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4/12/12 Problems
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PROBLEMS
sec.214Coulomb'sLaw•1 OfthechargeQinitiallyonatinysphere,aportionqistobetransferredtoasecond,nearbysphere.
Bothspherescanbetreatedasparticles.Forwhatvalueofq/Qwilltheelectrostaticforcebetweenthetwospheresbemaximized?
Answer:
0.500•2Identicalisolatedconductingspheres1and2haveequalchargesandareseparatedbyadistancethatislarge
comparedwiththeirdiameters(Fig.2121a).Theelectrostaticforceactingonsphere2duetosphere1is .Supposenowthatathirdidenticalsphere3,havinganinsulatinghandleandinitiallyneutral,istouchedfirsttosphere1(Fig.2121b),thentosphere2(Fig.2121c),andfinallyremoved(Fig.2121d).Theelectrostaticforcethatnowactsonsphere2hasmagnitudeF′.WhatistheratioF′/F?
Figure2121Problem2.
•3 Whatmustbethedistancebetweenpointchargeq1=26.0μCandpointchargeq2=47.0μCfortheelectrostaticforcebetweenthemtohaveamagnitudeof5.70N?
Answer:
1.39m•4 Inthereturnstrokeofatypicallightningbolt,acurrentof2.5×104Aexistsfor20μs.Howmuchcharge
istransferredinthisevent?•5Aparticleofcharge+3.00×106Cis12.0cmdistantfromasecondparticleofcharge1.50×106C.Calculate
themagnitudeoftheelectrostaticforcebetweentheparticles.
Answer:
2.81N•6 Twoequallychargedparticlesareheld3.2×103mapartandthenreleasedfromrest.Theinitial
accelerationofthefirstparticleisobservedtobe7.0m/s2andthatofthesecondtobe9.0m/s2.Ifthemassofthe
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firstparticleis6.3×107kg,whatare(a)themassofthesecondparticleand(b)themagnitudeofthechargeofeachparticle?
••7InFig.2122,threechargedparticleslieonanxaxis.Particles1and2arefixedinplace.Particle3isfreetomove,butthenetelectrostaticforceonitfromparticles1and2happenstobezero.IfL23=L12,whatistheratioq1/q2?
Figure2122Problems7and40.
Answer:
4.00••8InFig.2123,threeidenticalconductingspheresinitiallyhavethefollowingcharges:sphereA,4Q;sphereB,
6Q;andsphereC,0.SpheresAandBarefixedinplace,withacentertocenterseparationthatismuchlargerthanthespheres.Twoexperimentsareconducted.Inexperiment1,sphereCistouchedtosphereAandthen(separately)tosphereB,andthenitisremoved.Inexperiment2,startingwiththesameinitialstates,theprocedureisreversed:SphereCistouchedtosphereBandthen(separately)tosphereA,andthenitisremoved.WhatistheratiooftheelectrostaticforcebetweenAandBattheendofexperiment2tothatattheendofexperiment1?
Figure2123Problems8and65.
••9 Twoidenticalconductingspheres,fixedinplace,attracteachotherwithanelectrostaticforceof0.108Nwhentheircentertocenterseparationis50.0cm.Thespheresarethenconnectedbyathinconductingwire.Whenthewireisremoved,thespheresrepeleachotherwithanelectrostaticforceof0.0360N.Oftheinitialchargesonthespheres,withapositivenetcharge,whatwas(a)thenegativechargeononeofthemand(b)thepositivechargeontheother?
Answer:
(a)1.00μC;(b)3.00μC••10 InFig.2124,fourparticlesformasquare.Thechargesareq1=q4=Qandq2=q3=q.(a)WhatisQ/qif
thenetelectrostaticforceonparticles1and4iszero?(b)Isthereanyvalueofqthatmakesthenetelectrostaticforceoneachofthefourparticleszero?Explain.
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Figure2124Problems10,11,and70.
••11 InFig.2124,theparticleshavechargesq1=q2=100nCandq3=q4=200nC,anddistancea=5.0cm.Whatarethe(a)xand(b)ycomponentsofthenetelectrostaticforceonparticle3?
Answer:
(a)0.17N;(b)0.046N••12Twoparticlesarefixedonanxaxis.Particle1ofcharge40μCislocatedatx=2.0cm;particle2ofchargeQ
islocatedatx=3.0cm.Particle3ofchargemagnitude20μCisreleasedfromrestontheyaxisaty=2.0cm.WhatisthevalueofQiftheinitialaccelerationofparticle3isinthepositivedirectionof(a)thexaxisand(b)theyaxis?
••13 InFig.2125,particle1ofcharge+1.0μCandparticle2ofcharge3.0μCareheldatseparationL=10.0cmonanxaxis.Ifparticle3ofunknownchargeq3istobelocatedsuchthatthenetelectrostaticforceonitfromparticles1and2iszero,whatmustbethe(a)xand(b)ycoordinatesofparticle3?
Figure2125Problems13,19,30,46,and67.
Answer:
(a)14cm;(b)0••14Threeparticlesarefixedonanxaxis.Particle1ofchargeq1isatx=a,andparticle2ofchargeq2isatx=+a.
Iftheirnetelectrostaticforceonparticle3ofcharge+Qistobezero,whatmustbetheratioq1/q2whenparticle3isat(a)x=+0.500aand(b)x=+1.50a?
••15 Thechargesandcoordinatesoftwochargedparticlesheldfixedinanxyplaneareq1=+3.0μC,x1=3.5cm,y1=0.50cm,andq2=4.0μC,x2=2.0cm,y2=1.5cm.Findthe(a)magnitudeand(b)directionoftheelectrostaticforceonparticle2duetoparticle1.Atwhat(c)xand(d)ycoordinatesshouldathirdparticleofchargeq3=+4.0μCbeplacedsuchthatthenetelectrostaticforceonparticle2duetoparticles1and3iszero?
Answer:
(a)35N;(b)10°;(c)8.4cm;(d)+2.7cm••16 InFig.2126a,particle1(ofchargeq1)andparticle2(ofchargeq2)arefixedinplaceonanxaxis,8.00cm
apart.Particle3(ofchargeq3=+8.00×1019C)istobeplacedonthelinebetweenparticles1and2sothattheyproduceanetelectrostaticforce onit.Figure2126bgivesthexcomponentofthatforceversusthecoordinatexatwhichparticle3isplaced.Thescaleofthexaxisissetbyxs=8.0cm.Whatare(a)thesignofchargeq1and(b)theratioq2/q1?
Figure2126Problem16.
••17InFig.2127a,particles1and2havecharge20.0μCeachandareheldatseparationdistanced=1.50m.(a)
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Whatisthemagnitudeoftheelectrostaticforceonparticle1duetoparticle2?InFig.2127b,particle3ofcharge20.0μCispositionedsoastocompleteanequilateraltriangle.(b)Whatisthemagnitudeofthenetelectrostaticforceonparticle1duetoparticles2and3?
Figure2127Problem17.
Answer:
(a)1.60N;(b)2.77N••18InFig.2128a,threepositivelychargedparticlesarefixedonanxaxis.ParticlesBandCaresoclosetoeach
otherthattheycanbeconsideredtobeatthesamedistancefromparticleA.ThenetforceonparticleAduetoparticlesBandCis2.014×1023Ninthenegativedirectionofthexaxis.InFig.2128b,particleBhasbeenmovedtotheoppositesideofAbutisstillatthesamedistancefromit.ThenetforceonAisnow2.877×1024Ninthenegativedirectionofthexaxis.WhatistheratioqC/qB?
Figure2128Problem18.
••19 InFig.2125,particle1ofchargeqandparticle2ofcharge+4.00qareheldatseparationL=9.00cmonanxaxis.Ifparticle3ofchargeq3istobelocatedsuchthatthethreeparticlesremaininplacewhenreleased,whatmustbethe(a)xand(b)ycoordinatesofparticle3,and(c)theratioq3/q?
Answer:
(a)3.00cm;(b)0;(c)0.444••20Figure2129ashowsanarrangementofthreechargedparticlesseparatedbydistanced.ParticlesAandCare
fixedonthexaxis,butparticleBcanbemovedalongacirclecenteredonparticleA.Duringthemovement,aradiallinebetweenAandBmakesanangleθrelativetothepositivedirectionofthexaxis(Fig.2129b).ThecurvesinFig.2129cgive,fortwosituations,themagnitudeFnetofthenetelectrostaticforceonparticleAduetotheotherparticles.ThatnetforceisgivenasafunctionofangleθandasamultipleofabasicamountF0.Forexampleoncurve1,atθ=180°,weseethatFnet=2F0.(a)Forthesituationcorrespondingtocurve1,whatistheratioofthechargeofparticleCtothatofparticleB(includingsign)?(b)Forthesituationcorrespondingtocurve2,whatisthatratio?
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Figure2129Problem20.
•••21Anonconductingsphericalshell,withaninnerradiusof4.0cmandanouterradiusof6.0cm,haschargespreadnonuniformlythroughitsvolumebetweenitsinnerandoutersurfaces.Thevolumechargedensityρisthechargeperunitvolume,withtheunitcoulombpercubicmeter.Forthisshellρ=b/r,whereristhedistanceinmetersfromthecenteroftheshellandb=3.0μC/m2.Whatisthenetchargeintheshell?
Answer:
3.8×108C•••22 Figure2130showsanarrangementoffourchargedparticles,withangleθ=30.0°anddistanced=2.00
cm.Particle2haschargeq2=+8.00×1019C;particles3and4havechargesq3=q4=1.60×1019C.(a)WhatisdistanceDbetweentheoriginandparticle2ifthenetelectrostaticforceonparticle1duetotheotherparticlesiszero?(b)Ifparticles3and4weremovedclosertothexaxisbutmaintainedtheirsymmetryaboutthataxis,wouldtherequiredvalueofDbegreaterthan,lessthan,orthesameasinpart(a)?
Figure2130Problem22.
•••23InFig.2131,particles1and2ofchargeq1=q2=+3.20×1019Careonayaxisatdistanced=17.0cmfromtheorigin.Particle3ofchargeq3=+6.40×1019Cismovedgraduallyalongthexaxisfromx=0tox=+5.0m.Atwhatvaluesofxwillthemagnitudeoftheelectrostaticforceonthethirdparticlefromtheothertwoparticlesbe(a)minimumand(b)maximum?Whatarethe(c)minimumand(d)maximummagnitudes?
Figure2131Problem23.
Answer:
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(a)0;(b)12cm;(c)0;(d)4.9×1026N
sec.215ChargeisQuantized•24Twotiny,sphericalwaterdrops,withidenticalchargesof1.00×1016C,haveacentertocenterseparationof
1.00cm.(a)Whatisthemagnitudeoftheelectrostaticforceactingbetweenthem?(b)Howmanyexcesselectronsareoneachdrop,givingititschargeimbalance?
•25 Howmanyelectronswouldhavetoberemovedfromacointoleaveitwithachargeof+1.0×107C?
Answer:
6.3×1011
•26Whatisthemagnitudeoftheelectrostaticforcebetweenasinglychargedsodiumion(Na+,ofcharge+e)andanadjacentsinglychargedchlorineion(Cl,ofchargee)inasaltcrystaliftheirseparationis2.82×1010m?
•27 Themagnitudeoftheelectrostaticforcebetweentwoidenticalionsthatareseparatedbyadistanceof5.0×1010mis3.7×109N.(a)Whatisthechargeofeachion?(b)Howmanyelectronsare“missing”fromeachion(thusgivingtheionitschargeimbalance)?
Answer:
(a)3.2×1019C;(b)2•28 Acurrentof0.300Athroughyourchestcansendyourheartintofibrillation,ruiningthenormalrhythm
ofheartbeatanddisruptingtheflowofblood(andthusoxygen)toyourbrain.Ifthatcurrentpersistsfor2.00min,howmanyconductionelectronspassthroughyourchest?
•29 InFig.2132,particles2and4,ofchargee,arefixedinplaceonayaxis,aty2=10.0cmandy4=5.00cm.Particles1and3,ofchargee,canbemovedalongthexaxis.Particle5,ofcharge+e,isfixedattheorigin.Initiallyparticle1isatx1=10.0cmandparticle3isatx3=10.0cm.(a)Towhatxvaluemustparticle1bemovedtorotatethedirectionofthenetelectricforce onparticle5by30°counterclockwise?(b)Withparticle1fixedatitsnewposition,towhatxvaluemustyoumoveparticle3torotate backtoitsoriginaldirection?
Figure2132Problem29.
Answer:
(a)6.05cm;(b)6.05cm••30InFig.2125,particles1and2arefixedinplaceonanxaxis,ataseparationofL=8.00cm.Theirchargesare
q1=+eandq2=27e.Particle3withchargeq3=+4eistobeplacedonthelinebetweenparticles1and2,sothattheyproduceanetelectrostaticforce onit.(a)Atwhatcoordinateshouldparticle3beplacedtominimizethemagnitudeofthatforce?(b)Whatisthatminimummagnitude?
••31 Earth'satmosphereisconstantlybombardedbycosmicrayprotonsthatoriginatesomewhereinspace.Iftheprotonsallpassedthroughtheatmosphere,eachsquaremeterofEarth'ssurfacewouldinterceptprotonsattheaveragerateof1500protonspersecond.Whatwouldbetheelectriccurrentinterceptedbythetotalsurfacearea
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oftheplanet?
Answer:
122mA••32Figure2133ashowschargedparticles1and2thatarefixedinplaceonanxaxis.Particle1hasachargewitha
magnitudeof|q1|=8.00e.Particle3ofchargeq3=+8.00eisinitiallyonthexaxisnearparticle2.Thenparticle3isgraduallymovedinthepositivedirectionofthexaxis.Asaresult,themagnitudeofthenetelectrostaticforce onparticle2duetoparticles1and3changes.Figure2133bgivesthexcomponentofthatnetforceasafunctionofthepositionxofparticle3.Thescaleofthexaxisissetbyxs=0.80m.TheplothasanasymptoteofF2,net=1.5×1025Nasx→∞.Asamultipleofeandincludingthesign,whatisthechargeq2ofparticle2?
Figure2133Problem32.
••33Calculatethenumberofcoulombsofpositivechargein250cm3of(neutral)water.(Hint:Ahydrogenatomcontainsoneproton;anoxygenatomcontainseightprotons.)
Answer:
1.3×107C•••34Figure2134showselectrons1and2onanxaxisandchargedions3and4ofidenticalchargeqandat
identicalanglesθ.Electron2isfreetomove;theotherthreeparticlesarefixedinplaceathorizontaldistancesRfromelectron2andareintendedtoholdelectron2inplace.Forphysicallypossiblevaluesofq≤5e,whatarethe(a)smallest,(b)secondsmallest,and(c)thirdsmallestvaluesofθforwhichelectron2isheldinplace?
Figure2134Problem34.
•••35 Incrystalsofthesaltcesiumchloride,cesiumionsCs+formtheeightcornersofacubeandachlorineionClisatthecube'scenter(Fig.2135).Theedgelengthofthecubeis0.40nm.TheCs+ionsareeachdeficientbyoneelectron(andthuseachhasachargeof+e),andtheClionhasoneexcesselectron(andthushasachargeofe).(a)WhatisthemagnitudeofthenetelectrostaticforceexertedontheClionbytheeight
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Cs+ionsatthecornersofthecube?(b)IfoneoftheCs+ionsismissing,thecrystalissaidtohaveadefect;whatisthemagnitudeofthenetelectrostaticforceexertedontheClionbythesevenremainingCs+ions?
Figure2135Problem35.
Answer:
(a)0;(b)1.9×109N
sec.216ChargeisConserved•36Electronsandpositronsareproducedbythenucleartransformationsofprotonsandneutronsknownasbetadecay.
(a)Ifaprotontransformsintoaneutron,isanelectronorapositronproduced?(b)Ifaneutrontransformsintoaproton,isanelectronorapositronproduced?
•37 IdentifyXinthefollowingnuclearreactions:(a)1H+9Be→X+n;(b)12C+1H→X;(c)15N+1H→4He+X.AppendixFwillhelp.
Answer:
(a)9B;(b)13N;(c)12C
AdditionalProblems38 Figure2136showsfouridenticalconductingspheresthatareactuallywellseparatedfromoneanother.Sphere
W(withaninitialchargeofzero)istouchedtosphereAandthentheyareseparated.Next,sphereWistouchedtosphereB(withaninitialchargeof32e)andthentheyareseparated.Finally,sphereWistouchedtosphereC(withaninitialchargeof+48e),andthentheyareseparated.ThefinalchargeonsphereWis+18e.WhatwastheinitialchargeonsphereA?
Figure2136Problem38.
39 InFig.2137,particle1ofcharge+4eisaboveafloorbydistanced1=2.00mmandparticle2ofcharge+6eisonthefloor,atdistanced2=6.00mmhorizontallyfromparticle1.Whatisthexcomponentoftheelectrostaticforceonparticle2duetoparticle1?
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Figure2137Problem39.
Answer:
1.31×1022N40InFig.2122,particles1and2arefixedinplace,butparticle3isfreetomove.Ifthenetelectrostaticforceon
particle3duetoparticles1and2iszeroandL23=2.00L12,whatistheratioq1/q2?
41WhatequalpositivechargeswouldhavetobeplacedonEarthandontheMoontoneutralizetheirgravitationalattraction?(b)Whydon'tyouneedtoknowthelunardistancetosolvethisproblem?(c)Howmanykilogramsofhydrogenions(thatis,protons)wouldbeneededtoprovidethepositivechargecalculatedin(a)?
Answer:
(a)5.7×1013C;(b)cancelsout;(c)6.0×105kg42InFig.2138,twotinyconductingballsofidenticalmassmandidenticalchargeqhangfromnonconducting
threadsoflengthL.Assumethatθissosmallthattanθcanbereplacedbyitsapproximateequal,sinθ(a)Showthat
givestheequilibriumseparationxoftheballs.(b)IfL=120cm,m=10g,andx=5.0cm,whatis|q|?
Figure2138Problems42and43.
43ExplainwhathappenstotheballsofProblem42ifoneofthemisdischarged(losesitschargeqto,say,theground).(b)Findthenewequilibriumseparationx,usingthegivenvaluesofLandmandthecomputedvalueof|q|.
Answer:
(b)3.1cm44 Howfarapartmusttwoprotonsbeifthemagnitudeoftheelectrostaticforceactingoneitheronedueto
theotherisequaltothemagnitudeofthegravitationalforceonaprotonatEarth'ssurface?45Howmanymegacoulombsofpositivechargearein1.00molofneutralmolecularhydrogengas(H2)?
Answer:
0.19MC
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46InFig.2139,fourparticlesarefixedalonganxaxis,separatedbydistancesd=2.00cm.Thechargesareq1=+2e,q2=e,q3=e,andq4=+4e,withe=1.60×1019C.Inunitvectornotation,whatisthenetelectrostaticforceon(a)particle1and(b)particle2duetotheotherparticles?
Figure2139Problem46.
47 Pointchargesof+6.0μCand4.0μCareplacedonanxaxis,atx=8.0mandx=16m,respectively.Whatchargemustbeplacedatx=24msothatanychargeplacedattheoriginwouldexperiencenoelectrostaticforce?
Answer:
45μC48InFig.2140,threeidenticalconductingspheresformanequilateraltriangleofsidelengthd=20.0cm.The
sphereradiiaremuchsmallerthand,andthespherechargesareqA=2.00nC,qB=4.00nC,andqC=+8.00nC.(a)WhatisthemagnitudeoftheelectrostaticforcebetweenspheresAandC?Thefollowingstepsarethentaken:AandBareconnectedbyathinwireandthendisconnected;Bisgroundedbythewire,andthewireisthenremoved;BandCareconnectedbythewireandthendisconnected.Whatnowarethemagnitudesoftheelectrostaticforce(b)betweenspheresAandCand(c)betweenspheresBandC?
Figure2140Problem48.
49Aneutronconsistsofone“up”quarkofcharge+2e/3andtwo“down”quarkseachhavingchargee/3.Ifweassumethatthedownquarksare2.6×1015mapartinsidetheneutron,whatisthemagnitudeoftheelectrostaticforcebetweenthem?
Answer:
3.8N50Figure2141showsalong,nonconducting,masslessrodoflengthL,pivotedatitscenterandbalancedwitha
blockofweightWatadistancexfromtheleftend.Attheleftandrightendsoftherodareattachedsmallconductingsphereswithpositivechargesqand2q,respectively.AdistancehdirectlybeneatheachofthesespheresisafixedspherewithpositivechargeQ.(a)Findthedistancexwhentherodishorizontalandbalanced.(b)Whatvalueshouldhhavesothattherodexertsnoverticalforceonthebearingwhentherodishorizontalandbalanced?
Figure2141Problem50.
51Achargednonconductingrod,withalengthof2.00mandacrosssectionalareaof4.00cm2,liesalongthe
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positivesideofanxaxiswithoneendattheorigin.Thevolumechargedensityρischargeperunitvolumeincoulombspercubicmeter.Howmanyexcesselectronsareontherodifρis(a)uniform,withavalueof4.00μC/m3,and(b)nonuniform,withavaluegivenbyρ=bx2,whereb=2.00μC/m5?
Answer:
(a)2.00×1010electrons;(b)1.33×1010electrons52AparticleofchargeQisfixedattheoriginofanxycoordinatesystem.Att=0aparticle(m=0.800g,q=4.00
μC)islocatedonthexaxisatx=20.0cm,movingwithaspeedof50.0m/sinthepositiveydirection.ForwhatvalueofQwillthemovingparticleexecutecircularmotion?(Neglectthegravitationalforceontheparticle.)
53Whatwouldbethemagnitudeoftheelectrostaticforcebetweentwo1.00Cpointchargesseparatedbyadistanceof(a)1.00mand(b)1.00kmifsuchpointchargesexisted(theydonot)andthisconfigurationcouldbesetup?
Answer:
(a)8.99×109N;(b)8.99kN54Achargeof6.0μCistobesplitintotwopartsthatarethenseparatedby3.0mm.Whatisthemaximumpossible
magnitudeoftheelectrostaticforcebetweenthosetwoparts?55OfthechargeQonatinysphere,afractionaistobetransferredtoasecond,nearbysphere.Thespherescanbe
treatedasparticles.(a)WhatvalueofamaximizesthemagnitudeFoftheelectrostaticforcebetweenthetwospheres?Whatarethe(b)smallerand(c)largervaluesofathatputFathalfthemaximummagnitude?
Answer:
(a)0.5;(b)0.15;(c)0.8556 Ifacatrepeatedlyrubsagainstyourcottonslacksonadryday,thechargetransferbetweenthecathair
andthecottoncanleaveyouwithanexcesschargeof2.00μC.(a)Howmanyelectronsaretransferredbetweenyouandthecat?
Youwillgraduallydischargeviathefloor,butifinsteadofwaiting,youimmediatelyreachtowardafaucet,apainfulsparkcansuddenlyappearasyourfingersnearthefaucet.(b)Inthatspark,doelectronsflowfromyoutothefaucetorviceversa?(c)Justbeforethesparkappears,doyouinducepositiveornegativechargeinthefaucet?(d)If,instead,thecatreachesapawtowardthefaucet,whichwaydoelectronsflowintheresultingspark?(e)Ifyoustrokeacatwithabarehandonadryday,youshouldtakecarenottobringyourfingersnearthecat'snoseoryouwillhurtitwithaspark.Consideringthatcathairisaninsulator,explainhowthesparkcanappear.
57Weknowthatthenegativechargeontheelectronandthepositivechargeontheprotonareequal.Suppose,however,thatthesemagnitudesdifferfromeachotherby0.00010%.Withwhatforcewouldtwocoppercoins,placed1.0mapart,repeleachother?Assumethateachcoincontains3×1022copperatoms.(Hint:Aneutralcopperatomcontains29protonsand29electrons.)Whatdoyouconclude?
Answer:
1.7×108N58InFig.2125,particle1ofcharge80.0μCandparticle2ofcharge+40.0μCareheldatseparationL=20.0cm
onanxaxis.Inunitvectornotation,whatisthenetelectrostaticforceonparticle3,ofchargeq3=20.0μC,ifparticle3isplacedat(a)x=40.0cmand(b)x=80.0cm?Whatshouldbethe(c)xand(d)ycoordinatesofparticle3ifthenetelectrostaticforceonitduetoparticles1and2iszero?
59Whatisthetotalchargeincoulombsof75.0kgofelectrons?
Answer:
1.32×1013C60InFig.2142,sixchargedparticlessurroundparticle7atradialdistancesofeitherd=1.0cmor2d,asdrawn.The
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chargesareq1=+2e,q2=+4e,q3=+e,q4=+4e,q5=+2e,q6=+8e,q7=+6e,withe=1.60×1019C.Whatisthemagnitudeofthenetelectrostaticforceonparticle7?
Figure2142Problem60.
61Threechargedparticlesformatriangle:particle1withchargeQ1=80.0nCisatxycoordinates(0,3.00mm),particle2withchargeQ2isat(0,3.00mm),andparticle3withchargeq=18.0nCisat(4.00mm,0).Inunitvectornotation,whatistheelectrostaticforceonparticle3duetotheothertwoparticlesifQ2isequalto(a)80.0nCand(b)80.0nC?
Answer:
(a) ;(b)
62 InFig.2143,whatarethe(a)magnitudeand(b)directionofthenetelectrostaticforceonparticle4duetotheotherthreeparticles?Allfourparticlesarefixedinthexyplane,andq1=3.20×1019C,q2=+3.20×1019
C,q3=+6.40×1019C,q4=+3.20×1019C,θ1=35.0°,d1=3.00cm,andd2=d3=2.00cm.
Figure2143Problem62.
63Twopointchargesof30nCand40nCareheldfixedonanxaxis,attheoriginandatx=72cm,respectively.Aparticlewithachargeof42μCisreleasedfromrestatx=28cm.Iftheinitialaccelerationoftheparticlehasamagnitudeof100km/s2,whatistheparticle'smass?
Answer:
2.2×106kg64Twosmall,positivelychargedsphereshaveacombinedchargeof5.0×105C.Ifeachsphereisrepelledfromthe
otherbyanelectrostaticforceof1.0Nwhenthespheresare2.0mapart,whatisthechargeonthespherewiththesmallercharge?
65TheinitialchargesonthethreeidenticalmetalspheresinFig.2123arethefollowing:sphereA,Q;sphereB,Q/4;andsphereC,Q/2,whereQ=2.00×1014C.SpheresAandBarefixedinplace,withacentertocenterseparationofd=1.20m,whichismuchlargerthanthespheres.SphereCistouchedfirsttosphereAandthentosphereBandisthenremoved.WhatthenisthemagnitudeoftheelectrostaticforcebetweenspheresAandB?
4/12/12 Problems
13/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…
Answer:
4.68×1019N66AnelectronisinavacuumnearEarth'ssurfaceandlocatedaty=0onaverticalyaxis.Atwhatvalueofyshould
asecondelectronbeplacedsuchthatitselectrostaticforceonthefirstelectronbalancesthegravitationalforceonthefirstelectron?
••67 InFig.2125,particle1ofcharge5.00qandparticle2ofcharge+2.00qareheldatseparationLonanxaxis.Ifparticle3ofunknownchargeq3istobelocatedsuchthatthenetelectrostaticforceonitfromparticles1and2iszero,whatmustbethe(a)xand(b)ycoordinatesofparticle3?
Answer:
(a)2.72L;(b)068Twoengineeringstudents,Johnwithamassof90kgandMarywithamassof45kg,are30mapart.Suppose
eachhasa0.01%imbalanceintheamountofpositiveandnegativecharge,onestudentbeingpositiveandtheothernegative.Findtheorderofmagnitudeoftheelectrostaticforceofattractionbetweenthembyreplacingeachstudentwithasphereofwaterhavingthesamemassasthestudent.
69IntheradioactivedecayofEq.2113,a238Unucleustransformsto234Thandanejected4He.(Thesearenuclei,notatoms,andthuselectronsarenotinvolved.)Whentheseparationbetween234Thand4Heis9.0×1015m,whatarethemagnitudesof(a)theelectrostaticforcebetweenthemand(b)theaccelerationofthe4Heparticle?
Answer:
(a)5.1×102N;(b)7.7×1028m/s2
70InFig.2124,fourparticlesformasquare.Thechargesareq1=+Q,q2=q3=q,andq4=2.00Q.Whatisq/Qifthenetelectrostaticforceonparticle1iszero?
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