Download Science One Physics – Electrostatic Configurations

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?