The rate at which this work is done we call Power: W P = t

Transcription

1 We., 11/8 Thus., 11/9 Fi., 11/30.8-9,.6 Eegy, Diff. f, Supecucs Quiz Ch, Lab 10 Faaay s Law 3.1,,7 Apee- Maxwell, E&M Pulse Haus: Euipe: aglev wih supecuc e (iclues liui ige i a hes) RE8 Las Tie Faaay s law allws us uaiaively speak abu iucace (hw a ie vayig cue puces a -culbic elecic fiel which is espsible f a ef ha ppses he cue s vaiai). Thugh his echais, if a cue is vayig i e wie, i ca iuce a cue i a eaby wie. F ha ae, i he cue iself is subjec he -clubic fiel hus self-iuci. Iucs ae cicui cpes ha have bee piize exhibi his effec. Eegy i he Mageic Fiel T he exe ha Elecic a Mageic fiels uaify ieacis, i akes sese ha we ca phase he eegy ivese i hse ieacis i es f he fiels, a hus, ccepually absac f hikig f he eegy as assciae wih he ieacis bu wih he fiels. We ge w ha pah f Elecic fiels i he vey siple case f a capaci. We fu ha we cul phase he eegy ivese i pillig chages a capacis plaes cul be phase i es f he assciae elecic fiel as Eegy Vlue 1 ε E Nw we e psiie he sae hig f he eegy ivese i seig up a cue i a slei. S, hee we g. As always, whe a chage is ve acss a peial iffeece, wk is e he chage (jus like a ass vig f e elevai ahe has gaviaial wk e i). W V The ae a which his wk is e we call Pwe: W P V If we ake D be he ie f he chage clea he vlage iffeece, he we ca call /D he cue. P I V Nw le s specifically csie a vlage ha s esablishe by a ie vayig cue: I V L S, he ae a which eegy is beig asfee hese chage paicles is

2 P I V I LI L 1 I The, he au f eegy asfee i he pcess f apig up f 0 cue I is f I 1 P Eegy L i f i 1 LI Cvesely, his uch eegy wul have be eve f he cue i he slei if he cue wee ue ff. S hee is his uch eegy se i he cue cfiguai. The agai, cespig apig up I cue is apig up ageic fiel whee, µ NI f u slei,. S we cul say ha his uch eegy is ivese i he fiel cfiguai, a we ca eve phase he eegy sicly i es f he fiel: µ NI I a µ N S u eegy ca be ephase as L µ N π 1 1 µ N 1 Eegy LI πr µ ( πr ) µ N whee he e i backes is he vlue f he slei, s we ca ephase his as Eegy vlue 1 µ Thugh eive a jusifie i a vey specific case, his is a vey geeal esul he eegy assciae wih seig up a ageic fiel (by geig cues flwig) pe vlue hugh which he fiel exiss is his. I shul eieae ha yu ca euivalely hik f his eegy as a ppey f he cue cfiguai. This wul sugges ha yu absluely ee he ccep f he ageic fiel i s jus hay. The sae was ue abu he eegy assciae wih a Elecic Fiel / a Chage Cfiguai. Hweve, jus as wih he elecic ieaci, I see ay way au eaig he fiel as eal whe chages acceleae. The hey she eegy aiae, a i s g g sewhee i he fiel. Execises f Ch. R The Chaace f Physical Laws: (he ae f a ice lile bk by Richa Feya) Weesay, Apil. 1, 009

3 I isagee wih se f he eails, bu he spii f his seci f he chape. A he hea f he physics pga is akig bsevais abu aue; f hse, yu y euce he s fuaeal a ccise uhs, a he aificais. These s fuaeal uhs ae uexplaie. We ca sae he a use he, bu we kw why hey ae he laws f aue. Oe f aj pga i physics is iscveig he fuaeal uhs a ha fe leas uificai ealizig ha sehig we hugh was fuaeal acually fllwe f sehig else. F exaple, all ageic a elecic pheea (icluig Faaay s law) see fllw f Culb s law a elaiviy. u why ae Culb s law a elaiviy he way hey ae? We kw we igh be able ephase higs give ccepual ls, a subly chage he uesi (like, why is he spee f ligh csa? ), bu uelyig hese w ae w higs we jus have explaie. A se pi, eve i physics, a ialg wih a hee-yea-l (wh icesily asks why ) es i e kws. Tha sai, we keep pushig i hpes ha se ay we ll be able ve e e fac f he uexplaie he explaie sie f he lege. Diffeeial F f Faaay s Law: The au ha he elecic fiel (he -Culb pa) culs au a pi is elae he ae f chage f he ageic fiel hee: E l ˆ A u ecall ha i he pevius chape we efie (cas i vague / geeal ah es) [ ( )] F F l li cul z (hee, F is se aheaical fuci ha is a vec) A 0 A A he ie, he vec we wee csieig was,, he ageic fiel, bu geeally, his is wha we ea by he cul f a fuci. Applyig ha Faaay s elai gives [ cul( E) ] z z A li 0 E l A A Siilaly f he x a y cpes, s cul( E) we als shwe ha cul S we w have li 0 ˆ A A Weesay, Apil. 1, 009 3

4 E This is pefecly euivale Faaay s Law. S, hus fa we have hese laws: isie ρ E ˆ A E Gauss s law f eleciciy ε 0 ε 0 ˆ A 0 0 Gauss s law f ageis E l ˆ A E Faaay s law l µ 0 I isie pah µ Apee s law (icplee) I Ch. 3, we will fix up Apee s law, he we ll have he cplee se f Maxwell s euais! Ae wih hese, we ca ackle sehig pey exic: Supecucs: Qualiaive Descipi. Supecucs ae faus f havig esisiviy. As he bk als es, i fllws ha hey have peculia ageic ppeies. Hee s a vey ualiaive explaai. Cpe Pais. Elec Desiy / Laice Peiiciy Recall u picue f a cuc: a elec sea agais he backp f peiic i ces. Csie jus e elec vig hugh a cuc. T zeh e, we igh iagie ha i swis alg agais a uifly psiive backp. u, lk a lile clse, he psiive chages ae lcalize he peiically lcae is. The elec is aace he is, s is pah eflecs he peiiciy f he i laice. I paicula, i wul pefe spe a lile e ie clse a i. Nw iagie a whle sea f such elecs hey ll have a highe esiy ea he is ha away f he. A sea heae i a paicula ieci igh have a esiy like: Elec esiy x Weesay, Apil. 1, 009 4

5 Ne ha elecs flwig i he exac ppsie way wul have he exac sae esiy pfile as wul u sea. Elec Ph ieaci: a wake. Eugh abu hw he is ipac he elec flw f w, w le s csie hw he elec flw ipacs he is. us as he is aac he elecs, he elecs aac he is. Iagie jus e elec swiig alg. Whee eve i is, i aws he eaby is slighly wa i, bu sice hese is ae a bi assive a ae bu elasically each he, hey e a lile sluggish esp a he sceai lks uch like a ba leavig a wake acss he suface f wae he vig elec leaves a wake f i isplacee. Shul ahe elec ce alg s afe he fis, i will ecue his wake. If i ies i he wake i s a bi easie gig. This phee is failia i ay eius: bis fly i fai ake avaage f each he s wakes, a I fe ause yself uig y s s bah ie by pullig his ubbe ucky au wih u acually uchig i he wake f y ha aws he uck alg. Ph-eiae paiig. ack u picue f seas f elecs. Recall ha a elec sea vig he igh has he sae esiy pae as e vig jus as fas he lef hey ca pefecly ie i each he s wakes. I his way, hei ways ae ease. They ae efee as a Cpe Pai (afe he fellw wh fis ecgize ha his cul happe.) Of cuse, he wsie f paiig up like his is he failia elecical epulsi w elecs feel f each he. Which effec iaes eeies whehe pais ae fe, a hus whehe a aeial is supecucig (Abiksv p334 (he iscussi fcuses elecs ea he Fei level, pesuably because ly hese have eighbig fee saes i which hey ca ve, shul a fiel be ipse, a hus ly hey uliaely cibue cues, pehaps he paiig happes f lwe eegy elecs, bu hey e elecically ieleva). Oe gea feaue f his paiig is ha, sice he elecs ae swiig like a schl f fish, all ciae, hey ly ease he way f each he, he ciuus flw ca buil i he fligh pla eflecis au ipuiies a such. I his way, cllisis wih ipuiies ha ipee le elecs ae avie like a schl f fish swiig au se kelp. Meawhile, a heal jigglig f he is ca ieac wih he elecs, bu he effec is eihe ha hey ae sall ipee he (asbe i he flw) ae lage eugh beak a cpe pai eeig he al elecs agai. The agai, al elecs will seies ee a pai up a a give epeaue, hese w pcesses ae i euilibiu a eeie he ppulai f paie elecs. The esisiviy f iay aeials eceases a -ze value as he epeaue appaches abslue ze. F supecucs, he esisiviy ps ze belw a ciical epeaue T C. A cue ha is sae i a supecuc ca u f yeas! ( eegy asfe) Weesay, Apil. 1, 009 5

6 N Resisace N Due Mel: E fiel eas acceleai. Wihu eisisace, we lge apply he Due el: I s he elec s if velciy ha s ppial a ipse elecic fiel, i s he elec s acceleai ha is ppial. Mageic Effecs. Nw hik abu Faaay s law: while he ageic flux is chagig, a ef is iuce, a ha acceleaes (as ppse aiais ) a cue. u his acceleaig cue puces a chagig flux f is w, a i he ppsie ieci f he igial e. The cue will acceleae a acceleae uil i s chagig flux cues ha ue he wihawl f he age he hee will be e ef a he cue will aiai is ew value. The esul is ha hee s a feeback lp s ha hee s e chage i ageic flux if hee was flux hugh he aeial whe i we supecucig, he he flux says, eve whe yu eve he suce (he supecuc us i a elecage), a if hee was e befe, he hee eve will be e, eve if yu big a age ea. A supecuc is like a pefec i f ages. Type I supecucs expel he ageic fiel whe hey bece supecucig, which is kw as he Meisse effec. This was a expeieal supise ha ca be explaie wih a uau echaical el (CS hey). If a age is bugh ea a supecuc, hee us be iuce cues which puce a ageic fiel i he ppsie ieci isie he supecuc. Sice 0 isie, Apee s law ells us ha he cue us als be ze isie hey µ I flw ly he suface! (hewise, we have isie he supecuc.) π Quaiaive Descipi Nw we ca a leas skech a ague f hei beig eihe cue fiel isie a supecuc. Weesay, Apil. 1, 009 6

7 Wha is ha cue? Iagie he pcess f uig he cue by uig a exeal ageic fiel. Tuig he exeal ageic fiel eas ceaig a cule elecic fiel: E E. 1 These fiels will exis bh isie a usie he supecuc (wha cue fiels he supecuc ca geeae is ahe ae). E lieu f ay esisace, wheeve hee is elecic fiel, hee s a acceleai f chage: v E E E. hls (e ha w he ae f chage ahe ha he cue iself is ppial E). Apee s Law gives us ahe elaiship bewee cue esiy a ageic fiel. µ E. 3 Nw we have hee euais a hee ukws (E,, a ); ha shul su pisig. They ca be pu gehe slve f ( E f ha ae) iepeely.* µ µ A fuci wh s sec eivaive is iself ies a csa e / δ / δ e µ δ whee 8. δ is he L peeai eph, which is e f µ Weesay, Apil. 1, 009 7

8 Weesay, Apil. 1, *F isuc s eyes ly: (e eaile eivai f L legh) If we Cul bh sies f euai, we ca big i Faaay s Law elae he cue esiy he ageic fiel: E Sicly speakig, + v, bu Abiksv agues ha he sec e is egligible i his case (p. 330) 0 + S, wihi a ie-iepee csa, k, he e i he backes is ze: + +k 0 u we kw ha iiially 0 which iplies ha a ha ie (a s, f all ie) k 0. (E. 1) Nw, Apee s Law pvies a sec elaiship bewee he ageic fiel a he cue: µ. Subsiuig his i gives µ µ

9 I geeal ( ), bu Gauss s Law f ells us ha 0 s. Siilaly, e ca ague ha he cue is ciuusly flwig wih suce, hus ivegece:. S, µ µ saisfy E. 1) s e / δ e µ δ / δ (he egaive sig i he expe is euie whee δ is he L peeai eph, which is e f µ De: fla a age abve a piece f supecuc The supecuc acs like a age wih ples facig he ppsie way, s i epels he ba age. Thee is feeback because he supecuc s cue chages as he isace f he age chages. Desyig Supecuciviy Mageic Fiel. If a supecuc is expse lage a exeal fiel, H c, he supecuciviy is esye. This ca be siply ues i es f he effecs f a ageic fiel he ebes f he cpe pais say he fiel pis up, e half f he pai is vig igh a he he half is vig lef. I he pesece f his fiel, he igh bu e will wa ac cueclckwise up while he lef bu will wa ac cue clckwise w he fiel ies spli he pai. If he fiel is sg eugh, his ca vece he ieaci ha bis he pai gehe. Tepeaue. If he supecuc is h, supecuciviy ca be esye. A ay epeaue, hee is a ae a which cpe pais ae fe a hee s a ae a which hey ae bke by a heal jigglig f he is. The lae ae is epeaue epee he he i is, he e pweful jiggles hee ae, a hus he e likely ha a pai wul ge kcke apa. The balace f hese w pcesses eeies he euilibiu ppulai f cpe pais. Oly a lw epeaues is ha euilibiu ppulai subsaial. Weesay, Apil. 1, 009 9