Global Jounal of Reseaches in Engineeing: F Elecical and Eleconics Engineeing Volume 15 Issue 9 Vesion 1. Yea 15 Type: Double Blind Pee Reviewed Inenaional Reseach Jounal Publishe: Global Jounals Inc. (USA) Online ISSN: 49-4596 Pin ISSN: 975-5861 By F. F. Mende & A. S. Dubovin Absac- The concep of scala-veco poenial, he assuming dependence of he scala poenial of chage and i pou on fom he speed i made possible o explain a whole seies of he phenomena, conneced wih he moion of chage, which ealie in he classical elecodynamics an explanaion did no have. Such phenomena include he phase abeaion of elecomagneic waves, he ansvese Dopple effec, he phenomenon of Loenz foce. In his aicle he new law of eleco-elecical inducion, which explains naue of dipole emission, will be examined on he basis of he concep of scala- veco poenial. Keywods: maxwell equaion, scala-veco poenial, dipole momen, dipole emission, ampee law, helmholz heoem. GJRE-F Classificaion: FOR Code: 991 LawsofheElecoElecicalInducion Sicly as pe he compliance and egulaions of: 15. F. F. Mende & A. S. Dubovin. This is a eseach/eview pape, disibued unde he ems of he Ceaive Commons Aibuion-Noncommecial 3. Unpoed License hp://ceaivecommons.og/licenses/by-nc/3./), pemiing all non-commecial use, disibuion, and epoducion in any medium, povided he oiginal wok is popely cied.
F F. F. Mende α & A. S. Dubovin σ Absac- The concep of scala-veco poenial, he assuming dependence of he scala poenial of chage and i pou on fom he speed i made possible o explain a whole seies of he phenomena, conneced wih he moion of chage, which ealie in he classical elecodynamics an explanaion did no have. Such phenomena include he phase abeaion of elecomagneic waves, he ansvese Dopple effec, he phenomenon of Loenz foce. In his aicle he new law of eleco-elecical inducion, which explains naue of dipole emission, will be examined on he basis of he concep of scala- veco poenial. Keywods: maxwell equaion, scala-veco poenial, dipole momen, dipole emission, ampee law, helmholz heoem. I. Inoducion Maxwell equaions aes o he fac ha in he fee space he ansvese elecomagneic waves can exis [1, ]. Togehe wih he bounday condiions hese equaions give he possibiliy o solve he poblems of eflecion and popagaion of such waves in he locked and limied sucues. Wih he aid of Maxwell equaions i is possible o solve he poblems of emission. Bu since he equaions indicaed ae phenomenological, physics of such pocesses hus fa emains no clea. Simila poblems can be solved, also, wih he use of poenials. This appoach opens geae possibiliies, bu physics of he veco poenial of magneic field also up o now emained no clea. The developmen of he concep of scala- veco poenial, which dedicaed a numbe of woks [3-1], i made i possible o open he physical essence of a numbe of he fundamenal laws of elecodynamics, chages conneced wih he moion. This concep assumes he dependence of he scala poenial of chage on is elaive speed. I is obained by he way of he symmeizaion of he laws of inducion wih he use by he subsanional deivaive. This appoach made possible o explain such phenomena as he phase abeaion of elecomagneic waves, ansvese Dopple effec, powe ineacion of he cuen caying sysems and naue of Loenz foce. In his aicle he new law of eleco-elecical inducion, which explains naue of dipole emission, will be examined on he basis of he concep of scala-veco poenial. Auho α: e-mail: mende_fedo@mail.u II. Law of he Eleco-Elecical Inducion In he woks [3-1] is developed he concep of scala veco poenial, fom which i follows ha he scala poenial depends on speed. This dependence is deemined by elaionship. ϕ(,) v g ch c, wheev is componen of he chage ae g, nomal o o veco, connecing chage wih he obsevaion poin. Since pou on any pocess of he popagaion of elecical and poenials i is always conneced wih he delay, le us inoduce he being lae scala- veco poenial, by consideing ha he field of his poenial is exended in his medium wih a speed of ligh [1, ]: v g ch ϕ(,) c (.1) whee is componen of he chage ae of v g, nomal o o he veco a he momen of he ime c, is disance beween he chage and he poin, a which is deemined he field, a he momen of he ime. Using a elaionship of E gad ϕ(,), le us find field a poin 1 (Fig. 1) The gadien of he numeical value of a adius of he veco of is a scala funcion of wo poins: he iniial poin of a adius of veco and is end poin (in his case his poin 1 on he axis of x and poin a he oigin of coodinaes). Poin 1 is he poin of souce, while poin - by obsevaion poin. Wih he deeminaion of gadien fom he funcion, which conains a adius depending on he condiions of ask i is necessay o disinguish wo cases: 1) he poin of souce is fixed and is consideed as he funcion of he posiion of obsevaion poin. ) obsevaion poin is fixed and is consideed as he funcion of he posiion of he poin of souce. Yea 15 43 Global Jounal of Reseaches in Engineeing ( ) Volume XV Issue IX Vesion I 15 Global Jounals Inc. (US)
y v ( ) y Yea 15 44 Global Jounal of Reseaches in Engineeing ( F ) Volum e XV Issue IX Vesion I We will conside ha he chage of e accomplishes flucuaing moion along he axis of y, in he envionmen of poin, which is obsevaion poin, E y g x (1) ( ) Fig. 1 : Diagam of shaping of he induced elecic field. x and fixed poin 1 is he poin of souce and is consideed as he funcion of he posiion of chage. Then we wie down he value of elecic field a poin 1: ( y,) vy ϕ (,) e c (1) ch y y4 πε ( y,) c When he ampliude of he flucuaions of chage is consideably less han disance o he x x vy vy obsevaion poin, i is possible o conside a adius e (,) x sh veco consan. We obain wih his condiion: cx y c whee x is some fixed poin on he axis x. Taking ino accoun ha we obain fom (.) x x x vy vy vy 1 y y vy x x vy vy e 1 (,) x sh cx x c (.3) vy This is a complee emission law of he moving chage. If we ake only fis em of he expansion of vy sh, hen we will obain fom (.3): c (.) x x vy eay e (,) x cx cx (.4) whee is being lae acceleaion of chage. This ay elaionship is wave equaion and defines boh he ampliude and phase esponses of he wave of he elecic field, adiaed by he moving chage. If we as he diecion of emission ake he veco, which lies a he plane xy, and which 15 Global Jounals Inc. (US)
F consiues wih he axis y he angleα, hen elaionship (.4) akes he fom: eay sin α ( x,, α) (.5) cx The elaionship (.5) deemines he adiaion paen. Since in his case hee is axial symmey elaive o he axis y, i is possible o calculae he complee adiaion paen of his emission. This diagam coesponds o he adiaion paen of dipole emission. evz Since is being lae veco A x poenial, elaionship (.5) i is possible o ewie x x eay sin A α 1 ( x,, α) cx ε c A µ Is again obained complee ageemen wih he equaions of he being lae veco poenial, bu veco poenial is inoduced hee no by phenomenological mehod, bu wih he use of a concep of he being lae scala- veco poenial. I is necessay o noe one impoan cicumsance: in Maxwell's equaions he elecic fields, which pesen wave, voex. In his case he elecic fields bea gadien naue. Le us demonsae he sill one possibiliy, which opens elaionship (.5). Is known ha in he elecodynamics hee is his concep, as he elecic dipole and he dipole emission, when he chages, which ae vaied in he elecic dipole, emi elecomagneic waves. Two chages wih he opposie signs have he dipole momen: p ed, (.6) whee he vecod is dieced fom he negaive chage owad he posiive chage. Theefoe cuen can be expessed hough he deivaive of dipole momen on he ime Consequenly and d p ev e 1 p v, e v 1 p a e Subsiuing his elaionship ino expession (.5), we obain he emission law of he being vaied dipole.. 1 p ( ) E c c. (.7) This is also vey well known elaionship [1]. In he pocess of flucuaing he elecic dipole ae ceaed he elecic fields of wo foms. Fis, hese ae he elecical inducion fields of emission, epesened by equaions (.4), (.5) and (.6), conneced wih he acceleaion of chage. In addiion o his, aound he being vaied dipole ae fomed he elecic fields of saic dipole, which change in he ime in connecion wih he fac ha he disance beween he chages i depends on ime. Specifically, enegy of hese pou on he feely being vaied dipole and i is expended on he emission. oweve, he summay value of field aound his dipole a any momen of ime defines as supeposiion pou on saic dipole pou on emissions. The laws (.4), (.5), (.7) ae he laws of he diec acion, in which aleady hee is neihe magneic pou on no veco poenials. I.e. hose sucues, by which hee wee he magneic field and magneic veco poenial, ae aleady aken and hey no longe wee necessay o us. Using elaionship (.5) i is possible o obain he laws of eflecion and scaeing boh fo he single chages and, fo any quaniy of hem. If any chage o goup of chages undego he acion of exenal (sange) elecic field, hen such chages begin o accomplish a foced moion, and each of hem emis elecic fields in accodance wih elaionship (.5). The supeposiion of elecical pou on, adiaed by all chages, i is elecical wave. If on he chage acs he elecic field of, hen he acceleaion of chage is deemined by he equaion: Yea 15 45 Global Jounal of Reseaches in Engineeing ( ) Volume XV Issue IX Vesion I 15 Global Jounals Inc. (US)
e a E sin y ω. m Taking ino accoun his elaionship (.5) assumes he fom e sinα x K x y α y ω y ω c x c c mx E ( x,, ) E sin ( ) E sin ( ) (.8) Yea 15 46 Global Jounal of Reseaches in Engineeing ( F ) Volum e XV Issue IX Vesion I whee he coefficien e sinα K can be named he cm coefficien of scaeing (e-emission) single chage in he assigned diecion, since i deemines he abiliy of chage o e-emi he acing on i exenal elecic field. The cuen wave of he displacemen accompanies he wave of elecic field: vy esinα jy (,) x ε cx If chage accomplishes is moion unde he acion of he elecic field of, hen bias cuen in he disan zone will be wien down as e ω x jy( x, ) E y cosω c mx.. (.9) The sum wave, which pesens he popagaion of elecical pou on (.8) and bias cuens (.9), can be named he elecocuen wave. In his cuen wave of displacemen lags behind he wave of elecic field o π he angle equal. Fo he fis ime his em and definiion of his wave was used in he woks [3, 4]. In paallel wih he elecical waves i is possible o inoduce magneic waves, if we assume ha E j ε o div. (.1), Inoduced hus magneic field is voex. Compaing (.9) and (.1) we obain: ( x, ) e z ω sinα E y cosω x x c mx. Inegaing his elaionship on he coodinae, we find he value of he magneic field e sinα z( x, ) E y sinω cmx. (.11) Thus, elaionship (.8), (.9) and (.11) can be named he laws of elecical-elecical inducion, since. They give he diec coupling beween he elecic fields, applied o he chage, and by fields and by cuens induced by his chage in is envionmen. Chage iself comes ou in he ole of he ansfome, which ensues his pozess. The magneic field, which can be calculaed wih he aid of elaionship (.11), is dieced nomally boh owad he elecic field and owad he diecion of popagaion, and hei elaion a each poin of he space is equal: (,) x 1 (,) x ε c z µ ε, whee Z is wave dag of fee space Wave dag deemines he acive powe of losses on he single aea, locaed nomal o he diecion of popagaion of he wave: 1 P ZE. y Theefoe elecocuen wave, cossing his aea, ansfes hough i he powe, deemined by he daa by elaionship, which is locaed in accodance wih Poyning heoem abou he powe flux of elecomagneic wave. Theefoe, fo finding all paamees, which chaaceize wave pocess, i is sufficien examinaion only of elecocuen wave and knowledge of he wave dag of space. In his case i is in no way compulsoy o inoduce his concep as magneic field and is veco poenial, alhough hee is nohing illegal in his. In his seing of he elaionships, obained fo he elecical and magneic field, hey compleely saisfy elmholz's heoem. This heoem says, ha any single-valued and coninuous vecoial F, which uns ino zeo a infiniy, can be field epesened uniquely as he sum of he gadien of a ceain scala funcion ϕ and oo of a ceain veco funcion C, whose divegence is equal o zeo: F gadϕ + oc, divc. Z 15 Global Jounals Inc. (US)
F Consequenly, mus exis clea sepaaion pou on o he gadien and he voex. I is eviden ha in he expessions, obained fo hose induced pou on, his sepaaion is locaed. Elecic fields bea gadien naue, and magneic is voex. Thus, he consucion of elecodynamics should have been begun fom he acknowledgemen of he dependence of scala poenial on he speed. Bu naue vey deeply hides is seces, and in ode o come o his simple conclusion, i was necessay o pass way by lengh almos ino wo cenuies. The gi, which so hamoniously wee eeced aound he magne poles, in a saigh manne indicaed he pesence of some powe pou on poenial naue, bu o his hey did no un aenion; heefoe i uned ou ha all examined only ip of he icebeg, whose subsanial pa emained invisible of almos wo hunded yeas. Taking ino accoun enie afoesaid one should assume ha a he basis of he ovewhelming majoiy of saic and dynamic phenomena a he elecodynamics only one fomula (.1), which assumes he dependence of he scala poenial of chage on he speed, lies. Fom his fomula i follows and saic ineacion of chages, and laws of powe ineacion in he case of hei muual moion, and emission laws and scaeing. This appoach made i possible o explain fom he posiions of classical elecodynamics such phenomena as phase abeaion and he ansvese Dopple effec, which wihin he famewok he classical elecodynamics of explanaion did no find. Afe enie afoesaid i is possible o emove consucion foess, such as magneic field and magneic veco poenial, which do no allow hee aleady almos wo hunded yeas o see he building of elecodynamics in enie is sublimiy and beauy. Le us poin ou ha one of he fundamenal equaions of inducion (.4) could be obained diecly fom he Ampee law, sill long befoe appeaed Maxwell equaions. The Ampee law, expessed in he veco fom, deemines magneic field a he poin xyz,, 1 Idl 3 whee I is cuen in he elemendl, dieced fom dl o he poin xyz.,, I is possible o show ha and, besides he fac ha [ dl ] 1 gad dl 3 is veco, 1 dl 1 gad dl o o dl. bu he oodl is equal o zeo and heefoe is final whee dl o I o A π A 4 dl I (.1) he emakable popey of his expession is ha ha he veco poenial depends fom he disance o he obsevaion poin as 1. Specifically, his popey makes i possible o obain emission laws. A gv dl Fo he single chage of e his elaionship akes he fom: and since ha Since I gv, whee g he quaniy of chages, which falls pe uni of he lengh of conduco, fom (.1) we obain: A ev A E µ v g dl ga dl E µ µ, (.13) whee a is acceleaion of chage. This elaionship appeas as follows fo he single chage: µ ea E,,. (.14) If we in elaionships (.13) and (.14) conside ha he poenials ae exended wih he final speed and o conside he delay of, and assuming 1, hese elaionships will ake he fom: µ ε c ga( ) dl ga( ) dl E µ c c, (.15) c ea( ) E c c. (.16) Yea 15 47 Global Jounal of Reseaches in Engineeing ( ) Volume XV Issue IX Vesion I 15 Global Jounals Inc. (US)
Yea 15 48 Global Jounal of Reseaches in Engineeing ( F ) Volum e XV Issue IX Vesion I The elaionship (.15) and (.16) epesen, i is as shown highe (see (.4)), wave equaions. Le us noe ha hese equaions - his soluion of Maxwell's equaions, bu in his case hey ae obained diecly fom he Ampee law, no a all coming unning o Maxwell equaions. To hee emains only pesen he quesion, why elecodynamics in is ime is no banal by his mehod. Given examples show, as elecodynamics in he ime of is exisence lile moved. The phenomenon of elecomagneic inducion Faaday opened ino 1831 and aleady almos yeas is sudy undewen pacically no changes, and he physical causes fo he mos elemenay elecodynamic phenomena, unil now, wee misundesood. Ceainly, fo his ime Faaday was genius, bu ha hey did make physics afe i? Thee wee sill such billian figues as Maxwell and ez, bu even hey did no undesand ha he dependence of he scala poenial of chage on is elaive speed is he basis of enie classical elecodynamics, and ha his is ha basic law, fom which follow he fundamenal laws of elecodynamics. III. Conclusion Maxwell equaions aes o he fac ha in he fee space he ansvese elecomagneic waves can exis. Togehe wih he bounday condiions hese equaions give he possibiliy o solve he poblems of eflecion and popagaion of such waves in he locked and limied sucues. Wih he aid of Maxwell equaions i is possible o solve he poblems of emission. Bu since he equaions indicaed ae phenomenological, physics of such pocesses hus fa emains no clea. Simila poblems can be solved, also, wih he use of poenials. This appoach opens geae possibiliies, bu physics of he veco poenial of magneic field also up o now emained no clea. The developmen of he concep of scala-veco poenial, which dedicaed a numbe of woks [3-1], i made i possible o open he physical essence of a numbe of he fundamenal laws of elecodynamics, chages conneced wih he moion. This concep assumes he dependence of he scala poenial of chage on is elaive speed. I is obained by he way of he symmeizaion of he laws of inducion wih he use by he subsanional deivaive. This appoach made possible o explain such phenomena as he phase abeaion of elecomagneic waves, ansvese Dopple effec, powe ineacion of he cuen caying sysems and naue of Loenz foce. In his aicle he new law of eleco-elecical inducion, which explains naue of dipole emission, will be examined on he basis of he concep of scala-veco poenial. Refeences Réféences Refeencias 1. S. Ramo, John. Winne. Fieldsand Waves in moden eleconics.ogiz: 1948.. V. V. Nicolsky, T.I. Nicolskaya, Elecodynamics and popagaion of adio waves, Moscow, Nauka, 1989. 3. F. F. Mende, On efinemen of equaions of elecomagneic inducion, Khakov, deposied in VINITI, No 774 B88 Dep.,1988. 4. F. F. Mende. On efinemen of ceain laws of classical elecodynamics, axiv, physics/484. 5. F. F. Mende. Concepion of he scala-veco poenial in conempoay elecodynamics, axiv. og/abs/physics/5683. 6. F. F. Mende New elecodynamics. Revoluion in he moden physics. Khakov, NTMT, 1. 7. F. F. Mende, On efinemen of ceain laws of classical elecodynamics, LAP LAMBERT Academic Publishing 13. 8. F. F. Mende. The Classical Convesions of Elecomagneic Fields on Thei Consequences AASCIT Jounal of PhysicsVol.1, No. 1, Publicaion Dae: Mach 8, 15, Page: 11-18 9. F. F. Mende. On hephysical basis ofunipola inducion.a new ype of unipola geneao. EngineeingPhysics, 6, 13, p. 7-13. 1. F. F. Mende, Concep of Scala-Veco Poenial in he Conempoay Elecodynamic, Poblem of omopola Inducion and Is Soluion, Inenaional Jounal of Physics, 14, Vol., No. 6, -1. 11. R. Feynman, R. Leighon, M. Sends, Feynman lecues on physics, М..Mi, Vol. 6, 1977. 15 Global Jounals Inc. (US)
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