Hans Christian Ørsted

Transcription

1 Mgnetis is foce which cts on oving chges in the pesence of gnetic fiel. The ltte is siil to gvittionl fiel g (which cts upon ss) n n electic fiel E (which cts upon chges). Like gvittionl n electic fiels, gnetic fiels e lso souce by the se type of entity tht they ct upon i.e. oving chges. lthough gnetic effects hve been epeience n ecoe since ntiquity, the connection to electicity ws pehps fist e by Hns Chistin Øste in 8. He notice tht copss neeles wee eflecte fo gnetic Noth when plce in the pesence of cuent cying wie. f n electic fiel is essentilly whee chge will ccelete t pticul loction in spce, gnetic fiel is whee copss neele woul lign. on filings will eily lign with gnetic fiel, n inee will cluste whee the fiel is stongest. The stength of gnetic fiel is esue in Tesl. cuent cying wie will esult in gnetic fiel which fos loops oun the conucto. We cn use the ight hn gip ule to peict the iection of the gnetic fiel. Hns Chistin Øste on filings ligning with gnetic fiel genete by cuent cying wie Right hn gip ule on filings ligning with gnetic fiel genete by few loops ( ing ) of cuent cying wies Nikol Tesl Mgnetic fiel pouce by coil of cuent cying wie. This is clle solenoi. Mgnetic fiel lines e whee sll gnetic copsses woul point in gnetic fiel. The shing in the bove plots is elte to the stength of the gnetic fiel Physics topic hnout - Mgnetis D new Fench. PGE

2 The gnetic fiel of the solenoi is vey siil to tht of penent b gnet, o inee the Eth itself. t ppes to be the cse tht, unlike chges, souces of gnetic fiels e lwys pie with sinks. n othe wos, gnetic ipole ppes to be the bsic eleent of gnetis. Noth pole is efine to be gnetic fiel souce n South pole gnetic fiel sink. The gnetic fiel of the Eth esults fo the oveent of chge flui within its liqui inteio. The inteio fiel is vey cople, but outsie the Eth it esebles ipole. t pesent gnetic Noth is close to the geogphic Noth. The gnetic fiel of the Eth helps to shiel it fo chge pticles which constitute the sol win. N S Solenoi gnetic fiels e vey siil to those of penent b gnet ll teils contin tos, which copise of negtively chge electons istibute in obitls bout positively chge nucleus. lthough Quntu Mechnicl esciption is equie to unestn the otion of electons, tos will pouce sll gnetic fiel in the fshion of ipole. f n etenl gnetic fiel is pplie, the effect upon electon obits is fo teil to be epelle by the gnetic fiel. This is clle ignetis n is univesl. Howeve, if thee e ny unpie electons* then n pplie fiel will cuse lignent of the gnetic fiels esulting fo these electons. The net esult is n enhnceent of gnetis n is clle pgnetis. beutiful esult of this cceletion of chge pticles e the uo olis n uo ustlis. The iection of the Eth s gnetic fiel cn be peseve in cetin ocks such s coole lv eposite on the se floo of septing tectonic plte bouny like the i- tlntic ige. Polity evesls e coon n ppe to be chotic in egulity. Most oen estites e between n, yes between tnsitions. Vition in Eth s gnetic fiel stength is: T 65 T n few feognetic substnces such s ion, nickel n thei lloys thee is tenency fo unpie electons to pouce gnetic ipoles which lign with ech othe, whethe n pplie fiel is pesent o not. This is the oigin of penent gnetis. H gnetic teils (e.g. steel) etin thei gnetis once ligne. Soft gnetic teils (e.g. feite) will lign with n pplie fiel, then etun to oe isoee stte once fiel is switche off. This is why ion coes e useful in electognets bse upon solenoi.. They intensify gnetic fiel when cuent flows, but switch off when the cuent ceses. bove thei Cuie Tepetue, ll feognetic teils becoe pgnetic. pplying n etenl fiel will set the lignent, n then cooling n heing will ke the effect penent. The Puli Eclusion pinciple sttes up to only two electons cn hve the se Quntu stte chcteize by thei obitl. The spin of the electons ( fo of intinsic gnetis which is eithe up o own ) is wht istinguishes pie electons. Chnge of polity of the Eth s gnetic fiel ove the pst five illion yes Physics topic hnout - Mgnetis D new Fench. PGE

3 oving chge in gnetic fiel will feel foce in popotion to the stength of the gnetic fiel, n lso the velocity of the chge. F l sin f the conucto is not pepenicul to the gnetic fiel then the net foce will vy s sine of the ngle i.e. the egee of pepenicul pojection. F qe qv Electic foce Loentz gnetic foce The gnetic foce cts in utully pepenicul iection to both the chge velocity n the gnetic fiel. Since iect cuent is the flow of positive chge, we cn esily unestn the geoetic eltionship of these quntities using Fleing s Left Hn Rule. l Foce on cuent cying wie into pge Henick ntoon Loentz St John bose Fleing f electic cuent flows t velocity v though cyline of coss section n length l, n the chge ensity is n coulobs pe unit volue q nl nv v n F qv if v n pepenicul F nl n F l *CC Y-S., l ppliction of the Loentz foce the Hll Efffect We cn genelize the foce on cuent cying conucto eleent l F l seiconucto of with w n height h is plce in gnetic fiel. Cuent psses though the seiconucto s shown.the Loentz foce on chges will cuse chge seption, which in tun will esult in n electic fiel E pepenicul to both the gnetic fiel n the cuent iection. Equilibiu is eche when the electic foce n Loentz gnetic foces blnce. qe qv E v VH E w qnwhv v qnwh VH w V H qnwh qnh qnhv H n electic oto is pcticl ppliction of the Loentz foce, which esults in tuning oent on cuent cying coil which is fee to otte within gnetic fiel. split ing coutto swps the iection The electic potentil esulting fo the septe chges is clle the Hll Voltge w V H qe Eple clcultion: n 7 q e h. 9.6 C qnh. + + qv l split ing coutto of cuent once evey hlf evolution to intin toque, n hence ottion, continuously in the se nticlockwise o clockwise iection. The iu foce is when cuent n fiel e pepenicul. To optiise, pcticl oto will hve cuve gnets, n coils in iffeent oienttions V H Seiconucto with n chges pe unit volue Ech chge hs q coulobs t is possible to esue the Hll effect in sll seiconucto, so the effect cn be use to eteine the how non unifo gnetic fiel vies in tie n spce. cn be tio of neunity quntities, which e eily esueble i.e. fiels not too ny oes of gnitue less thn.t cn be esily esue. Ewin Hll Physics topic hnout - Mgnetis D new Fench. PGE h *

4 ppliction of the Loentz foce the ss spectoete The chge q to ss tio of the olecul constituents of teil cn be eteine using ss-spectoete. The teil is incinete n then be of the esulting pticultes is ccelete though n electic potentil V. The ccelete be is then bent into cicle vi the Loentz foce, esulting fo unifo gnetic fiel of stength. The chge to ss tio cn then be eteine fo the iete of the cicle. V v Detecto plce hee y Newton s secon lw, n noting cceletion is centipetl since the otion of the pticle be is unifo n cicul: pticle be qv v ˆ ppliction of the Loentz foce velocity selecto n ltentive syste fo eteining the chge q to ss tio of the olecul constituents of teil is the velocity selecto. n this cse secon electic potentil is vie until the Loentz foce blnces the electic fiel between two pltes, which e plce in unifo gnetic fiel. When these foces blnce, pticle be will not be eflecte n cn theefoe be etecte. pticle be V E qv v qe ppliction of the Loentz foce Cycloton Cycloton is spce efficient echnis fo cceleting chges to high spees. Much like ss-spectoete, be of chges e bent into cicle. Howeve, in this cse the chges eceive boost twice pe cycle fo ltenting potentil between two hlves ( Dees ) of the cycloton. Fo given c of ius, be entes gp between the Dees with velocity u v qv v q qv v u qv v u Detecto plce hee V Foce blnce qe qve v V E v qv v qv V qv V qv q V V Pths of poton be cycloton. Dee seption is kg q 9.6 C Note ny oen pticle cceletos (e.g. the LHC in CERN) e Synchnotons. Tie vying gnetic fiels intin fie cicul be s chges e ccelete. s of 5, enegies of 6.5TeV pe be t the LHC. v qv v qv v v q qv qv qv q q 8 8 V q q V Consevtion of enegy Note eltivistic effects ignoe hee! v g c Now since otion is unifo cicul q v v q q f cyc Since the cycloton fequency is inepenent of ius, n ltenting potentil of q V ( t) V cos t will lwys povie il boost in the ight iection when the pticles eit the ees. *Multiplying by the Loentz fcto g, o ltentively iviing the cycloton fequency by g, cn optiize powe tnsfe s v ppoches c. Note ost oen high enegy souces e typiclly Synchotons. Howeve, these e uch less copct! Note s pticles ppoch the spee of light, eltivistic effects becoe significnt* Physics topic hnout - Mgnetis D new Fench. PGE 4

5 Clculting gnetic fiel stength cuent will genete gnetic fiel, s inicte by the Right hn gip ule. ut wht is the fiel stength il istnce wy fo cuent cying wie? pèe s Theoe, cobine with Mwell s Displceent Cuent when electicl fiels vy with tie, escibes this eltionship S loop E l S t sufce i.e. n open sufce boune by loop coesponing to the integl on the left hn sie f thee e no gnetic onopoles (i.e. gnetic fiels e close loops n ll gnets coe in ipole, quopole etc sets of Noth,South pis) S closesufce Note this is iffeent fo electic fiels, which e souce by chges Q ES closesufce f neby electic fiels e sttic so we cn ignoe the Displceent cuent l loop l Guss s Lw pèe s Theoe Mgnetic quopole Right hn gip ule Cl Fieich Guss né-mie pèe nothe useful epession fo clculting gnetic fiels fo cuent eleents is the iot-svt lw ' l 4 l () Fo bity cuent cying line l ' 4 line ' We cn use the iot Svt lw to copute gnetic fiels fo oe cople geoeties, such s coil of cuent cying wie bent into tous. Note we cn fin the fiel insie the tous esily with pèe s theoe see pge 8 N Fo cuent cying wie, the gnetic fiel stength t istnce fo the wie is theefoe given by () gnetic fiel of ectly -7 Tesl is theefoe pouce t istnce of fo wie cying cuent of siil esult follows fo unifo cyline of ius, cying cuent, when <. When <, the cuent close by loop of ius is ' ' o Jes Clek Mwell is the peebility of fee spce. t is efine to be 4 N N being Newtons n being ps Physics topic hnout - Mgnetis D new Fench. PGE 5

6 Mgnetic fiel on is fo cuent loop of N tuns n ius, cying cuent Mgnetic fiel insie solenoi of n tuns pe unit length n ius cying cuent. Unlike the finite solenoi in the siultion plot below, let us consie n infinitely long. We ight nticipte this to be goo ppoition to finite solenoi in tes of the fiel within the coils. N yˆ y yˆ N sin sin N y ( y) N loops 4 N iot-svt Lw () l ' 4 line ' On the z is, the only gnetic fiel iection cn be in the z iection since the cicul syety of the sitution ens gnetic fiel in the n y iections ust cncel sin y N z C Let us efine loop CD which psses though the solenoi. Let us ssue the gnetic fiel is unifo within the solenoi tening to zeo outsie. We will tke loop whee C n D istnces ten to infinite lengths. CD C D n l l, l D C l nl l l l l l nl CD D pèe s Theoe Typicl gnetic fiel stengths in Tesl ntestell spce - Eth s gnetic fiel -5 Sll b gnet - Within sunspot.5 Sll Neoyiu gnet. ŷ Lge electognet.5 Stong lbotoy gnet Sufce of Neuton St 8 Mgnet Physics topic hnout - Mgnetis D new Fench. PGE 6

7 The fiel of Mgnetic ipole is theticlly vey siil to tht if n electic ipole (see Electic ipole notes). Electic ipole * * N S Mgnetic ipole The theticl iffeence between the electic n gnetic ipoles is the quntity q is the gnetic ipole oent Fo gnetic ipole foe fo sll cuent loop (o inee solenoi) of ius n genel fo volue with cuent ensity J (cuent pe unit e) in pticul iection Jyz volue ˆθ ˆθ ˆ ˆ q E ˆ sin θˆ cos 4 n both cses ssue is uch gete thn the iensions ssocite with the ipole 4 ˆ sin ˆ cos θ J S Volue N volue eleent yz Fo n to, the ignetic oent (i.e. the effect of gnetic fiel on n to, n not inte-to effects tht give ise to feognetis in ion, nickel etc) is: e 9.9 kg 9 e.6 C Electon ss n chge e 6 e Z toic nube en sque obitl ius Mny gnetic effects cn be unestoo in tes of the gnetic oent of n electon. Note this is elly quntu echnicl ttibute n theefoe it is pehps unwise to igine n electon consisting of tiny cuent loop! The toque on n electic ipole in gnetic fiel is: τ e e g J g "spin" e g obitl ngul oentu Foces between gnetic ipoles Pobbly the ost bsic popety of gnetis is tht Like poles epel, opposite poles ttct, but with wht foce? ttction F F F Totl ngul oentu vecto Note this hs the se sybol s cuent ensity. Tke ce to voi confusion! Repulsion The foce between two ielize gnetic poles is the se invese sque lw s between two chges F F Howeve, fo gnetic ipole in gnetic fiel, the foce epens on the locl gient of the gnetic fiel F ˆ yˆ zˆ y z f n e pllel: gient vecto opeto Fo chge q of ss M obiting oun cicle of ius J J Mvv ngul M oentu J T obit tie v q qv qj T M qj M e.g. electognets F ˆ, ˆ F Physics topic hnout - Mgnetis D new Fench. PGE 7

8 Effects of gnetistion ll tos will ehibit ignetis i.e. the effect of n pplie gnetic fiel on electon obits is to pouce gnetic fiel which opposes the pplie fiel. Howeve, ny teils will fo gnetic ipoles tht will lign with n pplie fiel, stengthening it. This is cuse pgnetis. Fo few feognetic teils (such s steel) the lignent pesists even when the fiel is eove, ceting penent gnet. To ccount fo gnetistion effects, the net gnetic fiel is efine s the su of gnetistion fiel M n n pplie fiel H H M f teil is isotopic in gnetic sense, we ight sensibly ssue gnetistion effects e pllel to the pplie fiel. hence: Mteil H Reltive peebility i, woo, wte, coppe Nickel, cbon steel Feite (Fe O, usully cobine with Nickel, Zinc...) Reltive peebility > 64 Pue ion > 5, f thee e gnetistion effects then we ust use H not * pèe s Theoe H l loop H N N H Moifiction to gnetic fiel equtions to inclue n isotopic coes of eltive peebility n nfinite solenoi of n tuns pe unit length Solenoi bent into tous with N tuns * i.e. within the otte fiel loop thee e N wies eiting, ech cying cuent Piee Cuie Pul Lngevin i.e. how gnetis vies with tepetue Cuie s Lw n Pgnetis Consie n isotopic gnetic eiu with gnetic ipoles ligne in no oienttions. Let gnetic fiel be pplie of stength. The gnetic enegy of ipole is given by E cos The vege gnetistion ligne with the fiel is theefoe: // p sine Physics topic hnout - Mgnetis D new Fench. PGE 8 cos p sin p e 4 fction of the sufce e of sphee which coespons to pol ngles of cos kt cos, sin kt p e cos kt oltznn fcto p p e e sinh sinh // cos p e sinh e // // e () sinh kt Noliztion of pobbility ensity function cosh e // sinh cosh sinh // sinh coth // Lngevin function So when T is lge, no gnetistion, when T is sll, the teil will lign with the pplie fiel