L 41 Magnetism 1.docx

L 41 Magnetism 1.docx

《L 41 Magnetism 1.docx》由会员分享，可在线阅读，更多相关《L 41 Magnetism 1.docx（12页珍藏版）》请在冰豆网上搜索。

L41Magnetism1

Electromagnetism1

Ferromagnetism

Allearlystudiesofmagnetismconcentratedonthepropertiesofpermanentandtemporarymagnets.

Magneticironoxideorlodestoneoccursnaturally.Thefactthatthismineralpossessesthepropertyofattractingironhasbeenknownformanycenturies.

Whenanironobjectisbeingattractedittemporarilybecomesamagnet-likethelodestone-andsomehardermaterials,suchassteel,canbemagnetisedpermanently.Magneticmaterials（or,morecorrectly,ferromagneticmaterials）arethosewhichareattractedbyamagnetandcanbemadeintoamagnet.Theseincludeiron,cobaltandnickelaswellascertainalloys,whichmayincludenoferromagneticelements.Materials,whicharenotferromagnetic,dohavesomemagneticpropertiesbutthesearesosmallastobedifficulttomeasure.Forexample,insertingasheetofcopper,plasticorglassbetweenmagnetsmakesalmostnodifferencetotheforcebetweenthem.Formostpracticalpurposesnon-ferromagneticmaterialscanberegardedasnon-magnetic.

Themagneticpowersofamagnetisedbarappeartobeconcentratedatpoints（oratleastsmallregions）nearitsends.Theseregionsarecalledmagneticpoles.Ifabarmagnetissupportedsoastobefreetorotateaboutaverticalaxisitalignsitselfinaconstantdirectionatagivenpointontheearth.Thisdirectionisapproximatelynorth-southgeographicallyandsoonebasicapplicationofmagnetismisthemagneticcompass.

Thepoleneartheendindicatingnorthiscalledthenorth-seekingpole-normallyabbreviatedtonorthpole.Theotherpoleisofcoursesouth.Thustherearetwokindsofmagneticpoleanditiseasilyshownexperimentallythatlikepolesrepelandunlikepolesattract.

TheMagneticField

Amagnetcanbethoughtofasbeingsurroundedbyamagneticfield-aregioninwhichmagnets（bothpermanentandtemporary）willexperiencemagneticforces.Thedirectionofthisfieldisdefinedasthedirectionofthemagneticforceonthenorth（seeking）poleofacompassneedle.Thustheearth’smagneticfieldisdirectedapproximatelysouthtonorthgeographically.

Amagneticfieldcanberepresenteddiagrammaticallybydrawinglinesofmagneticflux（alsoknownaslinesofmagneticforceorjustmagneticfieldlines）.

Amagneticfluxlineisonewhoseshapeissuchthatthefieldistangentialtoitatanypoint.Totheselinesweaddarrowstoshowthegeneraldirection.Thediagramshowsthemagneticfieldaroundabarmagnet.

Inaccordancewithourdefinitionofthedirectionofthefieldthefluxlinesgoinwardstosouthpolesandemergefromnorthpoles.Thelinesarealsoshownmorecloselyspacedwherethefieldisstronger.Notshownisthefieldwithinthemagnet.InternallythelineswillrunfromStoN,thefieldwillbeatitsstrongestandapproximatelyuniform.（Equallyspacedparallellinesofflux）.

Electromagnetism

In1820Oerstedshowedthatacurrent-carryingwireissurroundedbyamagneticfield.Thusitwasestablishedthatthereisacloseconnectionbetweenelectricityandmagnetism.AfterOersted’sdiscoverydevelopmentofthesubjectofelectromagnetismwasveryrapid.Importantadvancesweremadebyanumberofpeople-mostnotablyAmpereandFaraday.Bythemid1860sMaxwellwasabletoaccountforalltheknownphenomenaofelectricityandmagnetisminoneunifiedtheory.However,themodernexplanationofelectromagnetismwasonlypossibleafterthepublicationofEinstein’stheoryofrelativity.Itisnowknownthat:

Allmagneticeffectsareelectricalinoriginandarecausedbymovingcharges.Thatis,thefundamentalsourceofmagneticfieldsandforcesismovingelectricchargesandthefundamentaleffectofamagneticfieldistoexertaforceonamovingcharge

Thefamiliarbarmagnetturnsouttobeaverycomplexexampleofmagneticbehaviour.Itwaswellintothetwentiethcenturybeforeasatisfactoryexplanationofferromagnetism,usingphysicsbeyondthescopeofthiscourse,waspossible.

DefinitionofMagneticFieldVector

Supposeaparticlecarryingacharge+Qtravelsintoamagneticfieldwithvelocityvatanangle

tothefieldasshown.

ThemovingchargeexperiencesamagneticforceF.

Themagnitudeofthisforceisfoundexperimentallytobeproportionaltothemagnitudeofthechargeandtothecomponentofthevelocityofthechargeatrightanglestothefield.Thatis,

.

Wedefinethemagnitudeofthemagneticinduction,B,asthemagnitudeofthemagneticforceperunitchargemovingwithunitvelocityatrightanglestothefield.

Thatis,

.

Magneticforceonamovingcharge

TheSIunitofBisthetesla（T）.

ThedirectionofBwasdefinedearlierasthedirectionofthemagneticforceonanNpoleplacedinit.

Bisameasurablequantitywhosevaluetellsusjusthowstrongamagneticfieldis.AmuchbetternameforBwouldbemagneticfieldstrengthormagneticintensity.

SomebasicbooksdousethesetermsforB.Howevertheyarenotstrictlycorrectasmagneticintensityandmagneticfieldstrengtharenamesusedforanothermagneticvectorintroducedinmoreadvancedwork.CorrectnamesforBaremagneticinductionandmagneticfluxdensity.

DirectionoftheMagneticForce

ThedirectionofthemagneticforceisatrightanglestobothvandB.Thatis,itisnormaltotheplanedefinedbyvandB.

InthecaseshowninthediagramaboveFwouldbenormaltotheplaneofthepaperanddirectedinwards.

Itmayseemstrangethattheforceproducedbyamagneticfieldisatrightanglestothedirectionofthefield.（No,let’sfaceit,itisstrange.）Thisisanunfortunateresultofdefiningthedirectionofthefieldintermsofmagneticpolesratherthanmovingcharges.Thisisthehistoricaldefinitionanditwouldbetooconfusingtochangeit.

Thereareanumberofequivalentrulesforrememberinghowmagneticfielddirection,chargemotionandmagneticforcearerelated.Onesuchruleis:

Right-handpalmrulefordirectionofmagneticforceonmovingchargeorcurrent

Pointthefingersofyourrighthandinthedirectionofthemagneticfieldcomponentperpendiculartothemotionandyourthumbinthedirectionofpositivechargemotion（orconventionalcurrent）.Thedirectionofthemagneticforceisfoundbypushingwiththepalmofyourhand.

Ifyouhavealreadymasteredadifferentruleandfeelcomfortablewithityoushouldcontinuetouseit.Thediagramillustratestheapplicationoftherighthandpalmrule.

MagneticForceonaWireCarryingaCurrent

ConsiderawirecarryingacurrentIatanangle

toamagneticfieldBasshown.

Usingpalm（orother）rulethereisamagneticforcestraightupoutofthepage.

Supposethemovingchargeperunitlengthisq,movingwithaneffectivevelocity

（themeandriftspeed）.

Thentheforceperunitlengthonthewireis

.

However

isthechargethatflowspastafixedpointonthewireperunittime.

i.e.

TorqueonaCurrent-carryingLoop

Supposeasinglerectangularloopofwirecarryingacurrent,I,issituatedwithitsplaneinamagneticfieldBasshown.

Weseethattheloopissubjecttoatorquethatisanticlockwiseasviewedfromabovebecauseofthecoupleproducedbythemagneticforces.

Theturningmomentortorqueofacoupleisthesameaboutallpointsinitsplane.

eg.ForP

=（d+x）F–xF

=dF

Andthisdoesnotdependonx.

F

F

d

x

P

IfthereareNloopseachoneexperiencesthistorqueand

=NAIB

Ifthecoilrotatesundertheactionofthiscoupletheforcesdonotchangebutthedistancebetweentheirlinesofactionfallstozeroastheanglebecomes90o.Aftersomeoscillationthecoilendsupinequilibriumwithitsplaneperpendiculartothefield.

Examples

1.Determinethemagnitudeanddirectionofthemagneticforceonthemovingchargeineachofthefollowingcases.

（a）

（b）

（c）

（d）

（e）

Note:

Anαparticleis

2.TerrestrialMagnetism

Theearth’smagneticfieldisnotusuallyhorizontalortruenorth-south.Thefollowingdiagramshowstheusualsituationinthesouthernhemisphere.

Theanglebetweenthehorizontalandtheearth’smagneticfield（anangleintheverticalplane）iscalledtheinclination.Inthenorthernhemispherethisangleisusuallybelowthehorizontalandiscalledthedip.

Theanglebetweentruenorthandmagneticnorth（thedirectionofthehorizontalcomponentoftheearth’smagneticfield）iscalledthedeviationordeclination.

Inthediagramthedeviationordeclinationistotheeast.

InSydneytheearth’smagneticfieldisspecifiedasfollows:

∙Fluxdensity56.0T

∙inclination63.0

∙declination11.0E.

Calculate:

（a）themagnitudeanddirectionofthehorizontalcomponentoftheearth’smagneticfield;

（b）themagnitudeanddirectionoftheverticalcomponentoftheearth’smagneticfield.

（c）thecomponentoftheearth’smagneticfieldinthedirectiontruenorth.

3.Anapparatustodemonstratethemagneticforceonacurrentcarryingwireconsistsofaswingmadeoutofcopperwire,throughwhichacurrentpassesasshowninthediagram.

Theswingisdeflectedinwardstowardsthebackofthemagnet.

（a）Whichpoleofthemagnetisnorth?

Explainyouranswer.

（b）Averysensitivespringbalanceattachedtothehorizontalpartofthewireregistersapullof0.05Nperpendiculartothewirewhenthecurrentis1.5 A.Thewidthofthemagnetis40mm.Whatisthemagneticinductioninthegapbetweenthemagnet’spoles?

4.Arectangularcoil,XYZWhasasideWZoflength0.075m.Thecoilissuspendedfromaspringbalancewithitsplaneatrightanglestoauniformmagneticfieldasshown.

Thetableshowshowthereadingonthespringbalancevarieswithcurrentthroughthecoi