SP212 Lab: One Electrostatics Version: January 6, 2014

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Physics II

Lab 1

SP212

Electrostatics

I. Introduction

A. Physicsisanexperimentalscience,whichmeansthatsomephysicistsdiscoverlawsandprinciplesthroughcarefullyconductedexperimentsanddataanalysis.Oftentheresultisamathematicallydescribedphysicalprinciple.

B. Charles­AugustindeCoulombwasonesuchscientist.Inthe18thcentury,heandmanyofhiscolleaguessuspectedthatthemagnitudeoftheelectricalforcebetweentwochargedobjectsdecreasesasafunctionoftheirseparationsimilarlytothegravitationalforceasdescribedbyNewton’slawofuniversalgravity.

C. In1785,hepublishedreportsonthetheoryofelectricity,whichcontainedwhatisnowknownasCoulomb’sLaw.

D. Coulomb’sLaw:Themagnitudeoftheelectrostaticforcebetweentwochargedparticlesisdirectlyproportionaltotheproductofthemagnitudeofthechargesandinverselyproportionaltothesquareofthedistancebetweenthem.

1 2

2

q qF k

r=

v

E. Oneprimarydifferencebetweengravity(whichstudentslearnedaboutinCH13,PhysicsI)andelectrostaticforce,however,isthattheelectrostaticforcecanbeeitherattractive(likegravity)orrepulsive.

F. Thisrepulsiveforceisreadilyapparentinadeviceknownasanelectroscope.

G. Anelectroscopeisasimplescientificinstrumentinventedintheearly17thcenturytodetectthepresenceandrelativemagnitudeofthenetelectricalchargeonanobject.ElectroscopesdetectchargebytherelativedisplacementofareferenceobjectduetotheelectrostaticforceofrepulsiongovernedbyCoulomb’sLaw

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H. TheprimarypurposeofthislabistouseCoulomb’slawtomeasuretheelectricchargetransferredfromoneobjecttoanotherviaasimpleelectroscope.Asecondarypurposeistoobservethisrepulsivebehavior…tohelpstudentsrememberthatVECTORSareimportantandthatDIRECTIONMATTERSgreatly!

II. Discussion

A. Twoclassicaltypesofelectroscopesstillinusetodayarethegold­leafelectroscopeandthepithballelectroscope.

B. Evensince1900,homemadeelectroscopesweremadefromitemstypicallyfoundaroundthehousetoaidscientistsintheirlaboratoryexperiments.Duringtoday’slab,studentswillfollowsuitandbuildelectroscopesfromcommoneverydayobjectstoemphasizethatphysicsoccursintheworldaroundthem.

C. Tobuildtheelectroscopestodaystudentswillusecopperwireandaluminumfoil(oraluminumpaint)astheirconductors.Conductorsarematerialsthroughwhichchargecanmovefreely;examplesincludemetals(suchascopperwireandaluminumfoil),thehumanbody,andtapwater

D. Tohelpinsulatepartsoftheirelectroscope,studentswilluseplastic,glass,anddryairastheirnonconductors.Nonconductors—alsocalledinsulators—arematerialsthroughwhichchargecannotmovefreely;examplesincluderubber,plastic,glass,acrylic,dryair,andchemicallypurewater.

E. Yourinstructorwillexplainhowtobuildeachtypeofelectroscopethatwewillusetodaytomeasureelectrostaticobservablesandhowtoestimatetheuncertainties.

III.Objectives

Attheendofthisactivity,thestudentshould:

A. BeabletoexplainCoulomb’sLaw,includingtheeffectofeachtermontheresultantforce.

B. Observethatlikechargesrepelandunlikechargesattract.

C. Beabletodiscusshowanelectroscopeworkstodetecttherelativemagnitudeofthenetchargeonanobject.

D. Observeandbeabletoexplainthedifferencebetweenchargedbyinductionandchargedbyconduction.

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E. BeabletomanipulatetheCoulomb’slawequationandafree­bodydiagramtosolvefortheamountofchargeonpointchargesseparatedbyafixeddistanceduetotheelectrostaticforce.

F. (TimePermitting)Usetwoflexiblestrawstofeeltheelectrostaticforceofrepulsion.

G. (TimePermitting)Beabletocalculatethenumberofconductionelectronsthattransferredfromtheacrylicrodtothepithball.

IV. NeededEquipment

A. AMasonjar,about30cmofbarecopperwire,scotchtape,blankcompactdisk(CD),acrylicrod,clothorfur,aluminumfoil,twopithballs,astanchionforattachingthepiths,calculator,ruler,meterstick,calipers,twoflexibledrinkingstraws,apaperclip,andapencil/pen.

V. Procedure

A. UsingasimplefoilelectroscopetoobserveCoulomb’slaw

A.1.Buildingthefoilelectroscope

a) Cutasmallsquareofself­adhesivecorklargeenoughtocovertheholeinthecenterCD.

b) CarefullyremovethebackingandattachthecorktheholeinthecenterCD.Thepapercomesofftheglue,becarefulnottopullthecorkoffoftheglue.

c) Bendoneendofthepieceofbarecopperwireintoasmallspiralwithtotaldiameterbeingabout3cm.Leavetheotherendstraight.Thestraightendshouldbeabout9or10cmlong.Thebelowdrawingarenottoscale.

d) Punctureaholeinthecenterofthecorkusingthepaperclip,thenpushthenon­bentendthroughcorkedholeinthecircularpieceofplastic.Leaveabout3cmabovethecircularpieceofplasticandwrapapieceofscotchtapearoundthewiretopreventthewirefromfallingdownthroughthecork.

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e) Onthenon­bentend,bendtheendtomakea“J”orhookshape.

f) Cuttwostripsofthealuminumfoilapproximately1cminwidthand4cmlong.

g) Foldoverapproximately1cmononeendofeachstriptoreinforceandthenplacethefoilstripsontopofeachother.Thenusingamechanicalpencil(orsimilarlysharpobject,liketheendofthepaperclip)pierceaholeinthecenterofthefoldedoverpiece.

h) Smoothoutthealuminumstripstoensuretheyarenotstucktogether.

i) Nowplacethefoilstripsoverthe“J”youformedinthewireandinstallthemechanismontopoftheMasonjar.

j) Yourfinaldeviceshouldlooksimilartothediagrambelow.

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A.2.Usingtheelectroscopetoshowchargedbyinduction.

a) Here’show:Firsttransferchargesfromyourclothorfuratyourstationtotheacrylicrodbyrubbingthecloth/furovertherodtightlyacoupleoftimes.Thefrictionalchargingprocessinvolvesthetransferofelectronsbetweentwoobjectsbyrubbingthemtogether.

b) Now,let’sseeiftherodhasbeenchargedbyfrictionwhilealsotestingtheprocessofchargingtheelectroscopebyinductionfirst.Holdtheacrylicrodupto(BUTDONOTTOUCH)thecopperspiral.Noticethatthefoilleavesmoveapart.Let’sseewhy.First,assumeforthemomentthattherodhasanetpositivechargeasshowninthefigurebelow.Whentherodisnearthecopperspiral,negativelychargedparticlesinthecopperandthefoilareattractedupintothespiral,whilethepositivelychargedparticlesarerepelleddownintothefoilleaves.Sincebothleaveshavethesamesigncharge,theyrepeloneanother,andsomoveapart.

Figure1

IllustrationfromWikipedia:http://en.wikipedia.org/wiki/Electrostatic_induction:Yourchargesmightbereversedependingonwhetheryouchargedyouracrylicrod

withfurorcloth.

c) Slowlymovetherodawayandnoticethatthefoilleavesstarttomoveclosertogetherbecauselesschargeisinducedinthefoilleaves.

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d) Nowputmorechargeonyourrodbyrubbingitagainwiththeclothorfurafewmoretimes.Thenbringtherodupto(BUTDONOTTOUCH)thecopperspiral.Noticethatthefoilleavesmoverelativelyfurtherapartthanthefirsttime;supportingtheideathatthemagnitudeoftheelectricforceincreasesasthenetchargeincreases..Itworksbestifyoudonotletthefoilleavestouchthesideofthejar.Iftheydotouch,youmighthavetomovethemechanismsuchthattheleavesarenolongertouchingtheMasonjarside.

e) CompletelymovetherodawayandnoticethatthefoilleavesDONOTremaincharged.Thenetchargeinthecopperandfoiliszero,butwiththeabsenceoftherod,thepositiveandnegativechargesarenolongerbeingattractedorrepulsedbytherod.

1) Lookingbackatfigure1,howwouldthepicturechangeiftherodisnegativelycharged?Canwetellonlybythisanalysisifourrodispositivelyornegativelycharged?Whatexperimentwouldyousuggesttotellwhetherourrodwaspositivelychargedornegativelycharges?

2) Whenyourubanacrylicrodwithfur,electronsaretransferredtotherod,causingtherodtobecomenegativelycharged.Ifyourubtheacrylicrodwithsilkcloth,electronsaretransferredtothesilkclothandtherodbecomespositivelycharged.

A.3.Usingtheelectroscopetoshowchargedbyconduction.

a) Beforestartingthisnextexperiment,touchthecopperspiralwithyourfinger.Thisprovidesapathforanyexcesschargestogotogroundviayourbody.Itdoesnothurt,andyouprobablywon’tevenfeelanything.

b) Transferchargesfromyourclothorfuratyourstationtotheacrylicrodbyrubbingthecloth/furovertherodacoupleoftimesasyoudidinthepreviousexperiment.

c) Then,todemonstratechargedbyconduction,TOUCHtheacrylicrodtothecopperspiral.Noticethatthefoilleavesmoveapart.

d) Slowlymovetherodawayandnoticethatthistimethefoilleavesstayapart;indicatingthefactthatchargewaspermanentlytransferredtothefoilleavesbyconduction(touching).

e) Nowputmorechargeonyourrodbyrubbingitagainwiththeclothorfurafewmoretimes.Thentouchthecopperspiralwiththerod.Noticethatthefoilleavesmoveevenfurtherapart,againshowingthattheelectrostaticforceisproportionaltocharge.

f) Completelymovetherodawayandthefoilleavesremainapart.Chargewastransferredbyconduction.

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A.4.Discussionpoints:

a) Describetheoperationoftheelectroscope.BespecificanduseproperEnglishsentences.

b) DuringstepA.3,howdoesthemagnitudeofelectrostaticforceononeofthefoilleavescomparethatontheother?Drawafree­body­diagramtoassistyourdiscussion.

c) Explainthedifferencebetweenchargedbyinductionandchargedbyconduction.

d) Whatwouldbetheeffectonthefoilleavesifthehumidityintheroomwereraised?Why?Hint:humidairisbetteratconductingelectricitythandryair.

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B.UsingapithballelectroscopetoobserveCoulomb’sLaw

B.1.Buildingthesimplepith­ballelectroscope

a) Pithisthespongytissueonthestemsofsomeplants.Itisverysoftandlightweight.Thismakesitadvantageousforourpurposesbecauseitsgravitationalforceissmallenoughthattheelectrostaticforceiscomparable.

b) Inourcase,thepith­ballshavebeenpaintedwithaluminumpaintsothattheelectrostaticchargewilldistributeitselfuniformlyoverthesurfaceofthepith­ball.Thisisimportantforthisexperiment,becausewewilltreatthepithballasifitwereapointsourcewithallofitsexcesschargewerelocatedatitscenterofmass.

c) Before attaching anything to the stanchion we must make some initial measurements. 1) Measurethelengthofthestringfromthepivotpointtothecenterofthe

pithball(wearemakingtheassumptionthatthestringisnearlymassless

comparedtothepithball,sothecenterofmassofthesystemisthecenterofthepith‐ball.)Recordthislength.

2) Normallyyouwouldhavetodeterminethemassofthepithball.Sincethescalesintheroomarenotcalibratedtoalowenoughscale,assumethe

averagemassofapithballis40mg(thisisanexampleofpossibleuncertaintyinourexperiment.)

d) Attach both pith balls to your stanchion and make the two pith balls sit parallel to each other (same distance down from pivot point.) Do not tie strings into knots as they must be used by other students!

e) Touch each pith-ball with your finger to remove any net charge from them.

f) The pith balls should be touching each other at this point. Ensure that the strings are not tangled.

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B.2.Nowyouarereadytoplacechargeonthepith­balls

a) Wipetheacrylicrodvigorouslywiththeclothorfurthenrubtherodoneachpithballoneatimetotransferchargetothepithballs.Trynottotouchthepithballswithyourfingersasyouwillaccidentlygroundthemcausingthemtodischarge.

b) Whatdoyouexpectthepithballstodoaftertheyarecharged?Why?

c) Redostepa)afewtimestogetthetwopithballstobeseparatedbyapproximately1to2cm.

B.3.Measurementofthedistancebetweenthepithballs

a) Inordertotrytocalculatethechargeonthepithballs,youneedtoknowtheexactdistancebetweenthetwopithballs.

1) Thisisthemostdifficultpartofthislab.Therearemanydifferentwaystoachievethismeasurementwithoutdischargingthetwopith‐balls,trytodiscoverthemethodthatyouthinkworksbesttoachievethisgoal.Note:

JustlikemanytasksassignedtoyouintheNAVY,itisprobablynotbestachievedviaasingleperson!Trynottotouchthepith‐ballswithyourfingersortheruler/calipersasyouwillaccidentlygroundthemcausing

themtodischarge!

2) Whatwouldhappenifyoubroughtupameasuringscalenexttothepithballsinordertomeasurethedistancebetweenthecenters?Tryitifyouarenotsure.Explain.

3) Ifyoudischargeyourpithballs,andthedistancedropstobelow1cm,thenrechargeyourpithballstoachievethedesiredrangetopreventtheuncertaintiesfrombeinglargerthanthemeasurementsyouaretaking.

4) Ifyoucomeupwithagreatidea,shareitwiththeclass.Theprocessof

sharinglessonslearnedsothatyoudonotrecreatethesameerrorsoverandoveragaininthefleetisanencouragedpractice

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B.4.DataAnalysis(Findingthechargeonthepithballs.)

a) Firstlookattheforcesactingonahangingpithball.Labeleachoftheforcesontheprovidedfree­body­diagramoftheleftball.

b) Labelthetrianglebelowformedfromwherethepithballstartedtowhereitendedwiththeaboveforcesasappropriate.

c) Noticethatinreality,thatthereisasmallheightdifferencebetweentheverticalpositionoftheballanditsfinalposition.Callthisheight,h.IfyourememberfrompendulumsinCH15,thevalueofhistrulyverysmallandcanultimatelybeneglected,butlet’snotgetaheadofourselves.

d) Lookatthesimilartrianglethatisformedbetweentheelectrostaticforceandtheforceofgravityemphasizedinthedrawingabove.IfyoucallthelengthofyourstringL,asstatedabovetheheightdifferenceish,andifyoucallthehorizontaldistancefromvertical,x.ThentheratiooftheelectrostaticforcetothatoftheforceofgravitymustbethesameratioasxtoL­hbysimilartriangles.Writethisratioequation.

L L‐h

hx

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e) RearrangetheratioandsolveforFeintermsofFg.

f) Youalreadyknowthat:

1 2

2e

q qF k

r=

vand

gF mg=

g) Butsincewecanassumethatq1=q2andthatL­hisessentiallyL,thenyoucanrewritethetwoequationsforFeandsetthemequaltoeachother.Youshouldwindupwithasingleequationthathask,q,andrononesideandx,m,g,Lontheotherside.

h) Now,thinkabouthowrisrelatedtoxandthenrearrangetheequationtosolveforq.Afterwalkingyouthroughtheprocessthisfar,youshouldbeabletosolveforqintermsofg,k,m,L,andxallofwhichshouldbeknownvaluesatthispoint.

i) Determinethechargeoneachpith­ball.Youranswershouldbeinnanocoulombs.

Q=_______________________nC

B.5.Discussionpoints:

a) Describeatleastfourpossiblesourcesoferrororuncertaintyintroducedduringtheexperimentnotincludinghumanmistakesormathematicalmistakes.

b) Whatrecommendationsdoyouhavetominimizetheaboveerrorsifyouhadtoredothislab?

c) Howdoesthemagnitudeofelectrostaticforceoneachofthepithballscomparewitheachother?

d) Ifourassumptionthateachofthepithballshadequalchargetransferredtoitturnedoutnottobetrue,saytheleftballhad10%moreexcesschargeonitthantherightball,whataffect(ifany)wouldthishaveontherelativemagnitudeofelectrostaticforceoneachofthepithballs?

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C.(TimePermitting)Anexperimenttofeelthatelectrostaticforceofrepulsion.

C.1.Itturnsoutthatifyourubaplasticdrinkingstrawwithclothorfur,thatchargesaretransferredinamannersimilarrubbingtheacrylicrodwiththeclothorfur.

a) Rubaprovidedplasticdrinkingstrawwithclothorfur.

b) Handittoyourlabpartnerwhoshouldholditviathesmallendbeforetheflexiblepart.Trynottotouchtherestofthestrawwithyourfingersasyouwillaccidentlygrounditcausingittodischarge.

c) Rubanotherprovidedplasticdrinkingstrawwiththeclothorfur.

d) Nowyourlabpartnershouldtrytoholdthestrawsasshownbelow.

e) Yourpartner’sfingersshouldclearlybeabletofeeltheforceopposingtheirattemptstobringthetwostrawstogether.

f) Althoughitwouldbenicetodeterminetheamountofchargeonthestraws,thestrawscannotbemodeledaspointcharges.However,itwasagoodqualitativeexperiment.

D.(TimePermitting)Calculatethenumberoffreeelectronsthatwereplacedonthepithball.

a) Usingthefactthattheelementalchargeis1.602x10­19coulombs,calculatethenumberoffreeelectronsthatweretransferredfromyouracrylicrodtoasinglepithball.

#offreeelectrons=_______________________

b) Hopefully this now gives you a better feel for just how large a Coulomb of charge actually is, since we only transferred a few nanocoulombs here!

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E.LabReporttohandin:

E.1.SectionA­4’sdiscussionquestionanswers.

E.2.SectionCdata,drawings,andcalculations.(Ifaspreadsheetwasused,includespreadsheet.)

E.3.Section C-5’s discussionquestionanswers.

E.4.Part D: Calculation if assigned.

VI. Clean­Up

A. GoldenRule:“Dountoothersasyouexpectthemtodountoyou.”

ThisappliesasmuchhereinthelabasitdoesintheFleet.AsfutureNavalOfficers,howcanyouexpectyourenlistedsailorstomaintainacleanworkareaifyourstateroom,workareas,messarea,etcisa“pigsty?”SoasofficersitisimperativethatwecleanupafterourselvesnotonlytofollowtheGoldenRule,butalsotoleadbyexamplefortheenlistedpersonnelunderourcharge.

1. EndofLabCheckout:Beforeleavingthelaboratory,tidyuptheequipmentattheworkstationandquitallrunningsoftware.

2. Thelabstationshouldbeinbetterconditionthanwhenyouarrivedandmoreimportantly,shouldbeofanappearancethatyouwouldbePROUDtoshowtoyourlegalguardiansduringa“ParentsWeekend.”

3. HaveyourinstructorinspectyourlabstationandreceivetheirpermissiontoleavetheLabRoom.

4. YouSHALLfollowthisprocedureduringeverylabforSP212!

ManythankstoDr.KatzandMr.GaryBishopfortheirassistanceinproducingthisLaboratory

procedure;specificreferencescanbesuppliedonrequest.LCDRTimothyShivok