An Electrostatic Analogue for the Novel Temporary Magnetic Remanence Thermodynamic Cycles

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1 -1- An Elecosaic Analogue fo he Novel Tempoay Magneic emanence Themodynamic Cycles Absac emi Conwall Fuue Enegy eseach Goup Queen May, Univesiy of London, Mile End oad, London E1 4NS hp://webspace.qmul.ac.uk/oconwall o hp://vixa.og/auho/emi_conwall This pape follows on fom he exposiion of he new empoay magneic emanence cycles and looks a he similaiies and suble diffeences in he elecosaic analogue. Only he elecomagneics is analysed as he kineic heoy and hemodynamic analysis is almos exacly he same as he magneic case. 1. Inoducion The auho iniially conduced enquiy ino feofluids; hese maeials display empoay magneic emanence[1]. This phenomenon lead o he developmen of hemodynamic cycles[-4] by he auho. Indeed he claims of violaion of he nd Law of Themodynamics in one of he papes seems o be efleced elsewhee[5] and i has become necessay o look a he geneal pinciple egading elecosaic devices and whehe hee is any similaiy wih magneosaic devices due o he nea symmey o dualiy wih Maxwell s Classical Elecodynamic laws[6-8]: ρ E = B E = B = j E c B = + wih he Loenz foce F = q ( E + v B) eqn. 1 These equaions ae he so-called micoscopic fom of he laws and ae always classically ue, howeve in mae, a disincion is made beween and bound chages: ρ = ρ + ρ eqn. bound And we define he Polaisaion field, P, ρ = P eqn. 3 Whee he polaisaion veco epesens he field fom he chages inside he maeial ha ae polaised by he exenal elecical field: P =. xyz E eqn. 4 The elaive pemiiviy. xyz is wien as a enso such ha he induced polaisaion does no have o be collinea o he elecic field. We wie he Displacemen field, D: D = E + P eqn. 5 Subsiuing his concep ino he fis Maxwell equaion yields, D = ρ eqn. 6 Similaly wih he cuens (and hence cuen densiy when consideed ove he same suface aea) he same pocedue can be followed: j = j + j eqn. 7 bound The bound cuen is composed of Ampèian cuens fom he spins of he magneic maeial[6, 9-11], he magneisaion, M and he displacemen cuen due o he changing polaisaion: P jbound = M + eqn. 8 Similaly o eqn. 4, a consiuive elaionship beween he induced polaised veco and he agen causing he polaisaion is fomed: M = χ xyz H eqn. 9 Howeve in his case he magneising field H is consideed fundamenal (i isn, hee is only B field[6]) and his field is elaed o he cuen: H = j eqn. 1 Such ha fo magneosaics we can wie (fom eqn. 7 and he saic case of eqn. 1.3), 1 B = ( H + M ) µ ( H + M ) eqn. 11 c emi Conwall 14

2 -- Which hen leads o he way some of he lieaue wies he 4 h Maxwell equaion: E c B = j+ 1 P E c ( H + M) = j + M + + c D H = j + eqn. 1 Finally, he maeial esponse o he magneising field (eqn. 9) is ofen hidden in a elaive pemeabiliy em, hus: And, B = µ H + χh µ = 1+ χ eqn. 13 The macoscopic Maxwell equaions ae quoed hus: D = ρ B E = B = D H = j + eqn. 14 These uhfully aen fundamenal fo he hidden complexiy of he exa D and H vaiables. Howeve maeial chaaceisics in he fom of M and P ae inoduced and we can begin o analyse he suble diffeences beween he magneic hemo-cycle and he elecical vaian.. The Elecical Sae Equaions fo he Magneic Tempoay emanence Cycle Peviously[1, ] i was shown ha he magneisaion in he magneic hemo-cycle vey accuaely followed a 1 s -ode diffeenial equaion: dm 1 = ( M χµ H ) eqn. 15 The H-field is elaed o he magneising cuen hus, dm 1 N = M χµ i eqn. 16 D A sligh complicaion of he equaion above is he inclusion of a co-maeial wih high pemeabiliy µ o make he magneising cuen smalle. The auho[] analysed he dynamics and enegeics of eqn. 15 in elaion o he wok done magneising, he magneisaion enegy, he magneisaion loss and he ulimae fae of he magneisaion enegy, given ha a empoay flux decays. Biefly, if he magneisaion pocess occus a a ae subsanially slowe han he elaxaion ae τ, hen nealy all of he wok of magneisaion will end up as magneisaion enegy. If he pocess is much fase han τ, all he magneisaion wok will end up as inenal enegy wih no magneic momen esuling. Similaly, if he magneised maeial is disconneced fom exenal cicuiy, hen neglecing adiaive losses, he magneisaion enegy ges conveed o inenal enegy a a ae a funcion of dm/d. 3. The H-Field Cancellaion Mehod The basis of he hemo-magneic hea engine peviously consideed by he auho[, 3] was he convesion of hea enegy diecly ino eleciciy. The mechanism was seen by Kineic Theoy o involve he mico-mechanical disupion of he dipoles ha consiue he magneisaion, which by geneao acion (Faaday s Law, eqn. 1.) did dipole-wok MdM (M is he volume magneisaion). Dipole-wok can be consideed mico-mechanical shafwok which makes he elecical sysem an open sysem. I diecly lowes he inenal enegy of he magneised maeial: du = TdS + µ HdM + µ MdM eqn. 17 The aim was hen o make he dipole-wok geae han he inpu magneisaion enegy in a cycle: MdM > HdM This was shown o be impossible wih a simple esisive load as only pa of he magneisaion enegy is euned. Cogniion of his effec came by seeing he cuen wavefoms induced ino he elecical load: As he load esisance deceased, he cicui ime consan became slowe and slowe, wih a concomian slowing in he ae of magneisaion decay. Tha is, he elecical wok dumped ino he load was no some simple funcion of τ, db dm d d W = d d d Because τ was inceasing. I was ealised ha he induced cuen was e-magneising he woking subsance. This is he em χµ H in eqn. 15. A scheme was conived o eliminae his e-magneising H-field by supeposiion of a emi Conwall 14

3 -3- geneaed field a high fequency (so ha he esulan is effecively invisible o he woking subsance) and his esuled in eqn. 15 being endeed: dm M = eqn. 18 The enegeics and mehod o do his showed ha his was possible[]. A gaph of elecical wok agains 1/ fo one cycle yielded he following gaph: enegy cos of he polaisaion enegy. Boh oo would seem o have a lossy ank whee his inpu enegy is conveed o inenal enegy a he ae a funcion of: d φ φ =. Howeve, hee is no such analogue of he Faaday law eqn. 1. and changes in elecical flux canno diecly cause he geneaion of cuens by an elecomoive foce hee can be no dipole-wok em PdP simila o MdM (eqn. 17). Le us exploe his. Fom he 1 s Maxwell equaion/gauss Law: And hence, P ρ E + = P Q eqn. 1 E + da = A eqn. This epesens a combinaion of he elecic field a he plaes of he capacio and he elecic field fom he polaisaion. The movemen of he chages is he cicui cuen, hus: 1/ (S) Figue 1 de 1 dp 1 di A + = d d d eqn. 3 I can be seen ha he simple dipole wok ino a esisive load neve exceeds he magneisaion enegy inpu (his is no due o losses, i simply eflecs a flaw in he enegy coupling pocess). The uppe ace plaeaus a he field enegy of magneic woking subsance ha is, 1 1 W = c B d µ M d eqn. 19 The diffeence beween his wok, W and he magneisaion inpu enegy epesens hea enegy conveed o elecical enegy. 4. A device based on Elecical emanence Thee is an elecosaic analogue of empoay magneic emanence and i would seem a simple mae o sa fom he dual of eqn. 15: dp 1 = ( P χe E) eqn. In consucing he elecosaic dual of he empoay emanence cycle, hee ae suble similaiies and diffeences. Boh involve a chaging and dischaging phase: one wih magneic flux and an enegy cos of he magneising enegy, he ohe an elecic/polaisaion flux and he Muliplying boh sides he volage acoss he plaes, i.e. v = E dl yields, d de 1 dp 1 di Ed A + = v d d d Which upon inegaion w... ime, EdE + EdP = vi eqn. 4 This is jus seen o be he diffeenial elecosaic wok EdD and he insananeous elecical powe; is magneic dual is HdB. If we neglec he polaising and he magneic field enegy (hey ae ecoveable aound a cycle), we have he usual wok inpu ems: EdP d and HdM d In he fis case, we do wok on a lossy capacio ha seeks o un his wok ino inenal enegy bu we have no dipole-wok em MdM, as in he second case wih he magneic sysem o sumoun ou losses. Fuhemoe hee can be no dual o he H-field cancellaion mehod. No de-polaisaion cancelling emi Conwall 14

4 -4- mehod can be made o sike ou he em χ E, when we ealise ha he poenial acoss he load esiso is negaive and acs o incease he ae of decay fuhe. This only eflecs enegy leaving he capacio ank (in compeiion o ha being conveed o hea), as i should. In sho, he diffeence beween he elecical and magneic sysems is ha, a cicui canno be made wih magneic chages which could delive elecical enegy as elecic chages do; hey simply don exis (eqn. 1.3). To make he elecosaic analogue equies an inemediae sep of geneaion of empoay magneic field fom he collapse of he elecic polaisaion field and his hen can geneae elecic cuen. This, of couse, is an allusion o he displacemen cuen em E of he fouh Maxwell equaion (eqn. 1.4 o D eqn. 14.4). The only way a capacio-based hea engine could wok is eihe: 1) Convenionally: Take he woking subsance aound a cycle exposed o wo o moe esevois such ha he polaisaion is a funcion of empeaue. The changes in enopy and hea flow elae o he elecosaic wok: TdS = EdP ( T ) eqn. 5 ) Unconvenionally I: Fo devices pupoing o delive wok fom one hemodynamic esevoi[5], he elecical sysem mus be open, ha is exenally geneaed chages mus impinge on he elecical sysem. 3) Unconvenionally II: Elecosaic dipole wok mus ac via he inemediay of a magneic field o induce a cuen, as discussed peviously. This sysem, alhough elecically closed is hemodynamically open, as case. The discussion shall coninue wih he hid case and he displacemen cuen. We use he fouh Maxwell equaion wih a dielecic so he cuen densiy em is lef ou: E c B = eqn. 6 The elecic field esuls fom he polaisaion along he x-axis (figue ), which is he axis of he capacio, so we can wie: Dielecic composed of: Capacio +ve plae 1) Polaisable empoay emanence woking subsance ) High 3) High µ wih anisoopy aanged aound cicumfeence z y Induced cuen x Figue Polaisaion B field aound cicumfeence Capacio -ve plae Px c B = i eqn. 7 Whee he cul opeao in his conex can only have componens in he yz plane and a co-maeial has been included o boos he field. Fo simpliciy we shall conside cylindical symmey and we know ha he B-field will ciculae aound he changing P x veco. Using Soke s Ideniy o elae he line inegal of he cul of B o he suface inegal of he flux fom P, we find: P c B d l d l x ( π ) = ( π ) Thus he empoay independen magneic flux is: B yz Px = c eqn. 8 This B-field is iself changing and will lead o E emp (eqn. 9) and so on, as a seies in powes of 1/c, so we safely uncae i o fis ode in 1/c. The E- field is given by Maxwell s nd equaion: Byz Eemp = eqn. 9 Which we know fom Soke s Ideniy will lead o an E-field pependicula o he plane yz, ha is, in he ani- x axis diecion, inceasing wih magniude wih he adius (ou line inegal pah is an axially aligned loop hough he cene of he capacio, see figue ): λ v E dl eqn. 3 = = emp emp pah Solenoid winding hough cene of capacio Induced cuen emi Conwall 14

5 -5- The pah a he cene conibues nohing, so we can wie ( is he volume, n is he uns pe uni lengh): P x vemp = µ n eqn. 31 c A magneic co-maeial µ has been included o boos he magneic field (which mus be nonconducive, e.g. feie). The end esul of his aangemen is, once again, a empoay magneic flux. The polaising enegy of he elece has been ansfeed o magneising enegy of he feie. This seems o accue no benefi, unil we ealise ha he H-field cancellaion echnique can applied, o libeae dipole-wok in excess of he magneising enegy. The diffeence epesens hea enegy of he elece being conveed ino elecical enegy. 5. Conclusion The Maxwell Equaions have a ceain amoun of symmey which leads o he concep of elecical dualiy. Howeve sligh diffeences exis and his is manifes in making a empoay elecical emanence cycle as a dual o empoay magneic emanence cycle. Wha has been found, fo he fome case, is ha an inemediay sep of geneaion of a empoay magneic field is equied. Once his has been achieved, he same echniques of he H-field cancellaion mehod[, 3] ae applied as o he lae mehod. This pape hopefully explains he misconcepion abou he devices ha he sysem is closed and akin o filling and empying a ank eihe wih polaisaion enegy o wih magneisaion enegy. I has been shown ha elecical dipole wok PdP can only eun he polaisaion enegy, EdP. Howeve magneic dipole wok MdM can, via he H-field cancellaion mehod eun moe han he inpu magneisaion enegy. In his case, he Bownian disupion of boh he magneic case (and he coecly configued elecical case) consiues mico-mechanical shafwok and an open sysem. efeences 1. osensweig,.e., Feohydodynamics. Cambidge Univesiy Pess Conwall. O., Novel Themodynamic Cycles involving Feofluids displaying Tempoay Magneic emanence. 13(hp://vixa.og/abs/ ). 3. Conwall,.O., A Novel Tempoay Magneic emanence Themodynamic Cycle. 13(hp://vixa.og/abs/ ). 4. Conwall,.O., How o build a Maxwell Demon fom a nd ode Phase Change Sysem. 13(hp://vixa.og/abs/ ). 5. D Abamo, G., Themo-chaged capacios and he Second Law of Themodynamics. Physics Lees A, 1(374): p Feynman, L., Sands, The Feynman Lecues on Physics. Addison-Wesley, eading, Massachuses. ol. ol.1, ol , , Jackson, J.D., Classical Elecodynamics. nd ed. 1975: Wiley. 8. Landau, L., A Couse in Theoeical Physics: Classical Theoy of Fields. ol. ol. 198: Buewoh-Heinemann. 9. Ahaoni, A., Inoducion o he Theoy of Feomagneism. Oxfod Science Publicaions Bozoh,.M., Feomagneism. IEEE Pess Landau, L., A Couse in Theoeical Physics: Elecodynamics of Medias. ol. ol : Buewoh-Heinemann. emi Conwall 14

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