Laws oftheelectro-electricalinduction

Transcription

1 Global Jounal of Rsahs in Engining: Elial and Elonis Engining Volum 6 Issu 4 Vsion Ya 6 Tp: Doubl Blind P Rviwd Innaional Rsah Jounal Publish: Global Jounals In (USA) Onlin ISSN: & Pin ISSN: B Mnd & A S Dubovin BI Vkin Insiu, Ukain Absa- Th onp of sala-vo ponial, h assuming dpndn of h sala ponial of hag and i pou on fom h spd i mad possibl o xplain a whol sis of h phnomna, onnd wih h moion of hag, whih ali in h lassial lodnamis an xplanaion did no hav Suh phnomna inlud h phas abaion of lomagni wavs, h ansvs Doppl ff, h phnomnon of Lonz fo In his ail h nw law of lo-lial induion, whih xplains nau of dipol mission, will b xamind on h basis of h onp of sala- vo ponial Kwods: maxwll quaion, sala-vo ponial, dipol momn, dipol mission, amp law, hlmholz hom GJRE- Classifiaion : OR Cod: 454p Laws ofhelo-elialinduion Sil as p h omplian and gulaions of : 6 Mnd & A S Dubovin This is a sah/viw pap, disibud und h ms of h Caiv Commons Aibuion-Nonommial 3 Unpod Lins hp://aivommonsog/linss/b-n/3/), pmiing all non ommial us, disibuion, and poduion in an mdium, povidd h oiginal wok is popl id

2 Mnd α & A S Dubovin σ Absa- Th onp of sala-vo ponial, h assuming dpndn of h sala ponial of hag and i pou on fom h spd i mad possibl o xplain a whol sis of h phnomna, onnd wih h moion of hag, whih ali in h lassial lodnamis an xplanaion did no hav Suh phnomna inlud h phas abaion of lomagni wavs, h ansvs Doppl ff, h phnomnon of Lonz fo In his ail h nw law of lo-lial induion, whih xplains nau of dipol mission, will b xamind on h basis of h onp of sala- vo ponial Kwods: maxwll quaion, sala-vo ponial, dipol momn, dipol mission, amp law, hlmholz hom I Inoduion M axwll quaions as o h fa ha in h f spa h ansvs lomagni wavs an xis [, ] Togh wih h bounda ondiions hs quaions giv h possibili o solv h poblms of flion and popagaion of suh wavs in h lokd and limid suus Wih h aid of Maxwll quaions i is possibl o solv h poblms of mission Bu sin h quaions indiad a phnomnologial, phsis of suh posss hus fa mains no la Simila poblms an b solvd, also, wih h us of ponials This appoah opns ga possibiliis, bu phsis of h vo ponial of magni fild also up o now maind no la Th dvlopmn of h onp of sala- vo ponial, whih ddiad a numb of woks [3-], i mad i possibl o opn h phsial ssn of a numb of h fundamnal laws of lodnamis, hags onnd wih h moion This onp assums h dpndn of h sala ponial of hag on is laiv spd I is obaind b h wa of h smmizaion of h laws of induion wih h us b h subsanional divaiv This appoah mad possibl o xplain suh phnomna as h phas abaion of lomagni wavs, ansvs Doppl ff, pow inaion of h un aing ssms and nau of Lonz fo In his ail h nw law of lo-lial induion, whih xplains nau of dipol mission, will b xamind on h basis of h onp of sala-vo ponial Auho α σ: -mails: mnd_fdo@mailu, asd_kizilash@mailu II Law of h Elo-Elial Induion In h woks [3-] is dvlopd h onp of sala vo ponial, fom whih i follows ha h sala ponial dpnds on spd This dpndn is dmind b laionship ϕ(,) v g h =, whv is omponn of h hag a g, nomal o o vo, onning hag wih h obsvaion poin Sin pou on an poss of h popagaion of lial and ponials i is alwas onnd wih h dla, l us inodu h bing la sala- vo ponial, b onsiding ha h fild of his ponial is xndd in his mdium wih a spd of ligh [, ]: v g h () ϕ(,) = wh v g, nomal o is omponn of h hag a of o h vo a h momn of h im =, is disan bwn h hag and h poin, a whih is dmind h fild, a h momn of h im E gad Using a laionship = ϕ(,), l us find fild a poin (ig ) Th gadin of h numial valu of a adius of h vo of is a sala funion of wo poins: h iniial poin of a adius of vo and is nd poin (in his as his poin on h axis of x and poin a h oigin of oodinas) Ya 6 7 Global Jounal of Rsahs in Engining ( ) Volum XVI Issu IV Vsion I 6 Global Jounals In (US)

3 Poin is h poin of sou, whil poin - b obsvaion poin Wih h dminaion of gadin fom h funion, whih onains a adius dpnding on h ondiions of ask i is nssa o disinguish wo ass: ) h poin of sou is fixd and is onsidd as h funion of h posiion of obsvaion poin ) obsvaion poin is fixd and is onsidd as h funion of h posiion of h poin of sou v ( ) Ya 6 8 g E ( ) Global Jounal of Rsahs in Engining ( ) Volum XVI Issu IV Vsion I W will onsid ha h hag of aomplishs fluuaing moion along h axis of, in h nvionmn of poin, whih is obsvaion poin, x () ig : Diagam of shaping of h indud li fild x onsidd as h funion of h posiion of hag Thn w wi down h valu of li fild a poin : and fixd poin is h poin of sou and is (,) v ϕ (,) E () = = h 4 πε (,) Whn h ampliud of h fluuaions of hag is onsidabl lss han disan o h x x v v E (,) x = sh x wh x is som fixd poin on h axis x Taking ino aoun ha w obain fom () obsvaion poin, i is possibl o onsid a adius vo onsan W obain wih his ondiion: x x x v v v = = v () 6 Global Jounals In (US)

4 x x v v E (,) x = sh x v This is a ompl mission law of h moving hag If w ak onl fis m of h xpansion of wh a E v sh x x v a (,) x = = x x is bing la alaion of hag This laionship is wav quaion and dfins boh h ampliud and phas sponss of h wav of h li fild, adiad b h moving hag E a ( x,, α) = Th laionship (5) dmins h adiaion pan Sin in his as h is axial smm laiv o h axis, i is possibl o alula h ompl adiaion pan of his mission This diagam osponds o h adiaion pan of dipol mission E, hn w will obain fom (3): (3) (4) If w as h diion of mission ak h vo, whih lis a h plan x, and whih onsius wih h axis h anglα, hn laionship (4) aks h fom: sinα Sin x v z = AH x (5) is bing la vo ponial, laionship (5) i is possibl o wi x x a sin AH α ( x,, α) = = = x ε A = µ H Is again obaind ompl agmn wih h quaions of h bing la vo ponial, bu vo ponial is inodud h no b phnomnologial mhod, bu wih h us of a onp of h bing la sala- vo ponial I is nssa o no on impoan iumsan: in Maxwll's quaions h li filds, whih psn wav, vox In his as h li filds ba gadin nau Ya 6 9 Global Jounal of Rsahs in Engining ( ) Volum XVI Issu IV Vsion I 6 Global Jounals In (US)

5 Ya 6 Global Jounal of Rsahs in Engining ( ) Volum XVI Issu IV Vsion I L us dmonsa h sill on possibili, whih opns laionship (5) Is known ha in h lodnamis h is his onp, as h li dipol and h dipol mission, whn h hags, whih a vaid in h li dipol, mi lomagni wavs Two hags wih h opposi signs hav h dipol momn: p = d, (6) wh h vod is did fom h ngaiv hag owad h posiiv hag Thfo un an b xpssd hough h divaiv of dipol momn on h im Consqunl d p v = = p v =, v p a = = and Subsiuing his laionship ino xpssion (5), w obain h mission law of h bing vaid dipol p ( ) E = (7) This is also v wll known laionship [] In h poss of fluuaing h li dipol a ad h li filds of wo foms is, hs a h lial induion filds of mission, psnd b quaions (4), (5) and (6), onnd wih h alaion of hag In addiion o his, aound h bing vaid dipol a fomd h li filds of sai dipol, whih hang in h im in onnion wih h fa ha h disan bwn h hags i dpnds on im Spifiall, ng of hs pou on h fl bing vaid dipol and i is xpndd on h mission Howv, h summa valu of fild aound his dipol a an momn of im dfins as supposiion pou on sai dipol pou on missions Th laws (4), (5), (7) a h laws of h di aion, in whih alad h is nih magni pou on no vo ponials I hos suus, b whih h w h magni fild and magni vo ponial, a alad akn and h no long w nssa o us Using laionship (5) i is possibl o obain h laws of flion and saing boh fo h singl hags and, fo an quani of hm If an hag o goup of hags undgo h aion of xnal (sang) li fild, hn suh hags bgin o aomplish a fod moion, and ah of hm mis li filds in aodan wih laionship (5) Th supposiion of lial pou on, adiad b all hags, i is lial wav If on h hag as h li fild of, hn h alaion of hag is dmind b h quaion: a= E sin ω m Taking ino aoun his laionship (5) assums h fom sinα x K x α ω ω x mx E ( x,, ) = E sin ( ) = E sin ( ), wh h offiin K sinα = an m b namd h offiin of saing (-mission) singl hag in h assignd diion, sin i dmins h abili of hag o -mi h aing on i xnal li fild Th un wav of h displamn aompanis h wav of li fild: (8) v E sinα j(,) x= ε = x If hag aomplishs is moion und h aion of h li fild of, hn bias un in h disan zon will b win down as 6 Global Jounals In (US)

6 ω x j( x, ) = E osω mx (9) divh = Th sum wav, whih psns h popagaion of lial pou on (8) and bias uns (9), an b namd h loun wav In his un wav of displamn lags bhind h wav of li fild o h angl qual π o h fis im his m and dfiniion of his wav was usd in h woks [3, 4] In paalll wih h lial wavs i is possibl o inodu magni wavs, if w assum ha E j = = oh ε (), Thus, laionship (8), (9) and () an b namd h laws of lial-lial induion, sin Th giv h di oupling bwn h li filds, applid o h hag, and b filds and b uns indud b his hag in is nvionmn Chag islf oms ou in h ol of h ansfom, whih nsus hispozss Th magni fild, whih an b alulad wih h aid of laionship (), is did nomall boh owad h li fild and owad h diion of popagaion, and hi laion a ah poin of h spa is qual: E (,) x H (,) x z Inodud hus magni fild is vox Compaing (9) and () w obain: H x x mx z (, ) ω sin α = E osω Ingaing his laionship on h oodina, w find h valu of h magni fild sinα Hz( x, ) = E sinω mx () µ = Z ε = ε =, wh Z is wav dag of f spa Wav dag dmins h aiv pow of losss on h singl aa, load nomal o h diion of popagaion of h wav: P = ZE Thfo lounwav, ossing his aa, ansfs hough i h pow, dmind b h daa b laionship, whih is load in aodan wih Poning hom abou h pow flux of lomagni wav Thfo, fo finding all paams, whih haaiz wav poss, i is suffiin xaminaion onl of lounwav and knowldg of h wav dag of spa In his as i is in no wa ompulso o inodu his onp as magni fild and is vo ponial, alhough h is nohing illgal in his In his sing of h laionships, obaind fo h lial and magni fild, h ompll saisf Hlmholz's hom This hom sas, ha an singl-valud and oninuous, whih uns ino zo a infini, an b psnd uniqul as h sum of h gadin of a ain sala funion ϕ and oo of a ain vo voialfild funion C, whos divgn is qual o zo: = gadϕ + oc, divc = Consqunl, mus xis la spaaion pou on o h gadin and h vox I is vidn ha in h xpssions, obaind fo hos indud pou on, his spaaion is load Eli filds ba gadin nau, and magni is vox Thus, h onsuion of lodnamis should hav bn bgun fom h aknowldgmn of h dpndn of sala ponial on h spd Bu nau v dpl hids is ss, and in od o om o his simpl onlusion, i was nssa o pass wa b lngh almos ino wo nuis Th gi, whih so hamoniousl w d aound h magn pols, in a saigh mann indiad h psn of som pow pou on ponial nau, bu o his h did no un anion; hfo i und ou ha all xamind onl ip of h ibg, whos subsanial pa maind invisibl of almos wo hundd as Taking ino aoun ni afosaid on should assum ha a h basis of h ovwhlming majoi of sai and dnami phnomna a h lodnamis onl on fomula (), whih assums h dpndn of h sala ponial of hag on h spd, lis Ya 6 Global Jounal of Rsahs in Engining ( ) Volum XVI Issu IV Vsion I 6 Global Jounals In (US)

7 Ya 6 Global Jounal of Rsahs in Engining ( ) Volum XVI Issu IV Vsion I om his fomula i follows and sai inaion of hags, and laws of pow inaion in h as of hi muual moion, and mission laws and saing This appoah mad i possibl o xplain fom h posiions of lassial lodnamis suh phnomna as phas abaion and h ansvs Doppl ff, whih wihin h famwok h lassial lodnamis of xplanaion did no find Af ni afosaid i is possibl o mov onsuion foss, suh as magni fild and magni vo ponial, whih do no allow h alad almos wo hundd as o s h building of lodnamis in ni is sublimi and bau L us poin ou ha on of h fundamnal quaions of induion (4) ould b obaind dil fom h Amp law, sill long bfo appad Maxwll quaions Th Amp law, xpssd in h vo fom, dmins magni fild a h poin xz,, Idl H = 3 wh I is un in h lmndl, is vo, did fom dl o h poin,, xz I is possibl o show ha [ dl ] = gad dl 3 and, bsids h fa ha dl gad dl = o o dl bu h oodl is qual o zo and hfo is final wh dl H = o I = o A π A H 4 H dl = I () h makabl pop of his xpssion is ha ha h vo ponial dpnds fom h disan o h obsvaion poin as Spifiall, his pop maks i possibl o obain mission laws Sin I = gv, wh g h quani of hags, whih falls p uni of h lngh of onduo, fom () w obain: A H gv dl = o h singl hag of his laionship aks h fom: and sin ha v AH = A E µ = v g dl ga dl E = µ = µ wh a is alaion of hag,,, (3) This laionship appas as follows fo h singl hag: µ a E = (4) If w in laionships (3) and (4) onsid ha h ponials a xndd wih h final spd and o onsid h dla of µ ε, and assuming =, hs laionships will ak h fom: ga( ) dl ga( ) dl E = µ =, (5) 6 Global Jounals In (US)

8 a( ) E = (6) Th laionship (5) and (6) psn, i is as shown high (s (4)), wav quaions L us no ha hs quaions - his soluion of Maxwll's quaions, bu in his as h a obaind dil fom h Amp law, no a all oming unning o Maxwll quaions To h mains onl psn h qusion, wh lodnamis in is im is no banal b his mhod Givn xampls show, as lodnamis in h im of is xisn lil movd Th phnomnon of lomagni induion aada opnd ino 83 and alad almos as is sud undwn paiall no hangs, and h phsial auss fo h mos lmna lodnami phnomna, unil now, w misundsood Cainl, fo his im aada was gnius, bu ha h did mak phsis af i? Th w sill suh billian figus as Maxwll and Hz, bu vn h did no undsand ha h dpndn of h sala ponial of hag on is laiv spd is h basis of ni lassial lodnamis, and ha his is ha basi law, fom whih follow h fundamnal laws of lodnamis III Conlusion Maxwll quaions as o h fa ha in h f spa h ansvs lomagni wavs an xis Togh wih h bounda ondiions hs quaions giv h possibili o solv h poblms of flion and popagaion of suh wavs in h lokd and limid suus Wih h aid of Maxwll quaions i is possibl o solv h poblms of mission Bu sin h quaions indiad a phnomnologial, phsis of suh posss hus fa mains no la Simila poblms an b solvd, also, wih h us of ponials This appoah opns ga possibiliis, bu phsis of h vo ponial of magni fild also up o now maind no la Th dvlopmn of h onp of sala-vo ponial, whih ddiad a numb of woks [3-], i mad i possibl o opn h phsial ssn of a numb of h fundamnal laws of lodnamis, hags onnd wih h moion This onp assums h dpndn of h sala ponial of hag on is laiv spd I is obaind b h wa of h smmizaion of h laws of induion wih h us b h subsanional divaiv This appoah mad possibl o xplain suh phnomna as h phas abaion of lomagni wavs, ansvs Doppl ff, pow inaion of h un aing ssms and nau of Lonz fo In his ail h nw law of lo-lial induion, whih xplains nau of dipol mission, will b xamind on h basis of h onp of sala-vo ponial Rfns Réféns Rfnias SRamo, John Winnildsand Wavs inmodnlonisogiz: 948 VVNiolsk, TI Niolskaa, Elodnamis and popagaion of adio wavs, Mosow, Nauka,989 3 Mnd, On finmn of quaions of lomagni induion,-khakov, dposid in VINITI, No 774 B88 Dp,988 4 Mnd On finmn of ain laws of lassial lodnamis, axiv, phsis/484 5 Mnd Conpion of h sala-vo ponial in onmpoa lodnamis, axivog/abs/phsis/ Mnd Nw lodnamisrvoluion in h modn phsis Khakov, NTMT, 7 Mnd, On finmn of ain laws of lassial lodnamis, LAP LAMBERT Aadmi Publishing, 3 8 Mnd Th Classial Convsions of Elomagni ilds on Thi Consquns AASCIT Jounal of PhsisVol, No, Publiaion Da: Mah 8, 5, Pag: -8 9 Mnd On hphsial basis ofunipola induion A nw p of unipola gnaoenginingphsis, 6, 3, p 7-3 Mnd, Conp of Sala-Vo Ponial in h Conmpoa Elodnami, Poblm of Homopola Induion and Is Soluion, Innaional Jounal of Phsis, 4, Vol, No 6, - R nman, R Lighon, M Snds, nman lus on phsis, - МMi, Vol 6, 977 Ya 6 3 Global Jounal of Rsahs in Engining ( ) Volum XVI Issu IV Vsion I 6 Global Jounals In (US)

9 Global Jounal of Rsahs in Engining ( ) Volum XVI Issu IV Vsion I Ya 6 4 This pag is innionall lf blank 6 Global Jounals In (US)