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December 17, 2015 CH 21 ElectricCharge
I.
ElectricCharge
A. Youhavebeenexposedtoelectricchargeeversinceelementary
school…draggingyourfeetacrosscertaintypesofcarpetandthen
bringingyourfingernearmetaldoorknoborevenafriend….your
clothessticktoyourbodyifyoudidnotuseadryersheet…electric
chargeisallaroundus.
1.
ElectricChargeisanintrinsiccharacteristicofthefundamental
particlesmakingupthoseobjects;thatis,itisapropertythatcomes
automaticallywiththoseparticleswherevertheyexist.Forexampleusing
yourknowledgefromChemistry,ifanatomhasmoreelectronsthanprotons
thenthenetchargeisnegative;iftheatomhasmoreprotonsthanelectrons
thenthenetchargeispositive.
2.
Chargeswiththesameelectricalsign
___________________________________,andchargeswithoppositeelectrical
signs_______________________________eachother.
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December 17, 2015 B. Electrostaticforcetheforcecausedbyeitherstationarycharges
orchargesmovingveryslowly.
1.
Example(s)
II.
+ ‐ +
+ 1 2 1 2 ConductorsandInsulators
A. Conductorsarematerialsthroughwhichchargecanmovefreely;
examplesincludemetals(suchascopperincommonlampwire),the
humanbody,andtapwater.
B. Nonconductors—alsocalledinsulators—arematerialsthrough
whichchargecannotmovefreely;examplesincluderubber,plastic,
glass,andchemicallypurewater.
C. Semiconductorsarematerialsthatareintermediatebetween
conductorsandinsulators;examplesincludesiliconandgermaniumin
computerchips.
D. Superconductorsarematerialsthatareperfectconductors,
allowingchargetomovewithoutanyhindrance.
E. Thepropertiesofconductorsandinsulatorsareduetothe
structureandelectricalnatureofatoms.
1.
Atomsconsistofpositivelychargedprotons,negativelycharged
electrons,andelectricallyneutralneutrons.Theprotonsandneutronsare
packedtightlytogetherinacentralnucleus.
2.
Whenatomsofaconductorcometogethertoformthesolid,someof
theiroutermost(andsomostlooselyheld)electronsbecomefreetowander
aboutwithinthesolid,leavingbehindpositivelychargedatoms(positive
ions).Wecallthemobileelectronsconductionelectrons.
3.
Therearefew(ifany)freeelectronsinanonconductor.
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December 17, 2015 III.
Coulomb’sLaw
A. Remember,chapter13Newton’sLawofgravitation.Remember
howitwasaninversesquarelaw.
1.
Rememberthoughthatgrandgravitationalconstant
m3
kg  s 2
G
2.
r̂ ,wasalwaysattractiveforthegravitationalforce.
B. Welltheforceofrepulsionorattractionduetothecharge
propertiesofobjectsiscalledanelectrostaticforce.
1.
TheequationforelectrostaticforcetakesasimilarformtoNewton’s
lawofgravitation(inversesquarelaw).Theequationgiventotheforcefor
chargedparticlesiscalledCoulomb’slaw:
whereparticle1haschargeq1andparticle2haschargeq2,andFistheforce
onparticle1.Here r̂ isaunitvectoralonganaxisextendingthroughthetwo
particles,risthedistancebetweenthem,andkisaconstant.
2.
r̂ canbeeitherattractiveorrepulsivewithelectrostaticforce!
C. TheSIunitofchargeisthecoulombrepresentedbyCapitalC.
D. Theconstant k 
N  m2
C2

E. Thequantity0iscalledthepermittivity(offreespace)constant
 0  8.85 x1012
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C2
N  m2
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December 17, 2015 F. Directionoftheforce:
1.
Rememberchargeswiththesameelectricalsignrepel,andcharges
withoppositeelectricalsignsattracteachother;thus:
+ 1 +
2 ‐ 1 ‐ 2 + ‐ 1 2 G. Current
1.
Currentistherateatwhichchargemovespastapointorthrougha
region(dq/dt)
inwhichiisthecurrent(inamperes)anddq(incoulombs)istheamountof
chargemovingpastapointorthrougharegionintimedt(inseconds).
2.
Therefore,
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December 17, 2015 H. Superpositionprinciple:Iftherearenchargedparticles,they
interactindependentlyinpairs,andtheforceonanyoneofthem,say
particle1,isgivenbythevectorsum
inwhich,F1,4istheforceactingonparticle1duetothepresenceof
particle4,etc.
I.
Shelltheorem
1.
Ashellofuniformchargeattractsorrepelsachargedparticlethatis
outsidetheshellasifalltheshell’schargewereconcentratedatitscenter.
2.
Ifachargedparticleislocatedinsideashellofuniformcharge,thereis
nonetelectrostaticforceontheparticlefromtheshell.
IV.
ChargeisQuantized
A. SincethedaysofBenjaminFranklin,ourunderstandingofthe
natureofelectricityhaschangedfrombeingatypeof‘continuous
fluid’toacollectionofsmallerchargedparticles.Thetotalchargewas
foundtoalwaysbeamultipleofacertainelementarycharge,“e”:
q = B. Thevalueofthiselementarychargeisoneofthefundamental
constantsofnature,anditisthemagnitudeofthechargeofboththe
protonandtheelectron.Thevalueof“e”is:
e  1.602 x1019 C C. Table
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December 17, 2015 D. Elementaryparticleseithercarrynocharge,orcarryasingle
elementarycharge.Whenaphysicalquantitysuchaschargecanhave
onlydiscretevalues,ratherthananyvalue,wesaythequantityis
quantized.Itispossible,forexample,tofindaparticlethathasno
chargeatall,orachargeof+10e,or‐6e,butnotaparticlewitha
chargeof,say,3.57e.
E. Manydescriptionsofelectricchargeusetermsthatmightleadyou
totheconclusionthatchargeisasubstance.Phraseslike:
“Chargeonasphere”,“Chargetransferred”,“Chargecarriedontheelectron”
However,chargeisapropertyofparticles,oneofmanyproperties,
suchasmass.
V.
ChargeisConserved
A. Ifonerubsaglassrodwithsilk,apositivechargeappearsonthe
rod.Measurementshowsthatanegativechargeofequalmagnitude
appearsonthesilk.Thissuggeststhatrubbingdoesnotcreatecharge
butonlytransfersitfromonebodytoanother,upsettingtheelectrical
neutralityofeachbodyduringtheprocess.
B. Thishypothesisofconservationofchargehasstoodupunder
closeexamination,bothforlarge‐scalechargedbodiesandforatoms,
nuclei,andelementaryparticles.
1.
Example1:Radioactivedecayofnuclei,inwhichanucleustransforms
into(becomes)adifferenttypeofnucleus.
2.
(
Auranium‐238nucleus(
238
U)transformsintoathorium‐234nucleus
234
Th)byemittinganalphaparticle.Analphaparticlehasthesamemakeup
4
asahelium‐4nucleus,ithasthesymbol He.Herethenetchargeis+92e.
U  Th + He Page6
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December 17, 2015 3.
Example2:Anelectrone(charge‐e)anditsantiparticle,thepositrone
(charge+e),undergoanannihilationprocess,transformingintotwogamma
rays(high‐energylight):Herethenetchargeiszero.
4.
Example3:Agammaraytransformsintoanelectronandapositron.
Herethenetchargeisagainzero.
VI.
Sampleproblems:
A. Whatmustbethedistancebetweenpointchargeq1=36.0mCand
pointchargeq2=‐57.0mCfortheelectrostaticforcebetweenthemto
haveamagnitudeof7.70N?
B. Twoidenticalcharges,2.0mapart,exertforcesofmagnitude
4.0Noneachother.Thevalueofeitherchargeis:
A) 1.8 x 10‐9 C B) 2.1 x 10‐5 C C) 4.2 x 10‐5 C D) 1.9 x 105 C E) 3.8 x 105 C Page7
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December 17, 2015 C. Giventhebelowdiagram,whatisthemagnitudeofFnetonq?
Q1= 60nC 3.0 mm 4.0 mm Q2= 80nC q= 24nC 
Fnet on q  
Fnet on q in x dir  
Fnet on q in y dir  
Fnet on q  NOTE :
 result  tan 1 (
Fnet , y
Fnet , x
)  Page8
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December 17, 2015 D. ThefigurebelowshowstwoparticlesfixedinplaceadistanceofL
apartfromeachother:particleoneofchargeq1=+8qisattheorigin
whileparticletwoofchargeq2=‐2qliesLawayfromchargeone.
a)
Atwhatpoint(otherthaninfinitelyfaraway)canaprotonbe
placedsothatithasanonetforceactingonit?
(1)
Solution:
(a)
Let’sassumethattheprotoncouldbein‐betweenq1
andq2(youwillseeitcannot,butlet’spretendwedon’tknow
that.)DrawFBD.
See cannot add to zero! (b)
Nowlet’sassumethattheprotoncouldbetotheleftof
q1(youwillseeitcannot,butagainlet’spretendwedon’tknow
that.)DrawFBD.
See cannot add to zero! (c)
Soithastobetotherightofq2.DrawFBD.
See it is possible, if we chose X correctly for these vectors to add to zero! Mathematical Solution now that we know the proton is located to the right of q2: Page9
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December 17, 2015 E. Inanuclearreactor,Uranium‐238canundergoAlphadecayinto
Thorium‐234.IfthedistancebetweentheThoriumnucleusandthe
Alphaparticleis9.0fm,whatare(a)theMagnitudeofelectrostatic
forcebetweenthetwoand(b)theAccelerationoftheAlphaparticle?
1.
Solutionparta:
2.
Solutionpartb:
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