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ScienceOnePhysics–ElectrostaticConfigurations Inthisworksheetwe’llexplorethefieldsandpotentialsthatarisefromsomecommoncharge configurations. Question1 Sketchtheelectricfieldandequipotentialsforthechargeconfigurationbelow. Question2 Youmightrecognisethechargeconfigurationinquestion1asanelectricdipole,oneofthemost fundamentalchargeconfigurationsinscience.InchemistryclassChrismighthavementionedthatthe forcefromthedipolefallsoffas1/r3,ratherthanthe1/r2wewouldexpectfromanelectricfield(or hemighthavesaidthattheenergyfallsofas1/r2ratherthan1/r).Ourgoalistoderivethat dependenceonr. Considertwocharges+qand-qseparatedbyadistances.Placethezeroofthex-axisbetweenthe twochargesassuch.Theblackdotrestsadistancexawayfromtheorigin. Thedistancefromnegativechargetothepointisr-=x+s/2andthedistancefromthepositivecharge tothepointisr+=x–s/2. a) Usingthiswriteanexpressionfortheelectricfieldattheblackdot.Youshouldhavea differenceoftwoterms.Simplifyitbypullingoutkandq. b) Findacommondenominatorandbringthetwotermstogetherintoone. c) We’reinterestedinpointsmuchfurtherawayfromthedipolethanthechargeseparation,that isx>>s.Usingthisidea,canwesimplifytheterm(s/2+x)2,andthussimplifyourexpression fromb). d) Thecombinationqsiscalledthedipolemoment,andisdenotedbytheletterp.Thedipole momentisavectorthatpointsfromthenegativechargetothepositivecharge.Writethe electricfieldintermsofp.Atafixeddistancer,whatcanonechangeaboutthedipoleto increasetheelectricfieldstrength? e) ByplacingchargesveryclosetogetherinthePhETsimulationyoucanmakeadipole.Checkto seeiftheelectricfielddoesindeeddecreasebyininversecubedlaw. Question3(challengequestion) We’lldothesamethingagain,exceptthistimewe’llabusethedefinitionofthederivative. Thistimeconsiderthecoordinatesystemwheretheoriginofthex-axisisonthenegativecharge. Writeanexpressionfortheelectricfieldasbefore,butinsteadoffindingacommondenominator,see ifyoucanuseanabominationofthedefinitionofthederivativetorewritethedifferenceasa derivative. Question4 A) Theplaneabovehasanchargedensityofη.Writeanexpressionforthechangeinenergy requiredtomoveachargeqfromAtoB. B) WhatistheworkrequiredtomovethechargefromAtoC? C) Drawagraphofelectricpotentialvsy-position.Besuretogetbothsidesofthechargedplane. Question5 a) Onthepicturebelow,drawanddeterminethestrengthoftheelectricfieldsineachthe regionslabelled1,2,and3.(assumetheyareinfiniteplanes) b) Onthepicturebelow,drawtheelectricfieldofthechargeconfigurationandfindthe magnitudesabove,below,andinbetweentheplates. c) Whatisthepotentialdifferencebetweenthetwoplatesaboveintermsofthechargedensity andthedistancebetweenthem? Question6 Inaweird,aliensolarsystem,the“Sun”isalong,thin,nearlymasslessobjectcarryingachargeof 1C/m.Thereisaplanetwiththesamemass,orbitalradius,andorbitalperiodasEarth’s,buttheorbit resultscompletelyfromelectricforces.Howmuchchargedoesthisplanetcarry? Question6(challengeQuestion):Whatchargeconfigurationmightberesponsibleforthispotential?