9/16/2015 MasteringPhysics:Ch21HW

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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.

9/16/2015 MasteringPhysics:Ch21HW

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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.

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9/16/2015 MasteringPhysics:Ch21HW

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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.

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Themagnitudeoftheelectricfield1 awayfromthepositivechargeis

onequarterequaltotwotimesonehalffourtimes

themagnitudeoftheelectricfield2 away.

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7N N

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9/16/2015 MasteringPhysics:Ch21HW

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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.

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= 1 7N

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Theelectricfieldchangesdirection(nowpointsradiallyinward),buttheelectricfieldstrengthdoesnotchange.Nothingchangestheelectricfieldremainsdirectedradiallyoutward,andtheelectricfieldstrengthdoesntchange.Theelectricfieldchangesdirection(nowpointsradiallyinward),andthemagnitudeoftheelectricfielddecreasesatalllocations.

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.

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9/16/2015 MasteringPhysics:Ch21HW

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Letslookattheresultingelectricfieldduetobothcharges.Recallthattheelectricfieldisavector,sothenetelectricfieldisthevectorsumoftheelectricfieldsduetoeachofthetwocharges.

Whereisthemagnitudeoftheelectricfieldroughlyequaltozero(otherthanveryfarawayfromthecharges)?

ANSWER:

CorrectDirectlybetweenthetwocharges,theelectricfieldsproducedbyeachchargeareequalinmagnitudeandpointinoppositedirections,sothetwovectorsadduptozero.

PartG

Considerapoint0.5 abovethemidpointofthetwocharges.Asyoucanverifybyremovingoneofthepositivecharges,theelectricfieldduetoonlyoneofthepositivechargesisabout18 .Whatisthemagnitudeofthetotalelectricfieldduetobothchargesatthislocation?

ANSWER:

Theelectricfieldisnonzeroeverywhereonthescreen.Theelectricfieldiszeroatanylocationalongaverticallinegoingthroughthepointdirectlybetweenthetwocharges.Theelectricfieldisroughlyzeronearthemidpointofthetwocharges.

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7N

9/16/2015 MasteringPhysics:Ch21HW

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Correct

Noticethatthisnumberislessthantwicethemagnitudeofthefieldduetoeachcharge.Thisoccursbecausethehorizontalcomponentsoftheelectricfieldduetoeachchargeexactlycancelout(addtozero).Onlytheverticalcomponentsofthefieldsaddtogether.

PartH

Makeanelectricdipolebyreplacingoneofthepositivechargeswithanegativecharge,sothefinalconfigurationlookslikethefigureshownbelow.

ANSWER:

Correct

Theelectricfieldduetothepositivechargeisdirectedtotheright,asistheelectricfieldduetothenegativecharge.Sothenetelectricfield,whichisthesumofthesetwofields,isalsototheright.

zero25367N

7N

Theelectricfieldatthemidpointiszero.directedtotheleft.directedtotheright.

9/16/2015 MasteringPhysics:Ch21HW

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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.

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No,itdecreasesmorequicklywithdistance.No,itdecreaseslessquicklywithdistance.Yes,itdoes.

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9/16/2015 MasteringPhysics:Ch21HW

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PartJ

Makealonglineofpositivecharges,similartothatshowninthefigurebelow.Trytoplaceallofthechargescenteredalongahorizontalgridline.Feelfreetolookattheelectricfield,asitisinteresting.

Measurethestrengthoftheelectricfield1 directlyabovethemiddleaswellas2 directlyabove.Doesthestrengthoftheelectricfielddecreaseas1overdistancesquared( )?

ANSWER:

Correct

Infact,itturnsoutthatthestrengthoftheelectricfielddecreasesroughlyas .Sothefield1mabovethemidpointisroughlyhalfthestrengthat0.5 .Thisisanotherexampleshowingthatadistributionofchargesproducesanelectricfieldthatisverydifferentfromthatofasinglecharge.

PhETInteractiveSimulationsUniversityofColoradohttp://phet.colorado.edu

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No,itdecreaseslessquicklywithdistance.Yes,itdoes.No,itdecreasesmorequicklywithdistance.

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