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9/16/2015 MasteringPhysics:Ch21HW
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120373&view=print&offset=next 1/8
PhETTutorial:ChargesandElectricFields
LearningGoal:
Tounderstandthespatialdistributionoftheelectricfieldforavarietyofsimplechargeconfigurations.
Forthisproblem,usethePhETsimulationChargesandFields.Thissimulationallowsyoutoplacemultiplepositiveandnegativepointchargesinanyconfigurationandlookattheresultingelectricfield.
Startthesimulation.Youcanclickanddragpositivecharges(red)ornegativecharges(blue)intothemainscreen.IfyouselectShowEfieldinthegreenmenu,redarrowswillappear,showingthedirectionoftheelectricfield.Faintredarrowsindicatethattheelectricfieldisweakerthanatlocationswherethearrowsarebrighter(thissimulationdoesnotusearrowlengthasameasureoffieldmagnitude).Feelfreetoplayaroundwiththesimulation.Whenyouaredone,clickClearAllbeforebeginningPartA.
PartA
SelectShowEfieldandgridinthegreenmenu.Dragonepositivechargeandplaceitnearthemiddleofthescreen,rightontopoftwointersectingboldgridlines.Youshouldseesomethingsimilartothefigurebelow.
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9/16/2015 MasteringPhysics:Ch21HW
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120373&view=print&offset=next 2/8
ANSWER:
CorrectThismeansthatanotherpositivecharge,ifplacedneartheoriginalcharge,wouldexperienceaforcedirectedradiallyawayfromtheoriginalcharge.
PartB
Now,let'slookathowthedistancefromthechargeaffectsthemagnitudeoftheelectricfield.SelectShownumbersonthegreenmenu,andthenclickanddragoneoftheorangeEFieldSensors.YouwillseethemagnitudeoftheelectricfieldgiveninunitsofV/m(voltspermeter,whichisthesameasnewtonspercoulomb).
PlacetheEFieldSensor1 awayfromthepositivecharge(1 istwoboldgridlinesawayifgoinginahorizontalorverticaldirection),andlookattheresultingfieldstrength.
Considerthelocationstotheright,left,above,andbelowthepositivecharge,all1 away.
ANSWER:
Theelectricfieldproducedbythepositivecharge
wrapscircularlyaroundthepositivecharge.isdirectedradiallytowardthechargeatalllocationsnearthecharge.isdirectedradiallyawayfromthechargeatalllocationsnearthecharge.
N N
N
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9/16/2015 MasteringPhysics:Ch21HW
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120373&view=print&offset=next 3/8
Correct
Thisresultimpliesthatthestrengthoftheelectricfieldduetoonepointchargedependssolelyonthedistanceawayfromthecharge.Mathematically,wesaytheelectricfieldissphericallysymmetric.
PartC
Whatisthemagnitudeoftheelectricfield1mawayfromthepositivechargecomparedtothemagnitudeoftheelectricfield2maway?
Hint1.Howtoapproachtheproblem
UseanEFieldSensortodeterminethefieldstrengthbothat1 awayandat2 awayfromthecharge.Then,taketheratioofthetwofieldstrengths.
ANSWER:
CorrectThemagnitudeofthefielddecreasesmorequicklythantheinverseofthedistancefromthecharge.Themagnitudeoftheelectricfieldisproportionaltotheinverseofthedistancesquared( ,where isthedistancefromthecharge).Youshouldverifythisbylookingatthefieldstrength3or4metersaway.ThisisconsistentwithCoulombslaw,whichstatesthatthemagnitudeoftheforcebetweentwochargedparticlesis .
PartD
Ifthefieldstrengthis =9 adistanceof1 fromthecharge,whatisthefieldstrength adistanceof3 fromthecharge?
Forthesefourlocations,themagnitudeoftheelectricfieldis
thesame.greatestbelowthecharge.greatestabovethecharge.greatesttotheleftofthecharge.greatesttotherightofthecharge.
N N
Themagnitudeoftheelectricfield1 awayfromthepositivechargeis
onequarterequaltotwotimesonehalffourtimes
themagnitudeoftheelectricfield2 away.
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N
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7N N
N
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9/16/2015 MasteringPhysics:Ch21HW
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120373&view=print&offset=next 4/8
Hint1.Howtoapproachtheproblem
Themagnitudeoftheelectricfieldisinverselyproportionaltodistancesquared( ).Soifthedistanceisincreasedbyafactorofthree,thefieldstrengthmustdecreasebyafactorofthreesquared.Youcouldusethesimulationtomakeameasurement(youmighthavetodragthechargeawayfromthecentersoyouhaveenoughroomtoget3 away).
ANSWER:
Correct
Correct.Since ,ifthedistanceisincreasedbyafactorofthree,theelectricfieldisdecreasedbyafactorofnine.
PartE
Removethepositivechargebydraggingitbacktothebasket,anddraganegativecharge(blue)towardthemiddleofthescreen.Determinehowtheelectricfieldisdifferentfromthatofthepositivecharge.Whichstatementbestdescribesthedifferencesintheelectricfieldduetoanegativechargeascomparedtoapositivecharge?
ANSWER:
Correct
Theelectricfieldisnowdirectedtowardthenegativecharge,butthefieldstrengthdoesntchange.Theelectricfieldofapointchargeisgivenby .Becauseofthesignofthecharge,thefieldproducedbyanegativechargeisdirectedoppositetothatofapositivechargebutthemagnitudeofthefieldisthesame.
PartF
Now,removethenegativecharge,anddragtwopositivecharges,placingthem1 apart,asshownbelow.
.
N
= 1 7N
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Theelectricfieldchangesdirection(nowpointsradiallyinward),buttheelectricfieldstrengthdoesnotchange.Nothingchangestheelectricfieldremainsdirectedradiallyoutward,andtheelectricfieldstrengthdoesntchange.Theelectricfieldchangesdirection(nowpointsradiallyinward),andthemagnitudeoftheelectricfielddecreasesatalllocations.
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?
N
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9/16/2015 MasteringPhysics:Ch21HW
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120373&view=print&offset=next 5/8
Letslookattheresultingelectricfieldduetobothcharges.Recallthattheelectricfieldisavector,sothenetelectricfieldisthevectorsumoftheelectricfieldsduetoeachofthetwocharges.
Whereisthemagnitudeoftheelectricfieldroughlyequaltozero(otherthanveryfarawayfromthecharges)?
ANSWER:
CorrectDirectlybetweenthetwocharges,theelectricfieldsproducedbyeachchargeareequalinmagnitudeandpointinoppositedirections,sothetwovectorsadduptozero.
PartG
Considerapoint0.5 abovethemidpointofthetwocharges.Asyoucanverifybyremovingoneofthepositivecharges,theelectricfieldduetoonlyoneofthepositivechargesisabout18 .Whatisthemagnitudeofthetotalelectricfieldduetobothchargesatthislocation?
ANSWER:
Theelectricfieldisnonzeroeverywhereonthescreen.Theelectricfieldiszeroatanylocationalongaverticallinegoingthroughthepointdirectlybetweenthetwocharges.Theelectricfieldisroughlyzeronearthemidpointofthetwocharges.
N
7N
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9/16/2015 MasteringPhysics:Ch21HW
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120373&view=print&offset=next 6/8
Correct
Noticethatthisnumberislessthantwicethemagnitudeofthefieldduetoeachcharge.Thisoccursbecausethehorizontalcomponentsoftheelectricfieldduetoeachchargeexactlycancelout(addtozero).Onlytheverticalcomponentsofthefieldsaddtogether.
PartH
Makeanelectricdipolebyreplacingoneofthepositivechargeswithanegativecharge,sothefinalconfigurationlookslikethefigureshownbelow.
ANSWER:
Correct
Theelectricfieldduetothepositivechargeisdirectedtotheright,asistheelectricfieldduetothenegativecharge.Sothenetelectricfield,whichisthesumofthesetwofields,isalsototheright.
zero25367N
7N
Theelectricfieldatthemidpointiszero.directedtotheleft.directedtotheright.
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9/16/2015 MasteringPhysics:Ch21HW
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120373&view=print&offset=next 7/8
PartI
Makeasmalldipolebybringingthetwochargesveryclosetoeachother,wheretheyarebarelytouching.Themidpointofthetwochargesshouldstillbeononeofthegridpointintersections(seefigurebelow).
Measurethestrengthoftheelectricfield0.5 directlyabovethemidpointaswellas1 directlyabove.Doesthestrengthoftheelectricfielddecreaseas1overdistancesquared( )?
Hint1.Howtoapproachtheproblem
Ifthestrengthofthefieldisdecreasingas ,thentheratioofthemagnitudesoftheelectricfieldmeasuredattwodistances,say0.5 awayand1 away,wouldbe
.ComparethisvaluetothevalueyoumeasurewithanEFieldSensor.
ANSWER:
Correct
Infact,itturnsoutthatthestrengthoftheelectricfielddecreasesroughlyas !Sothefield1 abovethemidpointisroughlyeighttimesweakerthanat0.5 abovethemidpoint.Theimportantlessonhereisthat,ingeneral,adistributionofchargesproducesanelectricfieldthatisverydifferentfromthatofasinglecharge.
N N
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No,itdecreasesmorequicklywithdistance.No,itdecreaseslessquicklywithdistance.Yes,itdoes.
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N
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9/16/2015 MasteringPhysics:Ch21HW
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120373&view=print&offset=next 8/8
PartJ
Makealonglineofpositivecharges,similartothatshowninthefigurebelow.Trytoplaceallofthechargescenteredalongahorizontalgridline.Feelfreetolookattheelectricfield,asitisinteresting.
Measurethestrengthoftheelectricfield1 directlyabovethemiddleaswellas2 directlyabove.Doesthestrengthoftheelectricfielddecreaseas1overdistancesquared( )?
ANSWER:
Correct
Infact,itturnsoutthatthestrengthoftheelectricfielddecreasesroughlyas .Sothefield1mabovethemidpointisroughlyhalfthestrengthat0.5 .Thisisanotherexampleshowingthatadistributionofchargesproducesanelectricfieldthatisverydifferentfromthatofasinglecharge.
PhETInteractiveSimulationsUniversityofColoradohttp://phet.colorado.edu
N N
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No,itdecreaseslessquicklywithdistance.Yes,itdoes.No,itdecreasesmorequicklywithdistance.
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N
