Intermediate Physics - Professor of Physics ... Mastering Physics Online ... Coulomb’s law is a force law, and forces are vectors

IntermediatePhysics

PHYS102

Dr RichardH.CyburtAssistantProfessorofPhysics

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IntermediatePhysics

PHYS102

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DouglasAdamsHitchhiker’sGuidetotheGalaxy

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PHYS102

Thislecturewillhelpyouunderstand:Coulomb’sLawTheConceptoftheElectricField

PHYS102

VisualizingCharge

©2015PearsonEducation,Inc.

Text:p.635

ChargeModel


Text:p.635

Section20.3Coulomb’sLaw


Coulomb’sLaw


Text:p.642

Coulomb’sLawCoulomb’slawdescribestheforcebetweentwochargedparticles.


Coulomb’sLawCoulomb’slawlooksmuchlikeNewton’sgravityexceptthechargeq canbepositiveornegative,sotheforcecanbeattractiveorrepulsive.

ThedirectionoftheforceisdeterminedbythesecondpartofCoulomb’slaw.


UsingCoulomb’sLawCoulomb’slawisaforcelaw,andforcesarevectors.

Electricforces,likeotherforces,canbesuperimposed.

Thenet electricforceonchargej duetoallotherchargesisthesumoftheindividualsforcesduetoeachcharge:


UsingCoulomb’sLaw


Text:p.643

UsingCoulomb’sLaw


Text:p.643

QuickCheck 20.8

Thechargeofsphere2istwicethatofsphere1.Whichvectorbelowshowstheforceof2on1?

A.B.C.D.E.


QuickCheck 20.8

Thechargeofsphere2istwicethatofsphere1.Whichvectorbelowshowstheforceof2on1?

A.B.C.D.E.


Newton’s third law

QuickCheck 20.9

Thechargeofsphere2istwicethatofsphere1.Whichvectorbelowshowstheforceof1on2ifthedistancebetweenthespheresisreducedtor/2?

A.B.C.D. Noneoftheabove.


QuickCheck 20.9

Thechargeofsphere2istwicethatofsphere1.Whichvectorbelowshowstheforceof1on2ifthedistancebetweenthespheresisreducedtor/2?

A.B.C.D. Noneoftheabove.


At half the distance, the force is fourtimes as large:

QuickCheck20.10

Whichofthethreeright-handchargesexperiencesthelargestforce?

◦ q◦ 2q◦ 4q◦ q and2q aretied◦ q and4q aretied


+ +

r

+ +

2r

+ +

2r

+

+++

2q

4q

qQ

Q

Q

QuickCheck20.10

Whichofthethreeright-handchargesexperiencesthelargestforce?

◦ q◦ 2q◦ 4q◦ q and2q aretied◦ q and4q aretied


+ +

r

+ +

2r

+ +

2r

+

+++

2q

4q

qQ

Q

Q

QuickCheck20.11Ineachofthefollowingcases,anidenticalsmall,positivechargeisplacedattheblack dot.Inwhichcaseistheforceonthesmallchargethelargest?


QuickCheck20.11Ineachofthefollowingcases,anidenticalsmall,positivechargeisplacedattheblack dot.Inwhichcaseistheforceonthesmallchargethelargest?


C

QuickCheck 20.12

Ineachofthefollowingcases,anidenticalsmall,positivechargeisplacedattheblack dot.Inwhichcaseistheforceonthesmallchargethelargest?(Allchargesshownareofequalmagnitude.)


QuickCheck 20.12

Ineachofthefollowingcases,anidenticalsmall,positivechargeisplacedattheblack dot.Inwhichcaseistheforceonthesmallchargethelargest?(Allchargesshownareofequalmagnitude.)


A

QuickCheck20.15

Thedirectionoftheforceoncharge–q is

◦ Up◦ Down◦ Left◦ Right◦ Theforceon–q iszero


QuickCheck20.15

Thedirectionoftheforceoncharge–q is

◦ Up◦ Down◦ Left◦ Right◦ Theforceon–q iszero


–Q is slightly closer than +Q.

Example20.3AddingelectricforcesinonedimensionTwo+10nC chargedparticlesare2.0cmapartonthex-axis.Whatisthenetforceona+1.0nC chargemidwaybetweenthem?Whatisthenetforceifthechargedparticleontherightisreplacedbya-10nC charge?


Example20.3Addingelectricforcesinonedimension(cont.)PREPAREWeproceedusingthestepsofProblem-SolvingStrategy20.1.Wemodelthechargedparticlesaspointcharges.ThevisualoverviewofFIGURE20.16establishesacoordinatesystemandshowstheforcesF1on3 andF2on3.Figure20.16ashowsa+10nC chargeontheright;Figure20.16bshowsa-10nCcharge.


SOLVE Electricforcesarevectors,andthenetforceonq3 isthevector sumFnet =F1on3 +F2on3.Chargesq1 andq2 eachexertarepulsiveforceonq3,buttheseforcesareequalinmagnitudeandoppositeindirection.Consequently,Fnet =0.Thesituationchangesifq2 isnegative,asinFigure20.16b.Inthiscase,thetwoforcesareequalinmagnitudebutinthesame direction,soFnet =2F1on3.ThemagnitudeoftheforceisgivenbyCoulomb’slaw.

Example20.3Addingelectricforcesinonedimension(cont.)


Example20.3Addingelectricforcesinonedimension(cont.)Theforceduetoq1 is

Thereisanequalforceduetoq2,sothenetforceonthe1.0nC chargeisFnet =(1.8´ 10−3 N,totheright).


Example20.3Addingelectricforcesinonedimension(cont.)ASSESS Thisexampleillustratestheimportantideathatelectricforcesarevectors.Animportantpartofassessingouransweristoseeifitis“reasonable.”Inthesecondcase,thenetforceonthechargeisapproximately1mN.Generally,chargesofafewnC separatedbyafewcmexperienceforcesintherangefromafractionofamN toseveralmN.Withthisguideline,theanswerappearstobereasonable.


ExampleProblemPointchargeAhasachargeof–1.0nC,andpointchargeBhasachargeof4.0nC.Theyareseparatedby1.0cm.

WhatarethemagnitudeanddirectionoftheelectricforcesonchargesAandB?


QuickCheck20.13

Whichisthedirectionofthenetforceonthechargeatthelowerleft?

E.None of these.


QuickCheck20.13

Whichisthedirectionofthenetforceonthechargeatthelowerleft?

E.None of these.


B.

QuickCheck 20.14

Whichisthedirectionofthenetforceonthechargeatthetop?

E.None of these.


QuickCheck 20.14

Whichisthedirectionofthenetforceonthechargeatthetop?

E.None of these.


D.

Example20.5ComparingelectricandgravitationalforcesAsmallplasticsphereischargedto-10nC.Itisheld1.0cmaboveasmallglassbeadatrestonatable.Thebeadhasamassof15mgandachargeof+10nC.Willtheglassbead“leapup”totheplasticsphere?


Example20.5Comparingelectricandgravitationalforces(cont.)PREPAREWemodeltheplasticsphereandglassbeadaspointcharges.FIGURE20.20establishesay-axis,identifiestheplasticsphereasq1 andtheglassbeadasq2,andshowsafree-bodydiagram.TheglassbeadwillriseifF1on2 > w;ifF1on2 < w,thebeadwillremainatrestonthetable,whichthenexertsanormalforcen onthebead.


Example20.5Comparingelectricandgravitationalforces(cont.)SOLVE Usingthevaluesprovided,wehave

F1on2 exceedsthebead’sweightbyafactorof60,sotheglassbeadwillleapupward.


Example20.5Comparingelectricandgravitationalforces(cont.)ASSESS Thevaluesusedinthisexamplearerealisticforspheres≈2mmindiameter.Ingeneral,asinthisexample,electricforcesaresignificantly largerthanweightforces.Consequently,wecanignoreweightforceswhenworkingelectric-forceproblemsunlesstheparticlesarefairlymassive.


ExampleProblemTwo0.10ghoneybeeseachacquireachargeof+23pC astheyflybacktotheirhive.Astheyapproachthehiveentrance,theyare1.0cmapart.

Whatisthemagnitudeoftherepulsiveforcebetweenthetwobees?

Howdoesthisforcecomparewiththeirweight?


Section20.4TheConceptoftheElectricField


TheConceptoftheElectricFieldThefieldmodel explainshowtheforceduetochargesistransmittedthroughemptyspacefromonechargetoanother.

Thefigureshowsashallowpanofoilwithgrassseedsfloatingonit.Whenpositiveandnegativewirestouchtheoil,apatternemerges.

Somekindofelectricinfluencefromthechargesfillsthespace aroundthecharges.


TheConceptoftheElectricFieldIntheforcemodeloftheelectricfield,thepositivecharge AexertsanattractiveforceonchargeB.


TheConceptoftheElectricFieldInthefieldmodel,itisthealterationofspacearoundchargeAthatistheagent thatexertsaforceonchargeB.

Thealterationofspaceiswhatwecallafield.

Thechargemakesanalterationeverywhere inspace.


TheConceptoftheElectricFieldThespacearoundachargeisalteredtocreateanelectricfield.

Thealterationofspacearoundamassiscalledthegravitationalfield.

Thealterationofspacearoundamagnetiscalledthemagneticfield.


Thefieldmodeldescribeshowchargesinteract:

1. Agroupofcharges,whichwewillcallthesourcecharges,altersthespacearoundthembycreatinganelectricfieldE.

2. Ifanotherchargeisthenplacedinthiselectricfield,itexperiencesaforceFexertedbythefield.

TheFieldModel


TheFieldModelWedefinetheelectricfieldE atthepoint(x,y,z)as

Theunitsarenewtons/coulomb,N/C.

ThemagnitudeE oftheelectricfieldiscalledtheelectricfieldstrength.


TheFieldModel


ExampleProblemAhouseflywalkingacrossacleansurfacecanaccumulateasignificantpositiveornegativecharge.Inoneexperiment,thelargestpositivechargeobservedwas+73pC.Atypicalhouseflyhasamassof12mg.

Whatmagnitudeanddirectionofanelectricfieldwouldbenecessaryto“levitate”ahouseflywiththemaximumcharge?

Couldsuchafieldexistinair?


TheFieldModelYoucanusechargeq asaprobetodeterminewhetheranelectricfieldispresentatapointinspace.

Ifchargeq experiencesanelectricforceatthatpoint,thenthereisanelectricfieldatthatpointcausingtheforce.


TheFieldModelTheelectricfieldvectordefinestheelectricfieldatapointwhereachargeexperiencesanelectricforce.


TheFieldModelInthefieldmodel,thefieldistheagentthatexertsanelectricforceonaparticlewithchargeq.1. Theelectricfield,avector,existsateverypointinspace.Electricfield

diagramswillshowasampleofvectors,butthereisanelectricfieldvectorateverypointwhetheroneisshownornot.

2. Iftheprobechargeq ispositive,theelectricfieldvectorpointsinthesamedirectionastheforceonthecharge;ifnegative,theelectricfieldvectorpointsoppositetheforce.

3. Theelectricfielddoesnotdependonthemagnitudeofthechargeusedtoprobethefield.Theelectricfielddependsonlyonthesourcechargesthatcreatethefield.


TheElectricFieldofaPointChargeApointsourcechargeq createsanelectricfieldatallpoints.

Weuseasecondcharge,q¢,toprobetheelectricfield.


TheElectricFieldofaPointChargeIfbothchargesarepositive,theforceonqʹ isgivenbyCoulomb’slaw:


TheElectricFieldofaPointChargeTheelectricfieldduetothechargeqʹis:


TheElectricFieldofaPointCharge


Example20.6FindingtheelectricfieldofaprotonTheelectroninahydrogenatomorbitstheprotonataradiusof0.053nm.

Whatistheelectricfieldduetotheprotonatthepositionoftheelectron?


Example20.6Findingtheelectricfieldofaproton(cont.)SOLVE Theproton’schargeisq =e.Atthedistanceoftheelectron,themagnitudeofthefieldis


Example20.6Findingtheelectricfieldofaproton(cont.)Becausetheprotonispositive,theelectricfieldisdirectedawayfromtheproton:

E =(5.1´ 1011 N/C,outwardfromtheproton)

ASSESS Thisisalargefield,butTable20.2showsthatthisisthecorrectmagnitudeforthefieldwithinanatom.


TheElectricFieldofaPointChargeAnelectricfielddiagramforapositivepointchargeisconstructedbydrawingelectricfieldvectorsatanumberofpointsaroundthepositivecharge.

Allthevectorspointstraightawayfromthepositivecharge.


TheElectricFieldofaPointChargeTheelectricfielddiagramforanegativechargeisdrawnwiththevectorspointingtowardthenegativepointcharge.

Thiswouldbethedirectionoftheforceonapositiveprobecharge.


TheElectricFieldofaPointChargeForanelectricfielddiagram:1. Thediagramisjustarepresentativesampleofelectricfieldvectors.Thefield

existsatalltheotherpoints.Awell-drawndiagramgivesagoodindicationofwhatthefieldwouldbelikeataneighboringpoint.

2. Thearrowindicatesthedirectionandthestrengthoftheelectricfieldatthepointtowhichitisattached—atthepointwherethetail ofthevectorisplaced.Thelengthofanyvectorissignificantonlyrelativetothelengthsofothervectors.

3. Althoughwehavetodrawavectoracrossthepage,fromonepointtoanother,anelectricfieldvectordoesnot“stretch”fromonepointtoanother.Eachvectorrepresentstheelectricfieldatonepoint inspace.


QuickCheck20.16

Whichofthetwosetsofelectricfieldvectorsispossible?

◦ OnlyAispossible.◦ OnlyBispossible.◦ BothAandBarepossible.◦ NeitherAnorBispossible.


QuickCheck20.16

Whichofthetwosetsofelectricfieldvectorsispossible?

◦ OnlyAispossible.◦ OnlyBispossible.◦ BothAandBarepossible.◦ NeitherAnorBispossible.


QuickCheck20.17

Atwhichpointistheelectricfieldstronger?

◦ PointA◦ PointB◦ Notenoughinformationtotell


QuickCheck20.17

Atwhichpointistheelectricfieldstronger?

◦ PointA◦ PointB◦ Notenoughinformationtotell


QuickCheck20.18

Rankinorder,fromlargesttosmallest,themagnitudesoftheelectricfieldattheblackdot.

◦ 3,2,1,4◦ 3,1,2,4◦ 1,4,2,3◦ 3,1,2,4


QuickCheck20.18

Rankinorder,fromlargesttosmallest,themagnitudesoftheelectricfieldattheblackdot.

◦ 3,2,1,4◦ 3,1,2,4◦ 1,4,2,3◦ 3,1,2,4


QuickCheck20.19

Allchargesshownhaveequalmagnitudes.Forcases1through4shown,istheelectricfieldatthedottotheright(R),totheleft(L),orzero(0)?


Case A B C D

1 R L R 0

2 L R R 0

3 R L L L

4 L 0 0 0

QuickCheck20.19

Allchargesshownhaveequalmagnitudes.Forcases1through4shown,istheelectricfieldatthedottotheright(R),totheleft(L),orzero(0)?


Case A B C D

1 R L R 0

2 L R R 0

3 R L L L

4 L 0 0 0

B

L

R

L

0

QuickCheck20.20

Allchargesshownhaveequalmagnitudes.Rankinorder,fromlargesttosmallest,themagnitudesoftheelectricfieldattheblackdot.

◦ 3,2,1=4◦ 1,3,4,2◦ 4,1,3,2◦ 1,3,2,4


QuickCheck20.20

Allchargesshownhaveequalmagnitudes.Rankinorder,fromlargesttosmallest,themagnitudesoftheelectricfieldattheblackdot.

◦ 3,2,1=4◦ 1,3,4,2◦ 4,1,3,2◦ 1,3,2,4


QuickCheck20.21

Whichistheelectricfieldatthedot?

E. None of these.


QuickCheck20.21

Whichistheelectricfieldatthedot?

E. None of these.


B.

ExampleProblemAsmallbead,sittingattheorigin,hasachargeof+10nC.

Atthepoint(3.0cm,4.0cm),whatisthemagnitudeanddirectionoftheelectricfieldduetothisbead?


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Intermediate Physics - Professor of Physics ... Mastering Physics Online ... Coulomb’s law is a force law, and forces are vectors