《電子信息類專業(yè)英語(yǔ) 》課件-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.

當(dāng)定義一個(gè)量在一個(gè)給定區(qū)域中針對(duì)一整套數(shù)值所呈現(xiàn)出的行為特征,且在這一給定的區(qū)域中,每一個(gè)點(diǎn)對(duì)應(yīng)一個(gè)該量時(shí),定義這一量的這些行為特征為場(chǎng)。

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

雖然這些現(xiàn)象出現(xiàn)在原子或者微觀層面,但也足以達(dá)到了目的,即在宏觀層面上定義材料的特性,將問(wèn)題平均到與原子維度相比較大的體積上。

[3]Conductionisthephenomenonwherebythefreeelectronsinsidethematerialmoveundertheinfluenceoftheexternallyappliedelectricfieldwithanaveragevelocity

proportionalinmagnitudetotheappliedelectricfield,insteadofaccelerating,duetothefrictionalmechanismprovidedbycollisionswiththeatomiclattice.

傳導(dǎo)是一種現(xiàn)象,自由電子在外加電場(chǎng)的作用下在介質(zhì)中移動(dòng),平均的移動(dòng)速度與所施加的電場(chǎng)的幅度成正比,由于與原子晶格的碰撞所形成的摩擦機(jī)理,所以這不是一種加速過(guò)程。.

·frictionalmechanism的意思是摩擦機(jī)理。

·atomiclattice的意思是原子晶格。

[4]Polarizationisthephenomenonofcreationandnetalignmentofelectricdipoles,formedbythedisplacementsofthecentroidsoftheelectroncloudsofthenucleiofthe

atomswithinthematerial,alongthedirectionofanappliedelectricfield.

極化是電偶極子沿著一個(gè)外加電場(chǎng)的方向創(chuàng)建和基于網(wǎng)格基準(zhǔn)進(jìn)行取位的一種現(xiàn)象,其中,電偶極子是由材料中原子核的電子云的重心的移位所形成的。

·electricdipoles的意思是電偶極子。電偶極子是指兩個(gè)等量異號(hào)點(diǎn)電荷組成的系統(tǒng)。

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.

磁通量和電通量分別根據(jù)右手螺旋法則(RHS法則)判斷,即右手螺旋前進(jìn)的感覺(jué)像是按照字母C的方式旋轉(zhuǎn)。RHS法則通常應(yīng)用在包含有封閉曲線圍成曲面積分的電磁場(chǎng)法則當(dāng)中。

·right-hand

screw的意思是右手螺旋法則,是表示電流和電流激發(fā)磁場(chǎng)的磁感線方向間關(guān)系的定則,用右手握住通電直導(dǎo)線,讓大拇指指向電流的方向,那么四指的指向就是磁感線的環(huán)繞方向。

[2]TheminussignontherightsideofEq.(8.7)tellsusthatwhenthemagneticfluxenclosedbyCisincreasingwithtime,theinducedvoltageisinthesenseoppositetothat

ofC.IfthepathCisimaginedtobeoccupiedbyawire,thenacurrentwouldflowinthewirethatproducesamagneticfieldsoastoopposetheincreasingflux.

在公式(8.7)右邊的負(fù)號(hào)是指,當(dāng)被字母C“包圍”的磁通量隨時(shí)間增加時(shí),感應(yīng)出的電壓與字母C的方向相反。如果將字母C的路徑想象成導(dǎo)線,則該導(dǎo)線中變化的電流會(huì)產(chǎn)生磁場(chǎng)阻礙磁通量的增加。

[3]Thecutviewindicatesthatmagneticfieldlinesarecontinuous,havingnobeginningsorendings,whereasthecutviewindicatestheelectricfieldlinesarediscontinuouswherevertherearecharges,divergingfrompositivechargesandconvergingonnegativecharges.

從剖面圖可以看出磁場(chǎng)線是連續(xù)的,沒(méi)有開(kāi)始和結(jié)尾,而另一剖面圖則表示電場(chǎng)線在有電荷的地方是非連續(xù)的,都是從正電荷出發(fā)匯聚到負(fù)電荷。

·positivecharges的意思是正電荷。

·negativecharges的意思是負(fù)電荷。

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.

在外電場(chǎng)的作用下,無(wú)極分子的正電荷沿電場(chǎng)方向移動(dòng),負(fù)電荷逆電場(chǎng)方向移動(dòng),導(dǎo)致正負(fù)電荷中心不再重合,形成許多排列方向和外場(chǎng)大小一致的電偶極子,它們對(duì)外產(chǎn)生的電場(chǎng)不再為零。對(duì)于有極分子,它的每個(gè)電偶極子在外電場(chǎng)的作用下要產(chǎn)生轉(zhuǎn)動(dòng),最終使每個(gè)電偶極子的排列方向大體與外電場(chǎng)方向一致,它們對(duì)外產(chǎn)生的電場(chǎng)也不再為零。這種電介質(zhì)中的束縛電荷在外電場(chǎng)作用下發(fā)生位移的現(xiàn)象,稱為電介質(zhì)的極化。

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