MAGNETIC MONOPOLE THEORY
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1 AGNETIC ONOPOLE THEORY S HUSSAINSHA Rsarch schlar f ECE, G.Pullaiah Cllg f Enginring and Tchnlgy, Kurnl, Andhra Pradsh, India Eail: ssshaik80@gail.c Cll: Abstract: Th principal bjctiv f this papr is, finding a way t discvr agntic npl r an islatd agntic charg in a thrtical annr. This papr discusss nly thry with th supprt f Spcial Thry f Rlativity. In futur, if w fund agntic npl, this thry is unaltrd. In this thry I stat Gauss law fr agntic charg. S, I dify axwll s quatin by using Gauss law and athatical prcdur calld Gauss divrgnc thr. Th rsult f this papr givs Equivalnc f culbs and wbrs. Kywrds: agntic charg, Spcial Rlativity, axwll s nd quatin, Culb and wbr quivalnc, Gauss law fr agntic charg.
2 1. INTRODUCTION Its knwn fact that, agntic npl nt yt fund! Is it pssibl t find agntic npl thrtically? Basd n this qustin I dvlp agntic npl thry. This thry is lik axi which rains unaltrd in futur n practical vidnc f having agntic npl. S, lt fund it thrtically: 1.1.Pstulat f agntic npl Thry: Assu an lctrn is agntic npl as a rsult f Spcial thry f rlativity! Yu ay tak psitiv lctric charg r ngativ lctric charg in plac f lctrn. I hav drawn this pstulat fr Spcial Thry f Rlativity. Its knwn fact that, th rlatin btwn th agntic and lctric frc was nt fully undrstd until Einstin had cnstructd th Spcial thry f Rlativity. Basd n this statnt I dvlp agntic npl Thry. W hav sn hw agntic frc appars as a rsult f an lctrstatic frc and th spcial thry f rlativity. Spcial thry f rlativity dnstrats that a frc which is idntifid as lctrstatic in n fra f rfrnc is bsrvd as a agntic frc in anthr fra! In thr wrds, th lctric and agntic frc ar rally th sa [5]. What an bsrvr nas it dpnds upn his stat f tin. Nw hr y qustin is; with th supprt f Spcial rlativity; If lctric and agntic frc ar rally th sa, thn, what s wrng if I assu lctric charg as agntic charg? (Or) what s wrng if I assu a charg which is idntifid as lctric in n fra f rfrnc is bsrvd as a agntic charg in anthr fra? I think it s nthing wrng. Bcaus, Spcial thry f rlativity clarly says, a frc which is idntifid as lctrstatic in n fra f rfrnc is bsrvd as a agntic frc in anthr fra [5]. If it is agntic frc in anthr fra ans, I assu th charg shuld b agntic. By this assuptin I cnstruct thry f having agntic npl. Th rsult f this pstulat rvs cnflict. Thr ar tw cnflicting units in us fr agntic charg [ ] Wbrs [Wb] and apr-trs [A-] [4]. In this thry I rv this cnflict by shwing agntic charg will b asurd in Wbrs (Wb).
3 . THE EUIALENCE OF COULOBS AND WEBERS Lt us find agntic charg and its units; Elctric fild strngth is dfind as lctric frc pr lctric charg [][3]. F E (1) q Whr, E = lctric fild strngth. F = lctric frc. q = lctric charg. In a siilar way I can say agntic fild strngth (H) is dfind as agntic frc pr agntic charg r agntic npl. H F () unknwn Lt us dnt this unknwn quantity as a agntic charg. agntic charg r agntic npl = W knw that [][3], F q Bv (3) Whr, F = agntic frc. q = lctric charg. B = agntic flux dnsity. v = vlcity f lctric charg.
4 quatin F ( 3) B (4) q v W knw that, B H (5) Whr, H = agntic fild intnsity r agntic fild strngth. = agntic prability f fr spac r air. By substitut quatin (5) in quatin (4), H (6) F q v By cparing quatin () with quatin (6), unknwn q v (7) At rst v 0 0 Equatin (7) is what an bsrvr nas an lctric charg upn his stat f tin. T gt th quivalnc f culbs and wbrs I rplac vlcity f lctric charg with spd f light (c) in vacuu. Why I rplacd vlcity f lctric charg with spd f light (c) in vacuu? Bcaus it wrks practically. And this rplacnt unifis culbs with wbrs. Thrfr, q c (8) By substituting th valus f agntic prability, charg f lctrn, and spd f light in quatin (8) w gt,
5 Wbrs. Thrfr agntic charg will b asurd in wbrs (Wb) nt in apr-trs. Sinc, q (9) c 1 c (10) By substituting quatin (10) in quatin (9) q c (11) = prittivity f fr spac (a vacuu). Nw I want charg f an lctrn. T gt charg f an lctrn, substitut agntic npl ( = *10^-17) in quatin (11). Thrfr by substituting prittivity, agntic charg ( = *10^-17), and spd f light in quatin (11) w gt, 19 q culbs Equatins (8 & 11) ar cnsidrd as th quivalnc f culbs and wbrs r th quivalnc f lctric flux and agntic flux r th quivalnc f lctric charg and agntic charg. Equatin (7) is cnsidrd as changing lctric charg givs agntic charg. Lt us fra n prbl t undrstand ths quatins clarly; Prbl 1: w knw that currnt carrying cnductr cnstituts agntic fild arund it. Nw fr supps 10 aprs f lctric currnt is flwing thrugh a cnductr and th lngth f th currnt carrying wir is 10 trs. Thn;
6 a. Hw uch agntic charg assciatd with that cnductr r currnt carrying wir? b. What is th quivalnc f lctric charg f that assciatd agntic charg? Slutin: Givn; I = 10A L = 10 a. agntic charg assciatd with that cnductr; q v IL flux. BA = agntic Whr, B H A ara = 1.568*10^-4 wbrs. b. Equivalnc f lctric charg is; q c = 3.335*10^-7 culbs. (This prbl 1 is analgus t; a. Calculating kintic nrgy f a bdy having ass kg and ving with a vlcity 10/s. 1 K. E v Juls. b. Calculat quivalnc f ass f that kintic nrgy. E c Kg)
7 3. GAUSS LAW FOR AGNETIC CHARGE 3.1.agntic displacnt dnsity r agntic flux dnsity B Siilar t lctric flux dnsity, agntic flux pr unit ara is calld agntic flux dnsity. B 4r (1) 3..Gauss law fr agntic flux Statnt: agntic flux cing ut f a agntic chargd bdy is qual t th aunt f agntic charg nclsd. Cnsidr a pint agntic charg kpt at th rigin as shwn in figur (1). Lt us cnsidr infinitsial ara ds at a distanc r trs fr th rigin. Th agntic flux dnsity and ara vctr ds ar nral t th surfac ds as shwn in figur (1 ). Lt th flux crssing th surfac ds b d. Nt: n y assud thry I drawn figur (1) fr pint agntic charg at th rigin. Figur 1: rprsntatin f Gaussian surfac abut a pint agntic charg at rigin.
8 B d ds d B ds Bdscs d Bds (13) Sinc B and ds ar in sa dirctin Th ttal flux laving th ntir surfac can b btaind by surfac intgratin, Bds s (14) By substitut quatin (1) in quatin (14) w gt 4r 4r ds ds 4r Ara W knw that surfac ara f sphrical surfac f radius r is 4r Thrfr, (15) 3.3.difid axwll s Equatin: Lt b vlu agntic charg dnsity. If th bdy is unifrly chargd with th agntic charg dnsity fllws.. Ttal charg is givn as
9 vlu d d By gauss law r fr quatin (14) and (15) s Bds d (16) Gauss divrgnc thr rlats surfac intgral and vlu intgral []. Accrding t Gauss divrgnc thr surfac intgral f nral cpnnt f th agntic flux dnsity is qual t th vlu intgral f divrgnc f B. s Bds Bd (17) By substitut quatin (17) in quatin (16) w gt Bd d B (18) B is difid axwll s nd quatin. Nt: Fr supps, if an islatd agntic npl is discvrd in ur labratris thn als quatin (18) cannt b altrd. 3.4.agntic frc btwn tw agntic chargs r btwn tw currnt carrying wirs: F I1dl1I dl 4 4r 1 r (19)
10 3.5.Rsult tabl: Th significancs f this papr is shwn blw in tabl 1. Equatin aning q q q v v c Changing lctric charg givs agntic charg. Changing agntic charg givs lctric charg. Equivalnc f culb and wbr. (Or) q c B Thrtical xistnc f agntic charg r difid axwll s nd quatin. Tabl 1: rsultant tabl f this thry
11 4. CONCLUSION In this papr I dvlpd thry fr th xistnc f agntic charg. Th rsult givs nw way f unifying lctric flux and agntic flux and quatin fr quivalnc f lctric flux and agntic flux. This thry ds nt chang prsnt thry f lctragntis. I just rprsntd prsnt thry f lctragntis in a nw way t prv thrtical vidnc f agntic charg. ACKNOWLEDGEENT Authr wants t thank Irfan, kirran, yugandhar, vnkatsh and ghus fr thir cpratin in prparing this papr. REFERENCES Bks: [1] Stphn hawking, A stubbrnly prsistnt illusin (running prss bk publishrs, Philadlphia, Lndn). [] atthw N.O. Sadiku, lnts f lctragntics(xfrd univrsity prss,xfrd). [3] S.Raa rddy, lctragntic thry (scitch publicatins(india) Pvt.Ltd.,India). wbsits: [4] [5]
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