《大學物理簡明教程》 課件 11-1 Electrostatic field

Physics2:ElectricityandThermodynamicstoreviewElectricChargeElectricForceElectricFieldElectricPotentialcalculateforsomespecialcasesElectricforce

andElectricfieldElectriccharge

isthephysicalproperty

of

matterthatcausesittoexperienceaforcewhenplacedinanelectromagneticfield.Therearetwotypesofelectriccharges:positiveandnegative

++ADCB-FE+ADCBFEHydrogenHelium+Comparetheelectricforcesthatthetwoelectronsexperience.(giventhesamedistancebetweenelectronsandnuclei)

ElectrostaticForce–Coulomb’slawTheelectricforcebetween2pointchargesq1andq2is:Theelectricforceisavector!unitvector(toshowthedirection)Forceonpointchargeq2

duetopointchargeq1

(Permittivityofvacuum)Thecoulomb(unitsymbol:C)istheSIunitofelectriccharge.Itisthecharge(symbol:Qorq)transportedbyaconstantcurrentofoneampereinonesecond:1C=1A.1sThus,itisalsotheamountofexcesschargeonacapacitorofonefaradchargedtoapotentialdifferenceofonevolt:1C=1F.1VCharles-AugustindeCoulomb

(1736–1806)Electricchargeis“quantized”:Anypossiblechargeisamultipleoftheelementarychargee

e=1.6×10-19CElementary/subatomicparticlescarryelementarycharge:electronme=9.11×10?31kg-emp=1.6726×10?27kgeprotonneutron0mn=1.6749×10?27kg=1.6021766208(98)×10-19C

CoulombsineverydaylifeStaticelectricitybyrubbingmaterials:Alightningbolt:TotalchargefromAAbatteryfromfullychargedtodischarged:about15Cafewmicro-coulombs(μC=10-6C)~5000C1C1C1mF=9×109Nequivalenttotheweightof920,000metrictons!FFForceontwo1Coulombchargesseparatedby1mSo:1Cisaverybigcharge!-+-SuperpositionofelectricforcesQ2Q1Q3Q4qFtotFtotFtotForceonasmall

“test”chargeqWhatifthetestchargebecomes2q?Howabouttheforces?Atanypointinspace,wecandefine:E

istheElectricFieldNowwemaydefinetheelectricfield(throughtheelectricforce)ElectrostaticforceAnelectricfield

isafieldthatsurroundselectriccharges.ItrepresentschargesattractingorrepellingotherelectricchargesbyexertingforceelectromagneticfieldelectricfieldmagneticfieldvectorsElectricfieldlineThedensityoffieldlines(numberoffieldlinesperunitarea)atanylocationisproportionaltothemagnitudeofthefieldatthatpointFrompositivetonegative1positiveand1negativecharges(dipole)DirectionofelectricfiledistangentialtothefieldlineElectricfieldlinesnevercrosseachother!2positivechargesNearlyuniformfieldbetweenparallelplatesForceonachargeinanelectricfieldIf:Q

=

4

nCd=6cm-+dd+Q-QE=?

=2×104N/CallthesmallelementsgiveasameamountofelectricfieldintheverticaldirectionhrElectricfieldfroma

uniformlychargedring(onitsaxis)dividethecircleintosmallelementsthehorizontal

componentsfromelementsonoppositesidesofthecirclecanceloutnumberofelementsinacircle:areaofeachelement:chargeofeachelement:surfacechargedensity

σ=Q/AN=hrElectricfieldfroma

uniformlychargedring(onitsaxis)fieldfromoneelement:totalfieldfromthecirclesurfacechargedensity

σ=Q/AdθNElectricfieldfromaninfinite

uniformlychargedplatecontributionsfromrings,fromr=0toinfinitydividetheplaneintoconcentricrings

withequalwidthhrcontributionfromonering(r):Defineanewvariablex:Fieldfromchargesatradius

r=hxSurfacechargedensityσ=Q/AareaunderthecurveElectricfieldfromaninfiniteplatewithauniformdensityofchargeσ:perpendiculartotheplatedoesNOTdependonthedistance!Butofcourse,noplatecanbeinfiniteThisisonlyanapproximationthesign(direction)dependsonthechargePlateislargeClosetotheplateorWhatabouttheelectricfieldfromacharged

infinitewire?Thinkaboutit!ChargeacceleratedinanelectricfieldSimilartoaccelerationinagravitationalfield.Gaininkineticenergy:sowhatisthepotentialenergy?TheelectrostaticforceisaconservativeforceCorrespondingpotentialenergyQqdWhatisthepotentialenergyofachargebroughttoadistanced

fromanothercharge?Initialkineticenergy:justenoughtomovetodistanced,wherevelocitywillbezeroLossinkineticenergy=gaininpotentialenergy=thenegativeoftheworkdoneZeropotential-infinitelyfaraway(negative)but:FdependsonxForeachsmallinterval:Thetotalworkisthesumofallthosesmallintervals:SotheelectricpotentialenergyisWhythepotentialenergydoesn’tdependonthepathtaken?QqqdQqonlydependsonmovementintheradialdirectionTheelectricforceisalwaysradialSotheworkdoesnotdependonthepath!Q5Q6Q4Q2Q3Q1qd3d2d1d6d5d4totalpotentialenergyisthesumofpotentialenergyduetoallchargesPotentialenergyisalwaysproportionaltoqDefine:Visthe“potential”multiplecharges?Letusdefinethepotentialenergyperunitcharge:isthe‘electricpotential’,orjust‘potential’ChangeinpotentialbetweenpointsAandBis:(Joules/Coulomb=Volt)alsocalled“Voltage”Q5cmV=?

Wecandraw“equipotentiallines”wherethe

potentialisthesameSimilartoacontourmapcontour

line(isoline)EquipotentiallinesEquipotentiallines/surfaces

areperpendiculartoElectricFieldlinesPotentialatdistancerfromapointchargeisthesame100VoltsWhatwillbethespeedoftheelec