《电子信息类专业英语 》课件-第8章

Unit8ElectromagneticFieldandWavePassageATheFoundationofElectromagneticFieldPassageBMaxwellEquationsPassage

CEBGandMetamaterials

PassageATheFoundationofElectromagneticField

Whatisthefield?Isitascalarfieldoravectorfield?Whatisthenatureofafield?Isitacontinuousorarotationalfield?Howisthemagneticfieldproducedbyacurrent-carryingcoil?Howdoesacapacitorstoreenergy?Howdoesapieceofwire(antenna)radiateorreceivesignals?Howdoelectromagneticfieldspropagateinspace?Whatreallyhappenswhenelectromagneticenergytravelsfromoneendofhollowpipe(waveguide)totheother?

Priortoundertakingthestudyofelectromagneticfields,wemustdefinetheconceptofafield.Whenwedefinethebehaviorofaquantityinagivenregionintermsofasetofvalues,oneforeachpointinthatregion,werefertothisbehaviorofthequantityasfield.[1]Thevalueateachpointofafieldcaneitherbemeasuredexperimentallyorpredictedbycarryingourcertainmathematicaloperationsonsomeotherquantities.

Accordingtothetheoryofelectromagnetism,thevectorsEandBarethefundamentalfieldvectorsthatdefinetheforceactingonachargemovinginanelectromagneticfield.TwoassociatedfieldvectorsDandH,knownastheelectricfluxdensity(orthedisplacementfluxdensity)andthemagneticfieldintensity,respectively,takeintoaccountthedielectricandmagneticproperties,respectively,ofmaterialmedia.Materialscontainchargedparticlesthatundertheapplicationofexternalfieldsrespondgivingrisetothreebasicphenomenaknownasconduction,polarization,andmagnetization.

Althoughamaterialmayexhibitallthreeproperties,itisclassifiedasaconductor,adielectric,oramagneticmaterialdependinguponwhetherconduction,polarization,ormagnetizationisthepredominantphenomenon.Whilethesephenomenaoccurontheatomicor“microscopic”scale,itissufficientforourpurposetocharacterizethematerialbasedon

“macroscopic”scaleobservations,thatis,observationsaveragedovervolumeslargecomparedwithatomicdimensions.

[2]

Inthecaseofconductors,theeffectofconductionistoproduceacurrentinthematerialknownastheconductioncurrent.Conductionisthephenomenonwherebythefreeelectronsinsidethematerialmoveundertheinfluenceoftheexternallyappliedelectricfieldwithanaveragevelocityproportionalinmagnitudetotheappliedelectricfield,

insteadofaccelerating,duetothefrictionalmechanismprovidedbycollisionswiththetomiclattice.

Forlinearisotropicconductors,theconductioncurrentdensity,havingtheunitsofamperespersquaremeter(A/m2),isrelatedtotheelectricfieldintensityinthemannerwhereσistheconductivityofthematerial,havingtheunitssiemenspermeter

(S/m).Insemiconductors,theconductivityisgovernedbynotonlyelectronsbutalsoholes.

WhiletheeffectofconductionistakenintoaccountexplicitlyintheelectromagneticfieldequationsthroughEq.

(8.1),theeffectofpolarizationistakenintoaccountimplicitly

throughtherelationshipbetweenDandE,whichisgivenbyforlinearisotropicdielectrics,whereεisthepermittivityofthematerialhavingtheunitscoulombsquaredpernewton-

squaredmeter,commonlyknownasfaradspermeter(F/m),whereafaradisacoulombsquarepernewton-meter.

Polarizationisthephenomenonofcreationandnetalignmentofelectricdipoles,formedbythedisplacementsofthecentroidsoftheelectroncloudsofthenucleioftheatomswithinthematerial,alongthedirectionofanappliedelectricfield.[4]Theeffectofpolarizationistoproduceasecondaryfieldthatactsinsuperpositionwiththeappliedfield

tocausethepolarization.ThusthesituationisasdepictedinFigure8.1.Toimplicitlytakethisintoaccount,leadingtoEq.(8.2),webeginwithFigure8.1illustratestheeffectofpolarizationindielectricmaterial

Where,ε0

isthepermittivityoffreespace,havingthenumericalvalue8.854×1012,orapproximately10-9/36,andP

isthepolarizationvector,orthedipolemomentperunit

volume,havingtheunitscoulombspersquaremeter.NotethatthisgivestheunitsofcoulombspersquaremeterforD.ThetermaccountsfortherelationshipbetweenDandE

ifthemediumwerefreespace,andthequantityP

representstheeffectofpolarization.Forlinearisotropicdielectrics,P

isproportionaltoE

Where,adimensionlessquantityistheelectricsusceptibility,aparameterthatsignifiestheabilityofthematerialtogetpolarized.CombiningEqs.(8.3)and(8.4),wehave

Where

εr(=1+χe)istherelativepermittivityofthematerial.

Inasimilarmanner,theeffectofmagnetizationistakenintoaccountimplicitlyhroughtherelationshipbetweenHandB,whichisgivenby

forlinearisotropicmagneticmaterials,whereμ

isthepermeabilityofthematerial,havingtheunitsnewtonsperamperesquared,commonlyknownashenryspermeter(H/m),whereahenryisanewton-meterperamperesquared.

Notes

[1]Whenwedefinethebehaviorofaquantityinagivenregionintermsofasetofvalues,oneforeachpointinthatregion,werefertothisbehaviorofthequantityasfield.

当定义一个量在一个给定区域中针对一整套数值所呈现出的行为特征,且在这一给定的区域中,每一个点对应一个该量时,定义这一量的这些行为特征为场。

[2]Whilethesephenomenaoccurontheatomicor“microscopic”scale,itissufficientforourpurposetocharacterizethematerialbasedon“macroscopic”scaleobservations,thatis,observationsaveragedovervolumeslargecomparedwithatomicdimensions.

虽然这些现象出现在原子或者微观层面,但也足以达到了目的,即在宏观层面上定义材料的特性,将问题平均到与原子维度相比较大的体积上。

[3]Conductionisthephenomenonwherebythefreeelectronsinsidethematerialmoveundertheinfluenceoftheexternallyappliedelectricfieldwithanaveragevelocity

proportionalinmagnitudetotheappliedelectricfield,insteadofaccelerating,duetothefrictionalmechanismprovidedbycollisionswiththeatomiclattice.

传导是一种现象,自由电子在外加电场的作用下在介质中移动,平均的移动速度与所施加的电场的幅度成正比,由于与原子晶格的碰撞所形成的摩擦机理,所以这不是一种加速过程。.

·frictionalmechanism的意思是摩擦机理。

·atomiclattice的意思是原子晶格。

[4]Polarizationisthephenomenonofcreationandnetalignmentofelectricdipoles,formedbythedisplacementsofthecentroidsoftheelectroncloudsofthenucleiofthe

atomswithinthematerial,alongthedirectionofanappliedelectricfield.

极化是电偶极子沿着一个外加电场的方向创建和基于网格基准进行取位的一种现象,其中,电偶极子是由材料中原子核的电子云的重心的移位所形成的。

·electricdipoles的意思是电偶极子。电偶极子是指两个等量异号点电荷组成的系统。

Exercises

1.Fillintheblanks.

(1)Whatreally

whenelectromagneticenergytravelsfromoneendofhollowpipe(waveguide)totheother?

(2)Whenwedefinethebehaviorofaquantityina

regionintermsofasetofvalues,oneforeachpointinthatregion,we

thisbehaviorofthequantityasfield.

(3)Two

associated

field

vectorsDandH,known

as

theelectricfluxdensity(orthedisplacementfluxdensity)andthemagneticfieldintensity,

,takeintoaccountthe

dielectricandmagneticproperties,

,ofmaterialmedia.

(4)Conductionisthephenomenon

thefreeelectronsinsidethematerialmoveundertheinfluenceoftheexternallyappliedelectricfieldwithanaveragevelocityproportionalinmagnitudetotheappliedelectricfield,

accelerating,the

frictionalmechanismprovidedbycollisionswiththeatomiclattice.

(5)Whiletheeffectofconductionistakenintoaccount

intheelectromagneticfieldequationsthroughEq.(8.1),theeffectofpolarizationistakenintoaccount

throughtherelationshipbetweenDandE.

(6)Theeffectofpolarizationistoproduceasecondaryfieldthatacts

theappliedfieldtocausethepolarization.

2.Fillintheblankswiththebestchoice.

(1)

undertakingthestudyofelectromagneticfieldswemustdefinetheconceptofafield.

a.Withrespecttob.Owingtoc.Regardingtod.Priorto

(2)Althoughamaterialmayexhibitallthreeproperties,itisclassifiedasaconductor,adielectric,oramagneticmaterialdependinguponwhetherconduction,polarization,ormagnetizationisthe

phenomenon.

a.mainb.predominantc.principald.Foremost

(3)Insemiconductors,theconductivityis

bynotonlyelectronsbutalsoholes.

a.ruledb.definedc.governedd.managed

(4)Polarizationisthephenomenonofcreationandnetofelectricdipoles,formedbythedisplacementsofthecentroidsoftheelectroncloudsofthenucleioftheatomswithinthematerial,alongthedirectionofanappliedelectricfield.

a.alignmentb.benchmarkc.criteriad.specification

(5)AdimensionlessquantityPistheelectricsusceptibility,aparameterthattheabilityofthematerialtogetpolarized.

a.signifiesb.symbolizesc.denotesd.specifies

3.TranslatethefollowingparagraphintoChinese.

ElectricandmagneticphenomenaatthemacroscopiclevelaredescribedbyMaxwell’sequations,aspublishedbyMaxwellin1873.Thisworksummarizedthestateofelectromagneticscienceatthattimeandhypothesizedfromtheoreticalconsiderationstheexistenceoftheelectricaldisplacementcurrent,whichledtotheexperimentaldiscoverybyHertzofelectromagneticwavepropagation.Maxwell’sworkwasbasedonalargebodyofempiricalandtheoreticalknowledgedevelopedbyGauss,Ampere,Faraday,andothers.

Afirstcourseinelectromagneticsusuallyfollowsthishistorical(ordeductive)approach,anditisassumedthatthereaderhashadsuchacourseasaprerequisitetothepresentmaterial.

Severalreferencesareavailableherethatprovideagoodtreatmentofelectromagnetictheoryattheundergraduateorgraduatelevel.

PassageBMaxwellEquations

Wehaveintroducedthedifferentfieldvectorsandassociatedconstitutiverelationsformaterialmedia.Theelectricandmagneticfieldsaregovernedbyasetoffourlaws,knownasMaxwell‘sequations,resultingfromseveralexperimentalfindingsandapurelymathematicalcontribution.Togetherwiththeconstitutiverelations,Maxwell’sequationsformthebasisfortheentireelectromagneticfieldtheory.

Now,weshallconsiderthetimevariationsofthefieldstobearbitraryandintroducetheseequationsandanauxiliary

equationinthetimedomainform.Inviewoftheirexperimentalorigin,thefundamentalformofMaxwell’sequationsistheintegralform.Inthefollowing,weshallfirstpresentallfourMaxwell’sequationsinintegralformandtheauxiliaryequation,thelawofconservationofcharge,andthendiscussseveralpointsofinterestpertinenttothem.Itisunderstoodthatallfieldquantitiesarerealfunctionsofpositionandtime.

AmongtheMaxwellEquationGroups,theFaraday’sLawis

TheAmpere’sCircuitalLawis

TheGauss’LawfortheElectricFieldis

TheGauss’LawfortheMagneticFieldis

AndtheLawofConservationofChargeis

TherearecertainproceduresandobservationsofinterestpertinenttoEqs.(8.7)(8.11),asfollows.

1.Thatthemagneticfluxandthedisplacementflux,respectively,aretobeevaluatedinaccordancewiththeright-handscrewrule(RHSrule),thatis,inthesenseofadvance

ofaright-handscrewasitisturnedaroundCinthesenseofC.TheRHSruleisaconventionthatisappliedconsistentlyforallelectromagneticfieldlawsinvolvingintegrationoversurfacesboundedbyclosedpaths.

2.InevaluatingthesurfaceintegralsinEqs.(8.7)and(8.8),anysurfaceSboundedbyCcanbeemployed.InadditioninEq.(8.7),thesamesurfacesmustbeemployedforbothsurfaceintegrals.ThisimpliesthatthetimederivativeofthemagneticfluxthroughallpossiblesurfacesboundedbyCisthesameinorderfortheemfaroundCtobeunique.Likewise,thesumofthecurrentduetoflowofchargesandthedisplacementcurrentthroughallpossiblesurfacesboundedCisthesameinorderforthemmfaroundCtobeunique.

3.TheminussignontherightsideofEq.(8.7)tellsusthatwhenthemagneticfluxenclosedbyCisincreasingwithtime,theinducedvoltageisinthesenseoppositetothatofC.IfthepathCisimaginedtobeoccupiedbyawire,thenacurrentwouldflowinthewirethatproducesamagneticfieldsoastoopposetheincreasingflux.SimilarconsiderationsapplyforthecaseofthemagneticfluxenclosedbyCdecreasingwithtime.

TheseareinaccordancewithLenz’slaw,whichstatesthatthesenseoftheinducedemfissuchthatanycurrentitproducestendstoopposethechangeinthemagneticfluxproducingit.

4.IfloopCcontainsmorethanoneturn,suchasinanN-turncoil,thenthesurfacetightlywoundcoil,thisisequivalenttothesituationinwhichNseparate,identical,single-turnloopsarestackedsothattheemfinducedintheN-turncoilisNtimestheemfinducedinoneturn.Thus,foranN-turncoil.

Whereisthemagneticfluxcomputedasthoughthecoilisaone-turncoil.

5.Sincemagneticforceactsperpendiculartothemotionofacharge,themagnetomotive(mmf)force,thatis

doesnothaveaphysicalmeaningsimilartothatoftheelectromotiveforce.Theterminologyarisespurelyfromanalogywithelectromotiveforcefor

6.ThechargedensityinEq.(8.9)andthecurrentdensityJ

inEq.(8.8)pertaintotruechargesandcurrents,respectively,duetomotionoftruecharges.Theydonotpertaintochargesandcurrentsresultingfromthepolarizationandmagnetization

phenomena,sincetheseareimplicitlytakenintoaccountbytheformulationofthesetwoequationsintermsofD

andH,insteadofintermsofEandB.

7.Thedisplacementcurrentisnotatruecurrent,thatis,itisnotacurrentduetoactualflowofcharges,suchasinthecaseoftheconductioncurrentinwiresoraconvectioncurrentdueto

motionofachargedcloudinspace.Mathematically,ithasthe

unitsofd[(C/m2)m2]/dt

oramperes,thesameastheunitsforatruecurrent,asitshouldbe.Physically,itleadstothesamephenomenonasatruecurrentdoes,eveninfreespaceforwhichP

iszero,andD

issimplyequalto“Withoutit,theuniquenessofthemmfaroundagivenclosedpathCisnotensured”.

Infact,Ampere’scircuitallawinitsoriginalformdidnotcontainthedisplacementcurrentterm,therebymakingitvalidonlyforthestaticfieldcase.ItwasthemathematicalcontributionofMaxwellthatledtothemodificationoftheoriginalAmpere’scircuitallawbytheinclusionofthedisplacementcurrentterm.TogetherwithFaraday’slaw,thismodificationinturnledtothetheoreticalpredictionbyMaxwellofthephenomenonofelectromagneticwavepropagationin1864

evenbeforeitwasconfirmedexperimentally23yearslaterin1887byHertz.

8.TheobservationconcerningthetimederivativeofthemagneticfluxcrossingallpossiblesurfacesboundedbyagivenclosedpathC

initem2impliesthatthetimederivativeofthemagneticfluxemanatingfromaclosedsurfaceS

iszero,thatis,

Onecanarguethenthatthemagneticfluxemanatingfromaclosedsurfaceiszero,sinceataninstantoftimewhennosourcesarepresentthemagneticfieldvanishes.Thus,Gauss’

lawforthemagneticfieldisnotindependentofFaraday’slaw.

9.Similarly,combiningtheobservationconcerningthesumofthecurrentduetoflowofchargesandthedisplacementcurrentthroughallpossiblesurfacesboundedbyagivenclosedpathCinitem2withthelawofconservationofcharge,weobtainforanyclosedsurfaces

whereVisthevolumeboundedbyS.Onceagain,onecanthenarguethatthequantityinsidetheparenthesesiszero,sinceataninstantoftimewhennosourcesarepresent,itvanishes.Thus,Gauss’lawfortheelectricfieldisnotindependentofAmpere’scircuitallawinviewofthelawofconservationofcharge.

10.Thecutviewindicatesthatmagneticfieldlinesarecontinuous,havingnobeginningsorendings,whereasthecutviewindicatestheelectricfieldlinesarediscontinuouswherevertherearecharges,divergingfrompositivechargesandconvergingonnegativecharges.

Notes

[1]Thatthemagneticfluxandthedisplacementflux,respectively,aretobeevaluatedinaccordancewiththeright-handscrewrule(RHSrule),thatis,inthesenseofadvanceof

aright-handscrewasitisturnedaroundCinthesenseofC.TheRHSruleisaconventionthatisappliedconsistentlyforallelectromagneticfieldlawsinvolvingintegrationover

surfacesboundedbyclosedpaths.

磁通量和电通量分别根据右手螺旋法则(RHS法则)判断,即右手螺旋前进的感觉像是按照字母C的方式旋转。RHS法则通常应用在包含有封闭曲线围成曲面积分的电磁场法则当中。

·right-hand

screw的意思是右手螺旋法则,是表示电流和电流激发磁场的磁感线方向间关系的定则,用右手握住通电直导线,让大拇指指向电流的方向,那么四指的指向就是磁感线的环绕方向。

[2]TheminussignontherightsideofEq.(8.7)tellsusthatwhenthemagneticfluxenclosedbyCisincreasingwithtime,theinducedvoltageisinthesenseoppositetothat

ofC.IfthepathCisimaginedtobeoccupiedbyawire,thenacurrentwouldflowinthewirethatproducesamagneticfieldsoastoopposetheincreasingflux.

在公式(8.7)右边的负号是指,当被字母C“包围”的磁通量随时间增加时,感应出的电压与字母C的方向相反。如果将字母C的路径想象成导线,则该导线中变化的电流会产生磁场阻碍磁通量的增加。

[3]Thecutviewindicatesthatmagneticfieldlinesarecontinuous,havingnobeginningsorendings,whereasthecutviewindicatestheelectricfieldlinesarediscontinuouswherevertherearecharges,divergingfrompositivechargesandconvergingonnegativecharges.

从剖面图可以看出磁场线是连续的,没有开始和结尾,而另一剖面图则表示电场线在有电荷的地方是非连续的,都是从正电荷出发汇聚到负电荷。

·positivecharges的意思是正电荷。

·negativecharges的意思是负电荷。

Exercises

1.Fillintheblanks.

(1)In

oftheirexperimentalorigin,thefundamentalformofMaxwell‘sequationsistheintegralform.

(2)InevaluatingthesurfaceintegralsinEqs.(8.7)and(8.8),anysurfaceSboundedbyCcanbe

.

(3)This

thatthetimederivativeofthemagneticfluxthroughallpossiblesurfacesboundedbyCisthesameinorderfortheemfaroundCtobeunique.

,thesumofthecurrentduetoflowofchargesandthedisplacementcurrentthroughallpossiblesurfacesboundedCisthesameinorderforthemmfaroundCtobeunique.

(4)Thesearein

withLenz’law,whichstatesthattheoftheinducedemfis

thatanycurrentitproducestendstoopposethechangeinthemagneticfluxproducingit.

(5)IfloopCcontainsmorethanoneturn,

nanN-turncoil,thenthesurfacetightlywoundcoil,thisisequivalenttothesituationinwhichNseparate,

,single-turnloopsarestackedtheemfinducedintheN-turncoilisNtimestheemf

inducedinoneturn.

(6)ThechargedensityinEq.(8.9)andthecurrentdensityJinEq.(8.8)

totruechargesandcurrents,respectively,

motionoftruecharges.

(7)Infact,Ampere’scircuitallawinitsoriginalformdidnotcontainthedisplacementcurrentterm,

makingit

onlyforthestaticfieldcase.

(8)Theobservation

thetimederivativeofthemagneticfluxcrossingallpossiblesurfacesboundedbyagivenclosedpathCinitem2

thatthetimederivativeofthemagneticfluxfromaclosedsurfaceSiszero.

(9)Onecan

thenthatthemagneticfluxemanatingfromaclosedsurfaceiszero,sinceataninstantoftimewhennosourcesarepresentthemagneticfield

.

(10)Thecutviewindicatesthatmagneticfieldlinesarecontinuous,

nobeginningsorendings,

thecutviewindicatestheelectricfieldlinesarediscontinuous

therearecharges,divergingfrompositivechargesandconvergingonnegativecharges.

2.TranslatethefollowingparagraphintoEnglish.

在外电场的作用下,无极分子的正电荷沿电场方向移动,负电荷逆电场方向移动,导致正负电荷中心不再重合,形成许多排列方向和外场大小一致的电偶极子,它们对外产生的电场不再为零。对于有极分子,它的每个电偶极子在外电场的作用下要产生转动,最终使每个电偶极子的排列方向大体与外电场方向一致,它们对外产生的电场也不再为零。这种电介质中的束缚电荷在外电场作用下发生位移的现象,称为电介质的极化。

Passage

CEBG

and

Metamaterials

Periodicstructuresareabundantinnature,whichhavefascinatedartistsandscientistalike.Whentheyinteractwithelectromagneticwaves,excitingphenomenaappearandAmazingfeaturesresult.Inparticular,characteristicssuchasfrequencystopbands,passbands,andbandgapscouldbeidentified.

Reviewingtheliterature,oneobservesthatvariousterminologieshavebeenuseddependingonthedomainoftheapplications.Theseapplicationsareseeninfilterdesigns,gratings,frequencyselectivesurfaces(FSS),photoniccrystalsandphotonicbandgaps(PBG),etc.Weclassifythemunderthebroadterminologyof“ElectromagneticBandGap(EBG)”structures.

Generallyspeaking,electromagneticbandgapstructuresaredefinedasartificialperiodic(orsometimesnon-periodic)objectsthatprevent/assistthepropagationofelectromagneticwavesinaspecifiedbandoffrequencyforallincidentanglesandallpolarizationstates.

EBGstructuresareusuallyrealizedbyperiodicarrangementofdielectricmaterialsandmetallicconductors.Ingeneral,theycanbecategorizedintothreegroupsaccordingto

theirgeometricconfiguration:(1)three-dimensionalvolumetricstructures,(2)two-dimensionalplanarsurfaces,and(3)one-dimensionaltransmissionlines.Figure8.1shows

tworepresentative3-DEBGstructures:awoodpilestructureconsistingofsquaredielectricbarsandamulti-layermetallictripodarrayExamplesof2-DEBGsurfacesareplotted:a

mushroom-likesurfaceandauni-planardesignwithoutverticalvias..

Almostatthesametime,anotherterminology,“metamaterials”,alsoappearedandhasbecomepopularintheelectromagnetism’scommunity.TheancientGreekprefix,

meta(meaning“beyond”),hasbeenusedtodescribecompositematerialswithuniquefeaturesnotreadilyavailableinnature.Dependingontheexhibitedelectromagneticproperties,variousnameshavebeenintroducedintheliterature,including:

·Doublenegative(DNG)materialswithbothnegativepermittivityandpermeability;

·Left-handed(LH)materialsinsidewhichtheelectricfielddirection,magneticfielddirection,andpropagationdirectio