Time varying fields & Maxwell s equations (TOPIC 5)

Transcription

1 iayingils&maxwll sqaions OPC5 byonhsaysa iayingniilgnasanliil inion,anaiaying liilgnasaniil isplann l i l i l hisonpwasonsabyonohgasxpinsoalli,h sononwasisinobyonohgasahaialphysiissohisoy Whyowsyinailipnnils? Onlywihiayingilsiispossibloiholaohniilngy Onlywihiayingilsishonnionbwnliiyannisin 3 liahinsgnaos,oosanansoswowihiayingils 4 iayinghagsannsgnaloniaiaion: lighisaiayingli&niilloniwa ConnsoOPC5: looiowihsai&iayingniils:lonzo; Faaay s Faaayslawiningal&inialo;laionLonzo&Faaayslaw ingal& inial o; laion o& Faaay s Magningyannios,appliaions:gnao,oo,anso iayingliils:pèmaxwll slawanisplanns Maxwll sqaions,poyningoanpoyning sho,iaian loniwas,aiinxopinslaos,nll slaw Lonzolaw&looios Lonzoonoinghags on hags F Lonzo nsiy :, opniol q q,, i,,,,,, F Lonz xapl:oioninqasinioanils F:looio= looan,, =wopnihag happlio ishlonzo: l l q Polaaoa: opnihag F q Lonz F l l F l hawaysognaan: lilooan:bais&llls nilooan:gnaos looan gnaos q l l l V MPORN:hilosnowoonoinghags,bioswoonniipols anhsonniaials.moo,ngysbspnoaniils.

2 Magniinaoingloop F F q hag q i wi i ishspohhagwihsp ohwi:iispaalllojanhso l i wi loop l l saliibyc+ i wi wi loop loop l wi l,whishisplanowisgning l ishowaiaalnoasionohibbon.n: l n ˆ h i i h ibb =/,whishlxohoghhlaalsahingaionisonly poon sininhohiionhhinssisininisial.now,hlxo hoghasanlosingaolsbzo;hn hoghasanlosingaolsbzo;hn+c++c=, +C++C= whh n an3 sahlxhoghhppanlowsasinhig. nhiniionohlx,hiionoisowas.hiisoonnino nˆ inialwaysinhsaiionwihspohloop.lssayiisowaspaallli h sa iion wih sp o h loop L s say i is owaspaalll oohsa+;hniisanipaallloo;wihhisiniionhsign nˆ nˆ ocsbhang,ogi: C C C hisnilooiowhihosnosoanybay/olagin isnononsaihliningalof aonhlosloopisinozo. ppliaionsolonz slawanni owanonllwhihwayanigos?looahiionohnio, owanonllwhihwayanigos?looahiionohnio, oblnz slaw:hngnabyanialwayslowssoaso opposhhanginxnallx. Cgnao& gnao& lioo os sin Magniba yns siplpailalao l l yloon OhappliaionsohLonzo: Cliooassspo allal/siono&polaizaionoilioinginil

3 Faaay slaw:inion h hwosiaions&ahsa,onlysibbyobssoingwihlaisp: osi aions&ahsa onl sibb obs so ing ihlai sp n,hhagsinhloopaoinginasaiilana sbjohlonzo,whihasaslooioopi4: nhsanlooiosbpsnhy xisnohlonzobyisliplisaoiiaionohil qaionso:hliningaloannobzoin,isbqalo: l noohqaionoh..oholsoasnoawhahshapohloop,isb: Faaay slaw:ahangingniil posanliil&hsanin.. l&h i nhosgnalas,hoal...inaoingloopwhihisnoonnoapow spplyishsowos spplyishsowos,onohlonzo,anhohoinion: onohlonzo anhohoinion: a l.hoal...isalwaysqalo: a loop pliaionsofaaay slaw nhosgnalas,hoal...inaoingloopwhihisnoonnoapow spplyishsowos,onohlonzo,anhohoinion: a l.hoal...isalwaysqalo: a loop loniinion=gnaionoanilbyailhaaiswihi Faaay s Faaayslaw aallyisoinpnnlybyfaaayannyin8383 iplappliaion:finhiayingilhainshliil: h i lh h l i l sin ax y xˆ z yˆ os nsw: 4z xˆ 3ax y zˆ in,wanwifaaay slawas:o: hlasqaliyiplishahilinbasisaonsaiil,hnonanwi: V hisqaionhaswoxlyipoanonsqns: isnolongonsai: VV nhpsnoiaiaions,hngy=qvassoiawihlialinaions.g.insiabay,gosnoonlyinhaionolialils,balsooniils

4 hnologialappliaionsofaaay slaw ppliaionsofaaay sisois: in Magningyanslinan,inos 3 Foaloyns:inionsohaingoolan hyssislossooniionpanwhihalsoapliishniil yonaspialpanoaninionihn! 4 inionoo,anso, inionoo anso inionoo Cinp n MihalFaaay silia iniisanonpsinobym.f.: Foil,olinsliannilins,ionanion,aion,ol, loano/aho,loly,lolysis,ili,ia&paani Mosipoansiniiisois Faaay sinionlaw Linailiannispons: ianis ilionsan 3Faaay slawsolohisy 4Faaayoaionnoopi nnions lioo8 lignaoanpsooynao83 lignaoanpsooynao83 psooanso83 nis na a nisnaam.f.: aaapaian;aaaylohisy:hagon lons

5 ngybalaninaii Consiaiiinwhihhnnsiyisinasozoo in h n nsiy is inas o soal.hpowso.g.baynsospplyngyo alahlons;shngyisnoonlyoooiion,b alsohohopposingfaaayilgnabyhinn o opposing il gna inn o,hais,hosponingaiaiono. aanlnohii,oosssiona.l sallahwoonbyh sobayoinashnaossozooainial.hso ainainsaixolagopaossanywopoinsohii.aagininsanh nhoghhiiis,hinsananospowspplibyhsoisqalo: bay Vb Va V hwopoinsaanininisialisanaway,holagopbwnhisv, whihishaiaionohsalaponialilaoss: V V l n,sing,wg: V V V l l Now,wsawhaFaaay slawiplis V.Whsg: hanialpow hags Vaiaiononingy hisishhanialpowabsobbyhhags,whihisinallyissipaas olha.hsononisinsasoasningyaswshowinhnxsli Magningy hags hisishhanialpowqioalahhagsanph oingagainshisosiionagsponsiblohsisanohwi: q F F i i i i hags q Noihawanxnhingalsoallspa,sinanazoosihwi i h h n ishpowspagainshin ishpowspagainshin...abyhiaiaiono abyhi aiaiono hniil.ishiaiaionoaningysoinhniil: nlinaia.n: a a.ho: so hags wihan ishngysoinhniil=sobilphilagainsinion

6 linananningy hningyinlinaiaanalsobwinas naiis: hningyinlinaiaanalsobwinas.naiis: oingoioaa slaw,hil oaloopayinganion is: loop l a a oaloopayinganion is: Wshahilislinalypopoionalo.nhsaway,hlxohoghh saliibyhloopisalsopopoionalohn: 3 3 loop 4 4 L a a 4 3 l L hpopoionaliyoiinl bwnhlxoan ish slinanohlosloop.nsol,faaay slawbos: L hisisholayosiniihoy iilaly,winohningyoaloopsing: a a l l os ho Magningyoaloop: L L Magnislingyolas is insing o opa h ngy olas w js on wih hos o losais: isinsingoopahngyolaswjsonwihhosolosais: V V l L V Q C L CV QV l V x x p

7 *ponos:lononq.,missn poningnsanoallywoinsional:hyanosilyoninoh saohibaallypnainsiiashoisan,alllonon pnaionph.nanoalal,oh slawhols.hahaaonsan g is i ispopoionaloisaonsqnolonollisions.inaspono shollisionsonoo;ah,lonshaanalaoion: a inwhn=nsiyosponinglonswg,insaooh s n n n law,hlononqaion:wih.ainghlobohsisan singfaaay slawwobain:.napaoaonsanha i h wanisa,wha.cobininghiswihpè slawo, alisinasponoisnonni,wg:,whihyils,sing: wih=sinph L L n x x hsolionohisqaionisin: hisshowshaaysinsiasponoinasho isan.n=insi:hisishmissn! ai x L spono *Connsaionngyoaspono Wsawinopi4haaniilsoyshsponingsa.Wanshiso Wsawinopi4haaniilsoyshsponingsa.Wanshiso allahngynsiyohsponingsaaaginpa.aalong ylinaoasponingaial,iniiallyinhabsnoaniil.sw nonawaniil,iillsallspaxpohgionopibyhylin, sinsponingnsaishasnhinioohylinohil.whn happliilahshalohiialilahpa,h sponingsaassoxisbasiisngiallyoaoablohah gioniopisillbyhniil.nwanallahsoall onnsaionngy nsiyohsponoashqialnningy nsiy.hngynsiyassoiawihaniilo,whihishsa,wihh hsponingnnsiynoxpliis wonsihahnoalansponingsasabasiallynonni,so hahnoalalisinaapalipaan,balsoinhisas honnsaionngynsiy C ohsponoosponsohaloh ningynsiywhnhilisqaloisiialal: i h i li l i ii l l C hsiplolaohsponingonnsangynsiyisaallyonlyalio aylin.foohgoishaonongyqioxplhniilns oobqalohniilngyisagoialao. x

8 Mhanialoinanliii ConsialosiiosisanRaninanL,onnoasohapoisa onsann wih=ons,hpowansohlonsisissipaasha: hags ol R.pposhawooohiiinshawayasoayh inanlanhshlxhoghhii.holagopaosshsisanris: V in R h..spplibyhsohaainainshn onsansoohin... L L ohhangol,aswllashollosssn: R R R Onhohhan,byngyonsaion,hngypoibyhsosbqalo hhanginngysoinhniil,plshhalosbyolhaing,plsh hanialwowoohoil: W so ol ssinghahwoisonbyaofaossaisanx,win: L Qol W L Qol Fx no:q ol isha,nohag Plgginghlooioonaboinhlasqaionwinallyg: L R L Q ol Fx.inol shais,hisgis: Q ol R L Fx L L L.n: F x hislasxpssionohoanalsobwin,sing,as: F L x ons nan,ngy&oinaniii Wsawinopionhainaniiiopinson slawapplis: Wsawinopionhainaniiiopinsonslawapplis: M =N= N o o ishlxhoghaosssionohii;oaoilonns,hoallx ossingiis.nglinghniilosihii,wha: N o N o N N,o:.hslinanoa L oilonnswappaonaniiiolanishs: N L hningyoaniiiwihonlyonoilaoniayinganis: M M N L o hisagapinhniii,hisaobwnhopposipolsoh lonaosshgap,ginby: L M F N,hais: F o x x x x lhoghwallahisoinhpiossliassingaonsann,ho bwnhpolsannopnonhowhpowspplywos,biisalwayshsao aginpolnsiy,hais,oaginnilxhoghho.hisisnih nooioispoibyapannninsaoaoil.noihash is a pann insa o a oil ha sh oanbwin,singhxpssionohngyginabo,as: F x o o ons

9 liahins&hligi Classiiaionoliahins: Mahinshaonhanialngy/woinolingy:GNROR Mahinshaonlingyinohanialngy/wo:MOOR 3 Mahinshainonlingy:RNFORMR nassan,hahinonainsalasaoiloinginanxnalniil. Whnhishappns,his: a anin.../ba...inhoil,asaslohiayinglx; anin.../ba...inhoil,asaslohi ayinglx; b ahanialboos/iionoohlonzo isipossiblohaonwihohoh;how: gnaosasigninshawayasalsoiniizinghba...hawol hopolag; oosasigninshawayasalsoaxiizinghnhoghhloop. nbohasspaohasisahibynsinghahniilgnabyh ninhloopisngligiblwihspohxnalil OVRVWoan LCRCGR lipow liysys Cgnaospowplans os sin yoli/ yoli/ ialpowplan hal/nla powplan olangy onnaion winills

10 alanso hpiayoilonsisso N P ns,hsonayon on ns.pposanc olagisapplioh piayoil.yfaaay s law,hin...inh sonayoilis:oil is: inhsanilx goshoghhpiay oil,onalsosha: noanialanso,whaishwiningnsaio a wining ns aio oohasaoingpa ooanaixpasao. haanyypsooos: Rlanoo:C powsallywih inphassissppli ohwinings,,co hsao.hoal lanohni iiaosaoan oopnsonhi laioinaion C Moos C bshobshlss Coo:aCn, whosiionss yhaln,lows hoghhoo nionasynhonos ooansynhonosoo: Cpowisspplioh saowinings,poinga ilwhihassanin nananioin hoo,whihonainsih winingsoa sqilag

11 pèmaxwlllaw&isplann pè slawan holingnal.na: aainghignopè slawwg:.hisan b always,siniiolashhagonsaionlaw: wshapè slawonlyholsonosais bpè slawiningalo,applioh hagingoaapaio,gisonliingslson insasnlosbyhsaloop: l a a!!! a a Maxwll ix pè slawbyainganxa,obaining: bchagingoa apaioaa onsana n:q = Q l b a a a g l a a isplan nnsiy = isplan nnsiy isplannnsiy P Yosawh Yosawh s infisia infisia,iisall iisall a isplannnsiy Wnonh n piosly,iishbonhagnnsiy b Whnanhisplannbngl? nnosais,alwaysnoiaiaionohils ngnaloslowaiaionsqasisaiappoxiaion: ngnaloslowaiaionsqasi saiappoxiaion: slowayingil appoxiaion 3spiallyinsials,aallqnyaainablinlonisblowina/isibl: insi a aainabl in lonisblow ina/isibl: xapl:iayingninaal.,hn: sin g sin ax g g P os 8 =inaal ax g n 8 naal,noally: l ll g isplan hslowayingappoxiaionholsinalsaloniqnis ispla 8

12 osoan hpèmaxwll sqaion bsisiplyinghloaloohhag hpèmaxwllsqaion,bsisiplyinghloaloohhag onsaionlaw,oghwihgass slawooinailshahaoypso sosoan: a isplan M P P M Wshahsosoain4: Fns, aisplan nnsiy b hlom,whihwnowopè sqialnhoosponsoan qialnnnsiy hisplannnsiy,whihishso: M h pop aisplannnsiy,3 hbonhagnnsiy,4 P hlasisnospisingsinwalaynowhaishnobon hags,whihisanoalhagsanasshasoo.oboosina b P oal nnsiyas,sohaonanwianqaionsiilaoh pèmaxwllqaioninayosawinfísia: b o o ay:axiosolonis inhabsnoaialia,w, o o inhabsnoaialia,w gbahqaionsofísia: V Lonz b b b b Lonz, V MG= Maxwll sqaions + Lonzo + oonsqns: anilsainla!!! Poyning sho..ngyho xisno was!!! + Consiilaions xisno..was!!! niqnsshoomg

13 MXWLL s QON Gog, inbgh..ngypoyning shoina wahopoo wihpèmaxwll sqaionwg:.singhgnaloiniy,iis: walsos WihhiniionoPoyning so,hlasqaionanbwinas:.in: a lingy nsiy a ningy nsiy Poyning sho ina onsaionoloningy l ningaloingaingohol: V haiaionoloningyinaisqalohlxopoyning so; Poyning soas..ngyaosshbonayoaol :iaagoholsopoyningo=iaian= =loningylxpniaaannii

14 Poyning shoinlinaia WinhPoyning soas.ainghignohpoyningo, winsinghpoloiais: singfaaay slawanpèmaxwll slawhisnails: wh: inoalinai l ningy nsiy nsiy lingy l l Whng:,o: nsiy ningy.. hanial ningaloingaingoainiol: Poyning sho..ngyho: hlossoloningyinaginolospaisqalohlxo Poyning sowhihaisngyooholplshpowso alahags.hlaisqalool shaosaynsinsiaono Maxwll s q loniwaslighina sing h o iniy: w g h: Maxwllsq. ina singhoiniy: wgh: po popagaion: s 8 3..wa popagaion: gc g C s qaions sin, x x y y x y haoni solion: n: on/= = n3, any aos: sin, Y,,..wasaansswas ina,faaay slawiplis=/ hiionoisallpolaizaionoh..waligh

15 ..wasinnonnilinailis wih no hags no nsial ilis Maxwllqaionsoanonni,nononing i: wihnohagsnonsialilis, wih = singhlinaonsiilaiono,wg: n hisishwaqaionowaspopagaingwihsp wh=aioninxan=phasloiy n n FoFaaay slawwg n ishilionsanolosais.inopnonqny,n wolb onsan.hisisonlyinhlowqnylii,whilingnal ann pnon. Lighasloningy:iaian ngynsiyassoiawihanils: ; wih in,iis.. n wih sin sin <>= iaag Visiblligh:, 5 z,hiaiaionoan bas,nohao!!!wan onlyasiaagsshashaohngynsiy<>.foahaoniwa: ngylxiibyaa=ngyanspobyhwapniianaa..... <> iaag Foaplanwaina: l, Vol Vol,, l hlxisinhiiono.noo: l =Poyning so hiaagngyossingasapniiannisaisalliaian, aniqalshiaagaloholso.foaonohoai..wa: na,ispaalllo,an.. NO:ligh..waaisnoonlyngy, balsolinaananglaon

16 ypsoligh:spalangs haoniwasallingaspo/n:= o/n isaonsan isaonsan insiili=a/n= insiili a/n /n WaqnyanawalnghisassoiawihCOLOR onayoniionsinopis ˆn ˆn n n hlxohoghhaaagosozoin hliihahsgns an no g hyaanjsaosshbonay Noallyhisnihsahagnosanonhina.nsh ashobonayoniionshasbsaisiolinaiaa: sallyinopisonalswihnonniia.ninhasosoons,h nizaionannoollowappliilsaqnishighhanwmz,sohah onibionomoaroopialqnisisngligibl.nhbonayoniions i M R i l i i li ibl h b ii oopialilsbosiply: =ons, // =ons,

17 Rlion&aionaaplanaina onaybwnia:lighispaiallylran paiallyansihais,a.hoil onhlhansiohbonayishso an R, onhohsiiisqalo onayoniionsinopis:=ons, // =ons l R n n ansi hxissaixlaionbwnhilsaallpoins ohbonay.foaonohoaiininwa,his iplishahhwasinin,l&ansi inin shaqaloalphas: R R inghoiginaapoinonhbonay,ahoigin,hn onsisnwihhiniionophoonanwihngyonsaion R Fo=: R, R an aoplana aingoboplanawihhwaoswg: R sin R sin R hisiplis: sin sin sin R R R lawospla lion R ininanlwaspopagainhsai oaiinxhyhahsaalo n nll slaw n sin n sin hansiwapopagasiniwih n n wihsaqnyashininwa hangs Rlanonoalinin onayoniionsinopis:=ons, // =ons. Folighipinginganoalininonaplana bonayhisiplis: R R FoFaaay slaw: R n n n R hinssignasinoaonhhanginlai n n n R oinaiono&inhlwaas R olingohansianlilaplis: n Whsg: n n R n n n n R R n n R RFLCNC R n n n n n n hansianisinas.fongyonsaion,isb: R NO:lananansianahsailighipingsoonsiohoh. Fohaiglassina.g.aalanwinow,Risabo4%anoalinin,soa winowlsalas8%ohinoinglighrinasswihinasingininangl

18 pla lion s is lion oalinnallion:opialibs,pnapis hp:// Raioninnonhoognosia:iags y Consianinhoognosiwhosaiinxaiswihhialooina y.lighayngosaionwhhisahangoaiinx.onll s y.lighayngosaionwhhisahangoaiinx.onlls law,sinnisayingoninoslywihy,alighwaallinghoghhisi ngosaoninosaioniags: x hp:// hislasohphnonono iags,anisalsoxploioiallyoan is also xploi o ahisoallgainxaials GRN,solnss,wagisanibs. GRNwagi