4/12/12 Problems

1/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

Print this page

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

4/12/12 Problems

2/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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.

4/12/12 Problems

3/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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)

4/12/12 Problems

4/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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?

4/12/12 Problems

5/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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:

4/12/12 Problems

6/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

(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

4/12/12 Problems

7/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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

4/12/12 Problems

8/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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?

4/12/12 Problems

9/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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

4/12/12 Problems

10/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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

4/12/12 Problems

11/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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

4/12/12 Problems

12/13edugen.wileyplus.com/edugen/courses/crs4957/…/aGFsbGlkYXk5MDg4YzIxXzlfMC54Zm9ybQ.enc?…

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?

Copyright©2011JohnWiley&Sons,Inc.Allrightsreserved.