionis2.28whenilluminatedbylightofwavelength410is2.Acircularcoilofwirehasadiameterof5.0cmandcontains25loops,sothemagneticmomentofthecoilwhenitcarriesacurrentof1.5Ais.3.Ifanelectronthathasvelocitymovesthroughthemagneticfield,sotheforceontheelectronis.4.AccordingtoBorn’sstatisticalinterpretationtowavefunction,thestandardconditionsofwavefunctionare:(1)___________;(2)__________;(3)___________.I5.Awireisformedintotheshapeoftwohalfcirclesconnectedbyequal-lengthstraightsectionsasshowninfigure.AcurrentiflowsCinthecircuitanticlockwiseasshown,themagneticfieldatthecenterCis.6.Twolongparallelwires,bothofradiusaandwhosecentersareadistancedapart,carrycurrentinoppositedirections.Showthat,neglectingtheflux(磁通)withinthewires,theinductance(电感)ofunitlengthofapairofwiresis.7.Theground-stateenergyofelectronis-13.6eV,sotheenergyofthesecondexcitedstatesis. ScorereaderThree():TheplasticrodshowninfigurehaslengthLandanon-uniformlinearchargedensity,wherecisapositiveconstant.WithV=0atinfinity,findtheelectricPotential(a)atpointonthexaxis,adistancedfromoneendand(b)pointontheyaxis,adistanceyfromoneendoftherod.ScorereaderP1dLyP2Four():Asshowninrightfigure,aninfinitelengththinmetalplatecarriesacurrentIwhichuniformlydistributesintheplate,pleaseworkoutthemagneticfieldproducedbythecurrentatpointP.PadI ScorereaderFive():Figureshowsarectangularloopofwireimmersedinanon-uniformandvaryingmagneticfieldthatisperpendiculartoanddirectedintothepage.Thefieldmagnitudeisgivenby,withBinTeslas,tinsecondsandxinmeters.Theloophaswidthandheight.Whatarethemagnitudeanddirectionoftheinducedemf(感生电动势)aroundtheloopat?xyLhscorereaderSix():Thewavefunctionofparticlesinonedimensionalpotentialwellwithwidthais,pleaseworkoutthefollowingproblems:(1)NormalizationconstantA;(2)Whereisthemaximumprobabilityoffindingtheparticleswhenn=3? Appendix:answersfor0813-0815One:Selecttherightanswerinthebrackets(ineachproblem)1B2C3B4A5D6A7C8CTwo(ineachblank):Writetherightanswerinblanks1234(a)single-value;(b)continuous;(c)finite567Three():Solution:Weselectpointoastheoriginandselecttheelementchargeatthedistancetotheorigin,soaccordingtothedefinitionofelectricpotential(a):Theelectricpotentialatpointis(b):TheelectricpotentialatpointisFour():Solution:Weselecttheleftsideoftheplateastheoriginandselecttheelementcurrent()atthedistancetotheorigin,accordingthemagneticfieldoftheinfinitelongstraightwirecarryingcurrent:So:Direction:perpendicularthepaperinward. Five():Solution:Becausethemagnitudeofthemagneticfieldischangingwiththetime,themagneticfluxthroughtheloopisalsochanging.sowecantakethedifferentialarea()withitsnormalbeingparallelto,andthefluxthroughtheloopistakethisintegrationandinsertingtheintegrationlimitsandget:,when,accordingtoFaradylawatanytime:For,Direction:counterclockwisearoundtheloopatthistime.Six()Solution:(1)accordingtothenormalizationcondition:So:(2)Theprobabilitydensityoffindingtheparticlesis:,thepositionoffindingthemaximumprobabilitysatisfies:,Weget:Therefore:,Wecangetthepositionofmaximumprobabilityoffindingtheparticlesis:
