ElectricFieldFieldLinesSuperpositionWord格式.docx

ElectricFieldFieldLinesSuperpositionWord格式.docx

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TheunitvectorfromcapitalQtoli-littleQisthisvector.

AndsonowIknowthatthetwochargesiftheywerepositive--let'

ssupposethatlittleQispositive,theywouldrepeleachother.

LittleQisnegativetheywouldattracteachother.

AndletthisforcebeFandlasttimeweintroducedCoulomb'

slawthatforceequalslittleQtimescapitalQtimesCoulomb'

sconstantdividedbyRsquaredinthedirectionofRroof.

Thetwohavethesamesign.

It'

sinthisdirection.

Iftheyhaveoppositesignit'

sintheotherdirection.

AndnowIintroducetheideaofelectricfieldforwhichwewritethesymbolcapitalE.

AndcapitalEatthatlocationPwhereIhavemytestchargelittleQ,atthatlocationPissimplytheforcethatatestchargeexperienceddividedbythattestcharge.

SoIeliminatethetestcharge.

SoIgetsomethingthatlooksquitesimilarbutitdoesn'

thavethelittleQinitanymore.

Anditisalsoavector.

Andbyconvention,wechoosetheforcesuchthatifthisisapositivetestchargethenwesaytheEfieldisawayfromQifQispositive,ifQisnegativetheforceisintheotherdirection,andthereforeEisintheotherdirection.

SoweadopttheconventionthattheEfieldisalwaysinthedirectionthattheforceisonapositivetestcharge.

WhatyouhavegainednowisthatyouhavetakenoutthelittleQ.

Inotherwords,theforceheredependsonlittleQ.

Electricfielddoesnot.

TheelectricfieldisarepresentationforwhathappensaroundthechargeplusQ.

Thiscouldbeaverycomplicatedchargeconfiguration.

Anelectricfieldtellsyousomethingaboutthatchargeconfiguration.

Theunitforelectricfieldyoucanseeisnewtonsdividedbycoulombs.

InSIunitsandnormallywewon'

tevenindicatethe--theunit,wejustleavethatasitis.

Nowwehavegraphicalrepresentationsfortheelectricfield.

Electricfieldisavector.

SoyouexpectarrowsandIhavehereanexampleofa--achargeplusthree.

Sobyconventionthearrowsarepointingawayfromthechargeinthesamedirectionthatapositivetestchargewouldexperiencetheforce.

Andyounoticethatveryclosetothechargethearrowsarelargerthanfartheraway.

Thatit,thatsortofrepresents-istryingtorepresent-theinverseRsquarerelationship.

Ofcourseitcannotbeveryqualitative.

Butthebasicideaisthisisofcoursesphericallysymmetric,ifthisisapointcharge.

Thebasicideaishereyouseethefieldvectorsandthedirectionofthearrowtellsyouinwhichdirectiontheforcewouldbe,ifitisapositivetestcharge.

Andthelengthofthevectorgiveyouanideaofthemagnitude.

AndhereIhaveanotherchargeminusone.

Doesn'

tmatterwhetheritisminusonecoulomborminusmicrocoulomb.

Justit'

sarelativerepresentation.

AndyouseenowthattheEfieldvectorsarereversedindirection.

They'

repointingtowardstheminuschargebyconvention.

Andwhenyougofurtherouttheyaresmallerandyouhavetogoallthewaytoinfinityofcourseforthefieldtobecomezero.

BecausetheoneoverRsquarefieldfallsoffandyouhavetobeinfinitelyfarawayforyoutonotexperienceatleastinprincipleanyeffectfromthefromthecharge.

Whatdowedonowwhenwehavemorethanonecharge?

Well,ifwehaveseveralcharges--herewehaveQone,andherewehaveQtwo,andherewehaveQthree,andlet'

ssayherewehaveQofi,wehaveicharges.

AndnowwewanttoknowwhatistheelectricfieldatpointP.

Soit'

sindependentofthetestchargethatIputhere.

Youcanthinkofitifyouwanttoasthetheforceperunitcharge.

You'

vedividedoutthecharge.

SonowIcansaywhatistheEfieldduetoQonealone?

Well,thatwouldbeifQonewerepositivethenthismightbearepresentationforEone.

IfQtwowerenegative,thismightbearepresentationforEtwo,pointingtowardsthenegativecharge.

Andifthisonewerenegative,thenIwouldhavehereacontributionEthree,andsoon.

AndnowweusethesuperpositionprincipleaswedidlasttimewithCoulomb'

slaw,thatthenetelectricfieldatpointPasavectorisEoneinreferenceofchargeQone,plusthevectorEtwo,plusEthree,andsoonandifyouhaveicharges,itisthesumofallichargesoftheindividualEvectors.

Isitobviousthatthesuperpositionprincipleworks?

No.

Doesitwork?

Yes.

Howdoweknowitworks?

Becauseit'

sconsistentwithalloure