ΠΗΓΕΣ ΜΑΓΝΗΤΙΚΟΥ ΠΕΔΙΟΥ - ΠΑΝΕΠΙΣΤΗΜΙΑΚΗ ΦΥΣΙΚΗ YOUNG
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ΠΗΓΕΣ ΜΑΓΝΗΤΙΚΟΥ ΠΕΔΙΟΥ ΠΑΝΕΠΙΣΤΗΜΙΑΚΗ ΦΥΣΙΚΗ YOUNG ΚΕΦΑΛΑΙΟ 29
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ΠΗΓΕΣ ΜΑΓΝΗΤΙΚΟΥ ΠΕΔΙΟΥ - ΠΑΝΕΠΙΣΤΗΜΙΑΚΗ ΦΥΣΙΚΗ YOUNG
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- 5. 808 KEOAAA]O 29 IIHTEE MATNIITIKOY ITEAIOY rtqvdvqro! Dellori leplori ppioroupe druro B eivauorqv zqred0uvoltou + z (ptr.o1{prn)gr pdrpo ^ Faqv r+n f. Evol,lonrrzci, q Ef. (29-2) 6fuet _ ttnqfui)x j ttasu . B=G--;;==c7k' H TqXtTITorou efidvo npotoviou eivou-u xauq poyvrlrlxri &ivopl fidvcr os qllrd eivquF = q(- u) x B. Ax6 uni1, xat, xll oxdol ylq ro,B rraiQvol,p€ Fu = q( u) x B = q(- Di) x H pcrlvqrlx{ c},1,q},eni6poo4eivouen(o1gncuo.ur( cnroon- xri.O ),ciyoErorvgerpr:rvrurv6!o 6uvci;rctrvrwcr I- p llt 0'u' r r =-- - (Jrr€.)--:= €olou. I.E +Jt r. " q Ktlvovrog 1qrjo1q g nl. Q9-, eolt, = I/c2,to cLxor€Le- opLripognciqverr1v notrdcnl{ popgrj FR u2 ==--.r F c - 'Orav 1 o eivct nol,riplllQ6reQrlqE c, I,Fs €avcrr,olpc'Twd prxe6r€Qqqnd xlv Fr. AE or1lr€[crle€idrr €ivcr orti].urc crvcyncioorov lnoloyr- opriotrrdvo lplorpororlo€a dvo.l.isrp6vooUorqpoovogo- QdE.IleQryQdpolpetrg to16rryeExor ro ne6(c tincoEra c- wl,oppdveror naporqqrytjgoxirlrog oro orifiqpq qvqqo- pdgror )1. 29-2. )e dvc <i)"ooriorqpcr,fiou xw€ircr l.r€ro dvo.ond rd 6{0 poQric,1 pic cn<lrlE 6riorcxdqr€E 0a €i- vol pq6dv,xo.r,xotri ouvdnsrqder,0q urdplel pcrlvqrurrj 6dvopq. H epprlve(aouroi rou gcuvopevut<incpdOolou 1e.1ov<itogrivol[e dvcv crd rouE6qtipolg nou o6(111oov onlv er,6r,rrjOeopiaqE olerlx<ir1raE. - l1aq2u2 'a=G l, *1t,=*4t.lJl f' t+I t- - ll.. ,at q II J. 29-2 HiurfiQlrdE xor trdlvryLndE6wripe6 perclt 6riolptorovitov. 'Omog ro ll,eitrplrri fls6[o,droll(orro poyvprxriuorof etor4voQ1tirqE€rroll1- liog: Tooluui poyvqtlrriaebioaou0rlplouQy€iroro:rdli€qroodtegutou wrigzrvoripr- va gogr(ce(vorioopeto 0rovuopctlxdriOgolopottrwneiiov aoo8qplouplrodrtolanri to enrpfqougqogric.Xroendpevorbdqlo0dXQlor,pofior.rjooupeor-rr(rr;vaQXiyrovo ufiol.oyioo!pero n€6ionor-r6qprotrp,TeidvogQrrrtroroqdqoEo.yoydE. 29-2 MAfNHTTKo rrEAro AIIO PEYMATOOOPO AfO !TOIXEIQAOYI I{HKOY! Mnogorjpevc xivoupmXglioqrov oQX6vxouE6.29-1,r8roireqoqE aqpjEnlErrolll- l,[ag,1r.cvc rno],o1(ooupero pro^yvrylx6lrs6[onol 64plotrg1r(oeonoro6riroreolprio roQoxriQlolEP 6vaEQsrtrdroedqoEoyoyrig.To oirutdne6ioeivulro blavlopcrlxriri- Opoloporov rebiovfiouoqril,offiolo€dl"cra rlvodpevcqoQrfdpdooorovo.yoT6. Ap1(oupeperovr:ro),o'yr,o1rdrouFoyvlxlxoliJls6[orJnol blpuolqleievcEprupa- roq6qoEoyoy6Edrrrr.poorodprjxougdl,dno46e(per.ro 21.29-3a.O tiyrcoEror-rororye[- or EfuaLAdl,6nouA eivcuro eppoOtivr1Ebroropigrouo,yoyori.Av unriglou n qopn(o 4 ovdpovd6odyx,ol,ro ol.r,xdnrvoripevoqoqrfop6ooolovoror1sr661dyoyd€[vor dQ = nqAdl Tc xrvo{pevapogric sivar.roo8rivopa;.lr6vogoQriod0 fiouxtve[rr:lp€roXrirrpo[or1 rQoEl1v ralfqxd oiio9rTo1Euo.(Tc ne6iolroubrlplorQyolivraldlr6rlv ruyaia xbt1a1 rov qoQrfovd1ouv,rard pdoovripo,pl6svn(ddeQoLopo.)Xrlpqovcpsqv El. (29-1), ro pdrQorouo),[]iorifis6(oudBo€]rd0€olp€ioeivol ,^ po dQuosing po nquoAdlsrnq aD= 4r i = G ------t-. I'0
- 6. 29-2 MATNHTIKO IIEAIO AIIO PEYMATOOOPOAIOTO ETOIXEIOAO1E MHKOIE 809 29-3 (a) ArdMio[oio io! Iroyvrylrol rw6iorrro! 6qploupye(rcl qfid io! oror,X€dorlQ€upqioqdpo qolddl. (b) IpcppdEpoyvlutotj n€6ioundvo oro sfifurEborou bidQx€rqrqrid io ororxEfodl To Q€{pqxor€rJotv€rqlqjrd ro! cvqvrioq rpog o1oetri6orriOero fiQoE10efifne66q!. A),L(tnquoArfvorro Qrdpol oroorolxsiodl,dQo ,^ lta I dl sind 6 b = G , ' ' rj,oe6r.avuopcnm(poqprj, dB= Idlxi 1 2 ' (zvs) (2v6) tinol dl eivoldvubrlivuopc;rep6rqodl kdrxor€ti0lJvol€lt€(v!ror QstiporoEo'rovayo- Yo. OrE[. (29-5)ral (29-6)crors].orivrov?dporo? Biot]iorSavart.fro vo.BQo{ps ro oh,x6pc1v1rn6ne6[oB,rou 6qplorqle[rc.r,oerriOeorlpeiotou1c6qoroaoro peripa oe6vcnhjpeEnirl"urpa,rpfnel vooi'ox?'lpc6ootpep(cur6 rlgexqgdoeEaueE: Fo 4n 6= 4'lt dr-Zi +JTJ (zeJ) )ro endpevoe6dqr,o0o errel.6ootrpeornj q dLcvuopcrlxrjo),ox),rjqor11r,cpegr,xdnc- pc6e(1pcra. Ono4poiveroloro21.29-3a,ro 6r,ovrap"ar,w6nebiodBxcl ouyguppdgror.rpc- yvlxrxo{rr8iou e(voui6legonplB6gp€et€iveE[orJ6qpr,or-r.o^ye(6vc0erm6pop'tiodQ nol rlve(rcl oqv rcreriOrvolqg rc1rirryaEo),[o01o1goo.Or,lgcppdgeivcr,xrin].or,oe elrine6axd0erafio dl.Or,xorel0rivoelErongbivowclcnrirov i6r,orcvrivurou0eluoti lsglorj:ror lgqolponor(ocproto E6.29-11r,otc olpeLcxriqopric.To X1.29-3b6ei- pel lqcppdEtou poprlnrodne6[oroe6vcent"lre8ofiou8ldplerclandro d/xar efval ll,dOerooecurd'flcpcqg{ore r1v opol6't1'tcper,o2y.29-1b^yr.cdvaxlvoripevoolper- 01t6eoQlfo. OLEE.(29-5)ri (29-6)6evpnoporlvva el.o11OorjvonetOe(og,yr,oti6eveivol6rvo- trivvc yfveldvcrefqcpcpedvccnopovropdvooner,goordpeupotogtiporprjpottrinolou xunLr6pcrog.Ar,rrtinor efvcl8trvcrcivvo FrrQiooupeJleeoporLxdei,lsrxoo]"!lrdB Et6S ni'rjqor.rgxr,rxl.rripcrog.Mnoqorjpencivrorg,voenoll0tdoouperlg€E[o6o€rEow€g€ppsod rno?'o1(owogro B 1lc qulpcrooec1o^yodE8roqdQovolnpdrovtcL oulxq(vowcEtc cnorslr6opa.raporlgnelqcpcrLxdgpergrjoelg.Mropotipeer(o1gva ercLl0etioolpeqv E!. (29-1),cr6 qv onofoEsraiwlo€I d),1dnd60rh. Av o ripog yiqo on6dvopeupcroqdpoayoydefvclnfigr1Ecn6xdnolou]urx6,ro re6iooexri0eolpeiorcqcljprlorlgP oqv nrglopjroucloyor-r0c 61elplc onurldovou- verogogdnor ngodpyaruan6nl paywptorTtouullrori.To ou^yxexprpdvoOdpa0aro e-
- 7. 810 KEOA AIO 29 IIHTEE MAINHTIKOY I]EAIOY fiov€qerdoolpsmo E6.29-8.IliwoE 11ouveL.orpopriou'nieiror.tdoopllq{ ror ouv{Oog nopo),efneror,emdgcv ro lhxj eivalanrioibrlqo{ on6trirolo ti}.}"oor.blQopoyvrlrl)i6 u)"r.x6.Ilpdooeregsnur)'oxdgngor{nrotlvciravtlnriglolv lgovrxdperopa}.},6ptvoq}.e- xrplxtlrj pclvrlrLnrine6(crj rircvro lh.xri eivcluepo1t6.ppo0aenovdi.Oolpeorc 0d- l.ldTo (I1,"[00QYoIrQ(r. ffi- ETPATHTIKH ETIIAYEHI TIPOBAHMATAN Ycol,oyropoi pcyvqnxdv ae8iolv 1. flQoooIli qrrE ?.iqr€uo{vq€rErrov dlovoopoflnriv peye- 06!. To ororxer66eE qtf1pa dl €yat ndwo'ce xrp &qte{Ouv- o1 too perlporoE.To povo6uo(oDldtrolr.o i roleuOdvetol .td/xoLEafi6 r,odl ltqoE ro onp€io P 6rou (rpeircr, to re- 5io.6ql,o6{ oad to o4pcio n4y{g rpog ro o1p€io ndpdrri- atolE. 2. >€ oplop6v€EJr€eurrc6oerEro lB oro o1p€(oP d1ouvrI1 i6ro xoteilOuvorl yro 6Lo ro oror,1erc66qqedpqrq. To pftQo tou ol,uxoJ neOiou B r<ire eival ioo pe ro d0Qorqpq i@v pd- tpcov ron dB. )u1vd ndwtoE xq dB d1ow 6tdeopstuidE rcc- r€!o{!oe[E luq otqeopeturri otoryelr-'15qpeipoto. @c rgd- nertdre vo enuldfete dvc orioqpo o!<ivov rqr vq rtQoq6[o- Qio€r€xlg ouvufi6oeE'rolj ^ dgE dB-'E'rot to o],on],r{gortrlc ylo ro o],rx6 rE6[o B owrxa0iororat cnd rpio o]'o&]'1e0ipq- I II ,{PA.EIl- NI, 29_2 >ra0eQ6Q€{ps 125A pdo(oXdl,rrvqlJo{QporoEe6€rnQoE 6elcpev{ avo6e[coo1g.Yro]"oyiotero poyvrlrr].ldre6aorou 54prorpyritar on6 rprjpo rol cnipporogpiliottq 1,0cm,o€ dvq ollreio ro! ordx€r ofld (Iurd 1,2m, <rvro olpeio pqi- oxeror a) rldvo o€ €uo€aoxdo€rnoro rpripq, b) ndvo o€ euOefonotro'Xltrorc€ryovio 30' peau6, <ino4Oeilvelro 27.294. AzH a) ,416rov n<rvtivcrou dellorj leglo{ Bqioxouperi- x[ I xo.refolJvolTouB oe l4(io€oII€(o €(vcr?id0€fl]fio e- nine0o tr1Eoe),i6cg,nQoErq otli6o. 'H, xdrowqE XerioI re, 6voyuondoeolv[or0ioq,MfioQeir€,d'Iore€ivcrl6uvd- rd!, vo Xprlqqronor,€ir€q olpll€reaorou npoB].rjporog1lc vc crobeuxrnie,e <iTtrd[o[o ouvloidoc eivql FI6da.OQo- w(ere ndwore vc enpetcl,le{eote tr1vriaopft ouppetpioE, <rvOdl"etevo orr),ooorerioereto rp6pl,qpo. 3. Mq ldv€Te€uxoroiqvq r(dv€r€Xpiqrl rns qptiE rIE r- rolJ,l)"iog. Av yvrop(ete tc ne6[orou b4plonpyoiwcr.urci ldnoror-rgcyrrryotiEor-rynexprpdvouad,o{ crpi!.oloE,l{o! qv owqertonilereplc 6erircpqnepOwrooqrou p:[oQsi100€to- p10eitogouv6r-roopcigortr6v oxitpdxov,l<irepnoqeitevo rda€r€XQioyllrlE €riol.l"ql,icrgrcr vo ppeiteto nebiotou o{veerorloxiForog.Qgnoq<i6rtypocvcgdqcrcto rcrpti- yovogBpdlogr.rcudvqlpumi&truopeeuodyQqpp€Efipo€tird- q€lEorq 6riorqu drieo. povo6rniorvbrnvuol.rtirrov,flolpe d/ = dl (- i).Ilcr 10 oI- peioP,, i =j, onc5reorlv El. (29-6), dt x i = dt (_ i) x j = dt (_ k). H cpvlrlx{ qopd rou dlovaz eivornpogt1 oe)'i64. Iuo vc Bgorjpero pldrQoxo! I XQlortlofior,oriper4v El. (29 5). >ro ol[€aoPr Lo.ni€r, I dl sir0 f ' I 125A 29-4 Yno).oyroFdEiou [olvl(No{ d€6iooJrorblllouQyeirolard peuparorpdporpjpa clcoyori,prjxotrg1,0cm. B= (10?r .m/A)11E4X!9!0-1,-)Gin 30") = 4,3x 10 8T. AE olpeloOsi dr! ra pdrpc rov p<rlv4rlxrrivne6icrweivcu nol,dprxpriouyxprvdlrvc[r flgXoQq]rrnQrorr].!€grr[€gnou ovaedpolxovoro t6. 28 2 xal Frln),Fovorrol T|UF(GUrd( 6rv cvrrnpootunruoovraotrwd lr6io. oro ovriororxcon- prein.al"LtiprdvorrgouvcrogopdEol<i ro ouyxcxprprfvorprri- p0 TouoYoYor'. = (10-?r .n/A){144X14tr10'pGi"e0") = 8,7x 10-8T. b) :ro orlpEfoP2,
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- 9. 8r2 KEOAAAIO 29 TIHTET MAfNHTIKOY TIEAIOY ToX1.29-66eipel ta polvryLzdne6[coerpripcrr1gneplopjEliqrrr a:rdpaxgrl,el0i- lgoppoc1o1i. H 6rdra!1rov lqcppt6vroupoplntori ne6iot'oeau{ qv neqinronl ei:vclteLeitog8tocpoperLz{c:rdersivl rouowimollol lrpoB}.tjpctoE1lcto q},exrplt6re- 6[o.Ol lleztgut6g6waprxdgygcppdgprr,cgel0{1pcppt1Enoravoptjg0etlxotlqoprfou zcrer0rjvoucrontvrxrinpogrc dlo (nqogrc;rdoo,1roratavop(cpvqnxotjtpoqriou). Avri0etc,or.^lpappdErotrpalvrlrLxodre|iot nepLBci)'),ouvto geripcnourr,g61pr.olp1ei. Or,rlLerrqLrdE6r-rvcpr,ndgypcppdElexlvotivucLxaral"{.1ouvot eoQtio,evdotlpcgpeE ror pclvrlnxoi:rebior,reivorndr'roteowexeigxcpnriLeEnor 6erdxottvzozfaQfi rcLtd- l.og,cvelrigqtc andro o4jparor-ralolori nor 64plolq1eira re6(4. 2lLldocpe qv rOrdqrcorrnjrorv1.ro.1vqtx6vne6iarvoroE6,28-3,pali peto 1e- lovdgdrL1 ol,lxrielepldpevrlpolvrytrj porjcnripLax)'eloni enLqtlver,oeivo.rndwote p16dv.O vripogrol Gauss1L.opo.lvqnxdre6[c, (yr,aonorc8riro,edeLonienrqdveuu), (2e-10) erqqriler,ro pyovrigdrr.6evurriglouvorqqjoq pepovopdvcpcyqntd cpoqria64trc6ri palvqrrxripov6ro),o,O cprOpdgrov elegldpevrovlqoppr-'lvtol l.lcpqntotine8iolcrd onolo6{norerlelor( elr"pdveLc:rpineLra eivaLioogperov oqr,0pdttrlveloegldpevol Yp0trpov. w 29-6 Mc,"vrpwdreoiolipo cnri [qrci EU0ilQa[[ooloryd.Or 1,ocp;rdgToupcyvlnlodnebioutfvct rdlil"or,F€qoQdroufiQoo0rop(elcl cr6 tovitovrivoTou8eftorllepLoi. {' ^=o 29_4 AYNAMH AIAIAN H 6r1vcpr1o),h1l,eni6goo1gpeta[d611operpcrocpdqovc1o16vpey ,oup(xouEdlel l6t- ofreqr1orlpcroicoenolti].orpomrxdn.oopltjpcradleLeriolg 0epehc66r1orlyaoioovc- qoqlxdperovopr,op<iror-rampdre.ToX1.29-76eipelrprjpcracnd6tioeu0flqoppolg, :rcpd "ql,olEoltoloriEpsY(i)..ouprjxotrgoecndo,col r ;rerali rolg roo 6r.cppeowclanci peljpcrcl rcL1',ovrforor1c,:rqoEqv i6lctqogri.O xdOeoloy<iEpQfoteroulioc oropc- pqurd ne6ionol 64plolp1eioriLLog,xrenopdvoE661eroltdnolc 6rjvcpr1.To6Lrilqap- po6eiXrer.peqr"ndEan6rLg8trvcplxdglgap;rdgnor.r61pLlotp1eiro peipctou xriro c'yu,'- Yof. Xriptptrivcpeqv El . Q9-9),'topdrqoror I oexriOeoqpefotol e:rdvoro^yr.oyotici- vr'l B=Y lltf META=Y IIAPAAAHAON
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- 11. 814 I II ,{PAAEII-M,4 29-4 I IIAPAIEIf NIA 29*5 Af o elo{yQaL4ro,noQci},},Ila,uJreQqyliyrpcrxo}"cibrodrrd- Xouvp€ToEfrorJE4,5 mm rcr 6l<rppdovtcrrcrndqvri0ero qelpcro 15000A. @on,odner vc lioEsrrcroxolsiI pr]xqvr- xrj cwofi row rctrolbicrrv; AYEH Ereu6rjtn pedpcrc 61ouvcwioeteg gogdg,or 6rio alo"/oi oroOo{vrcr trrero.lrjrouE.Xripcpcovcpe qv E!. (2q-l l) rl bdvcuqGvcipovcibcrprjxougeivar L _,oo' _ (4r x 1orT m/A)(15l]o()A)'] L 2nr (2r)(4,5x 103m) =1,0x 101N/m. llqdxercn gr ro),ri pelcil4 6dvclp1,xdrl neproodrepocnd dvor<ivoovri LldrQo.AQo rio€T(I[erlr(rrrlxti to odpc trlg pqXavrxrjgcvrolrjg rdoo rrovoytulurvcioonol I(uv l.lovo,rr- rrfv ulrlzriv. Pedpcrc rcr cnootrioer,Ecu{g r4g tcilrlE pe- ydOorEoxlovrorivorougulepcryc6llpouE1],errpopalv{reg rov erllroxrrvrc6voo)porr6irov.H crvtitrloqrrrlvprllavlnc'iv rdo€ov eJropdvossnotetreipla rgiolpl rcrgcipetpooro orci6lorou ole6loopof . KEOAAAIO 29 IIHTEI MAINHTIKOY IIEAIOY ps[EoxrdEJrQo]rdlorivdvaef6oEoumohjErol a1o1ori,ocvva adleral1 e:rLqciveLdrou plosqorrQr.x{n(eo1npogro pr6oa.Ar-rni1 ororo}"rjtor,ra1o1or.iovop(lurl.rEatvoptvo ),aBftaE.Ot ugrl[tg0e.oponqaofegnol 6lplolgloriwcl pdocmo r]dopc elcr.t(aErol qcr,vopldvolLapf6aEdlouv1pr1or,ponor,10eitc rel,etnciolptivld ostt,t,ooro rLEx€IvrxdE .7raqv enirelfunuplvlx(Eouvrqftg. Mqlovrxri rrioq oe orolqvoer86g Eferdore tg zareu- O{voeugrc'rvpolvqtlrt6v 6uvdpetovoe ocu},1voe16dEruqvio a) perolri yrr,rovrxc6vonrpc6v b) perol{ buaperpluicr.ri- OetrovnLeupoivqE (6r,crEoreiQaE. ^YEH a) Afo y€Lrovu.(dEorr€ipeEorcrgpdowar-ord no- pril"l,1l,operjporolir €nopdvoEdltovrol perclri roug, npoxdlcivtoE 6'cav0).mruEEr6.oerExord prjtoErou <i!o- voxou nlvaor'. b) Alio orop€rQrlidovrfo€ro morx€fq fici- vtl o"rlv i6uooneipo 6lo.ppdovrolord avri0€Tc QE{poro, xl enopdvorEonoroodKa[ p€TqEfTouE.Ap<roro rlvio <r- o?rofvrcrclllLvL&6E6lv<ipelgnpogra dlo, 6lpuougyc6- vrcg 6roLrdoElE€E,xuopotj a'covgayotlo{g.Or arvdperg st'rds€avoLavd)'oy€Er[QoEro 1€rQdyovorou pe{plaroE' drroEi6I ovoqdQolneonoretrorivpfioolpcvtlrf rcrpdple- tpo oro ole0raopti rcovql.exrgopo.lvqr6v. I 29_5 MAINHTIKo IIEAIo KYKAIKOY BPOXOY Av noporlg{oerero eorlreqLrtievriEqlezrglxo{rorbouro{, evriEpeld,evriEpLeroog- parLorrj,rjevdgrlleitrglxofxlvpjpc, 0a6aitedt udpXorrvouppdtrvonqvio,rou nulvri onotsl.ofvrmcndnolldgone(qeg.Toge{pa.rou 6upp6elclrti ro r1v(olg4olpetieror1 8qprolglic pcyvrlrLx6vne6[ov,Al(el rov xdnova cno6e(oltrreplaoporl yroro po- .1vryrclne6[onol ncgdlerclcnriplc gei.rparoqdqoxtrxhxrjc16'yr,p1oneipo(|3pr11o)j alt5oumqpcNxuxl.lxt6voreL.oc6voenuxvrj6Ldrc!r1,dnoEoedvcn4v(o. ToX1.29-8befiveL6vcxrx),r,rriayoyi axr(vcga,nol blcggdercucn<igeipa.L To pr{pao8rlleilclngogxcl dlrocrd rovBpdlope6rioeuO{^ypappolgoytrryodErovdvo6i 22-8 Moyvfluid fieofoxurtrrxori FQ6Xor.To oror,lEilodl bn||[ouQy€f ne0iodB,ro! treircrloro €din€00'r1,. A?,).oororleiodl drlprouQyorivne6io dB u€6rdqoQ€rr)tdEowrm6oEE xdo€x€Eo[ovdqovsx dJ"€Scrurds dxouvouvrm0u6,Itll66v,sv(6I ouvLcnopdvrldkov rov ouvLoro:ot6v kard xovdEovar 6iv€rxool,Lrd r€bfo-Boro olrc[oP.
- 12. 29-5 MATNHTIKOTIEAIOKYK{IKOY BPOXOY rr)d orovdll"o' ro QedpdxdrouEe(l,orcwi0eqE qoQdE,r{o[Tdpayl,lrnid xorlEr€6[c'a].- l,ql.ocvcLporiwcl,oelo),6 ro),ringood11r1. Mroqofpevc 1pr1orpofiolrioolperovvdpoBiotror Savart,6qlo6{nEE[. (29-5) ncL(29-6),y.cvc lrolo^yfooupero pa'yv1rLn6[e6(ooexdfior,oolpefoP rrivrrrorovri[o- voroupqtilol, oecncimco4.randro rdvrpo.OnrogOeflveLro opjpa,ra d! xol r e[va.r. rci0ero,ral l 6r,eii0uvoqror.rne8ioudBnou6lplolpyefralurti ro oulxexgLpdvooroLle[o d/re(raloroenins6oxy.En(or1g,r1=x! + a2.To pdrgodBroune8iotrroudl e(vcr 815 ,^ lrol dl AD = -- -t-----:----a- , + 1 t x ' + 0 - ) (2e-12) /r0-r1 ()a-1L (2e-17) OrouvLortrroeEtou dBelvcl Ere16{ro ng6Bllpc lcpcrrqq(ercl cn<ixl}.rv6puxrjorprpretpicoglpoErov rilovcx, 6evproqeivcrlnriqXeLouvLort6ocrotrI rdOeqoror. fic xri0sfiorxEfod/ufidQ1€rfla dw(orollo fiorlsio pecvr(0er4qoqdorqvrurdvcvrLntrrugdrou pprilor.Tc 6rioclrri morl€iaoivouv(orgouvLonioeEnebfolxcrdrovdlovc.r,orjpgovcperqvEl. (29-13), ctLLdcw(9erEou,ttmrioeErtd0eraorovrilovax. 'EroL, dlegoLxd0eregouvr.or6oeEcL- 1,1),oavcr,qor3wau,xol 6lcqge(rclprivov11ouvrorrriocx. In vo Bpodpeqv otrmrjauvrcr,jl,aax, oluorllqrivor-rper4vE[. (29-13),ouvuno].o- 1(ovrcEr'),crc d/xotri prjnoEroupp<'1or.Elr6gcrd ro d/,ril'crc pe'y601oeotrr{fi1 oxdo1s(va[oTd0sQdxcLpropodpevcrc peragdgorLpredltocndro o].ox],ripopra,on<fte ^ | !,,t a dl lola L, "'= I on(r,17tr = 4;tx'+-+,Ylar To ol,oxlrigopororrdl eivor.anl,6E1 neprqdperc rol xdxl.ou,ldl = 2na,xt trct tgouytt rs]'txd (rud'rx6gpp<i1oE). (2e-15) AEuno06ootrperc6po.rin cwirlg puoEoneipogrol X1.29-8dloupedvcr4v(ocrd N nurvri6rcroyp6vegone(peEqE i6L.ogorrivag.Kti0eore[poolveloqdper.elioor oro :re6io,xclro o),urdne0ioe(varNgopdEro n€6foqE [rdE: u"NIa' B, = ;ii ,;Xa (Nxox?'LxdgomipeE). Q9-16)L V - u ) lro xdwgoqg oreipcg,ritrrrvonep6v, lopielr = 0xur,11E!. (29-16)yivercL ^ 4,,1 dl a ar=abcosv = T; @r+i, ir, +4--_tr, '^ ,^. ^ !"1 dl x AD. = AD SlnV = "i- ':"'j"'.""'1 .:--i .-r:iV ,' + t f x - + a ) x - + q ' ) - B,= !# (oroxdwgoNxuzlrxrivonerE6v). Kc0rriEuropanpv<ipcorecrti q oreipc,rdvo movdlovriqE, ro pdrpororrrebfoue- ]'axroiv€ror.tro tX. 29-9dlolpe q rlgcqrx{ rcgdoraol rouB,ocvouvriprlorlrou.r. I TIAPAAEIf MA 29_6 'Eva p€ydi'ofiqvio arorei'earoLon6 100lurci'LrcriEoneipeE, olcrfvcE0,60m, xar Oro.ppderclcrd peripc5,0A. a) Yro- )'o'y(orero pc'yvtprxd neoio oro oqF€aorou dlovo rou cotri- Xer0,80m 016 ro r{twqo. b) )e roLa an<ioroo4orrriro xd- weo, r[dvo o[ov dEovo,liverar ro pitqo rotr ne6iouioo pe ro 1/8€r€ivo! o[o rdwpo; AYEH a) Xr4v El. (29-16)Oftoupe1 = 5,0d a = 0,60m, xaLr = 0,80m, onrire a =(o'"'9,1,1,'',1xt901!to,t]l,0n0')'=t,txr0-"r.' 2[(0,80rn)'+ (0.60m)']'''
- 13. 816 KEOAAAIO 29 IIHTTI MATNHTIKOY TIEAIOY flpdrewcr llc plrtp6ne6(o,oeoUpqro4 pero yjuvo po1'vq- rlrt'6ne6io.4rt6 ro np6p),1paaord wcripve'vepuer6do1uo'vo r[6006foxo]'o €ivoLrro6qpuotrgyjoerene6io ioo ( pe^ycr]'ri- r€Qorolj 1T. b) @€oQc6woErlv EE.Q9-16),0d?'oupevc urol.oyiooupe €x€ivoro,r l[ou Lliq.vororeiTl crxdorl 1 1 1 V'- "f' = 8 (o'+/)|,-' fia vc ?vriooupeoEnpoE.r,owuorpdgoupeT 1v eliorooqxouu- lr6voup€ oTn6dvap1J rc 6rjor4g pdi'q' ro o:ror6?'eopoeivar x = z { 3 a = 1 1 , 0 4 m . !e owdorcoqon<lro xdvrponepunouio1 pe 1,7popdgrqv qyfiiNu,ao pdrqorou nebiou dxet,€trclxrcoeeioro 1/8qg ru- prjgrou o'roxdwpo. Mnopeirevc erlpepcuc6oerecut{ tqv l,p:f xat,an6 ro 2y. 29-9; 29-9 fQqqrx{rqQdmqoliou [ayvliniod ?rebiou,{aid[]ir'ioE'iou cilovo.ruxl,wotqviou peN oreipeg. 'Orcv:r>> o,ro FdiQoxo! :rebioleiucrrtive,ol rpooelllonrci oripqorvcpero 1/xr. To)1. 29-106e(psr p€Qrl(dEyQoppdgroupoyvT1r,l(o{ns6l:ou1r-rQoord dvoru}},r- lrdpQdxo,or erirrs8ororl brdQloworon6rovdEovdrort.OrlQop[6Eroupcyvryrxodnr- 6ior-rnrgr.BdllouvrovoTcrTd,xorrlr4oledOuvorjtorgop(etor,o16rovxcvdvotou6elroti XrQr,ori,drroEoxQrp6g1{ororovpffrQ{,suorilqcppocrulti. Il.dorr tovcru^ydpeto 6e!( ooEXdQr,droLc6o1€o ovrixelQoEvo Esixvsr,rrQoExI qoQdroljQriporoE'ro6drru].{iooE rdrr brixvouvq qoQdxorvl,Qopprc6vroupoyvryxoljr€6iou.Ouypopp6grol prdTvTprori lrsbiourolJxuxl.rlro{oyoyolid€vefva!fii}r}.or,eivoldpog}i}.s!fidg}idl.ur{}.sErou [sQF xlsioljvrovcvovd, 29-10 lpoppdE polvrlnxori m6ior,r fiou blu,ouQyodwqrqjrd ro peli[q EvdEMrduiot BQdXo!.:xq DdqoQq ol[eio ToudEolo10,rE6ioBdxsrqv i6raxai€deuvoq[e q p0yvlrr i Oomiiotl 0Q6Xo0. 29-6 o NoMor, ToY AMPERE O vdpogrouAmpdrenagdleldvovevuLl.cxnx6rg6nonqoo6r,ogr,opo{qE otrro4gperc- Irl pclvrlrlxorirs6(ouxolrownq16vror. XengoBhjpcrapsoupperg[cpeldlotrBc0pori, eivcl nol,riorlvd ewol'dre91111q{o1ror v6pouotrro{cn6 drl rou vtipouBiot xor, Savart.O qdtrogror vdpourouAmpdre1lo,pcl,l"rplxdre6(oeivclcvtlloloErxe(vouror vtipouror:Gauss'yr.o1)'exrpmdne6io,rou p€}.€nioqp0oroKep.23.Ei6cpeexeidrr.cmo xovvdporouGauss0op:roporjoopevonQoobroQaoorpero ll,exrpr.xtlnebiaror.rrpodp- 1ol,ro.roruixorovopdEqoqric'rvpe^ydl1gouppetp(oE,{ va xa0op[ooupen1popq(tcorr xorovopc6vgopr(trrvrou npoxa),ofrrou,prenprpdvlpopqrill.enrplxtivne6iov.Kot' ovo- l.oy(o,proporlprevc lprlorponororiperovvdporouAmpdreyrcvo uno),o1(olperc pc- yvlrlxd:rs6[a nou:rgoxc],ofvrclcnd xdnoleExcrcvopdEpeupdtrrrvpeyrillgouppe- rQidg,( vo lro0oQGoupeng rcncvopdEgeupdrovnou:rpoxc)"o{voulxexqr,pdvl;roqgri po^yvlrr,xdvne6(ov.
- 14. 29_6ONOMOETOYAMPiRT OvripoErouAmpdresrcpQdqrroloJTdro enLlcpnri].Loo],on].rjpc'.rpLarorrd ncrrip(- tog evtigrLeLorod6pdpouxaLoupBo)'(srcLpe to.*. Ilpdxetror,1lc ro i6Loei6oEolox),1gt6ForoEfiouXQIolUoJToLrjocpemovo,oLopciroudp- ^you(Keg.6)acltor llez,rpLxori8uvctpurof(Kecp.24).frc val:ro).oyioolpeo.urito o).0- xl"rjqopa,uno6ror.goriperov6gdpooemrcpoordoroLXeicdl,unolol(oupero eoore.or- zdyLvtipevoB ' dl y.ax(fit cnolle(o,zarct0go(olpero lLvdpevc.Ievrxri,ro B ci.).ri(eL ord oqtrre(ooeolpefo,lor,0o.nqdnelvalpqorponoro{pero ne6ioB noucvnmoLleioe xd0ed/,'Evcgevall,oxflrdgoupLBol,Lop6geivarro B dl,6rouB eivcl11ouvrortlocrou B noqd),},1),cnpogro dl oezdOeolprero.O zrixiognrivoorooupBotrorouol"ox),r1poipa- toglnobeLw{erdrLro o},or}.r]gopclno},oy(erctndvrorexord prjnogxieLmorl6pdpol, ploEElcbqoprjE61),o6rjrou aq1(elzcl re),er.c6veLoro(6Looqpeio, fro vc.6o{pero paolxdvdqpctol vripolrol Ampdre,OeolporipexcrncilLro pc- ptplx6 ne6ioevrigpaxqLoiel0dlpoppLouclroyo{nol 6lo.qq6erctLondpe{pc1.Ei8cpe oroE6.29-36rr,ro pdrgoroune6foloeordrrroorlr cntirovc1trt16eivcr o - l o l "- 2nr ncLtitt oLpatlvqrr,zdgduvcpLxdElpoppd<eivorr.uix),olperc xdwgcrol< rdvo orovo.ytr.r- 1ti,Av rtigorpero errrcpni).Loo),onLrjgr.oporou,Bnarriprjz,ogxixLoupecxrfvar (pLo lpcgp{ rol pLayvrluxor3re6[ou),ro -B sirormoe€Qd,ioopeB,oezd0eo4peiororrnf- zl.ol.To enrxo.prnjl"roo),ox),riQopi:rrou-81l autdtov bpdpLoe(r,cLcn),6qro B eli ro prj- zog14gregLcpdperagrounjtLol: To enurcp:ni),Lool,ortl.!propongorf:rreldrLeivaLcveldgqrorq<cxrirc.<rorrzix).ol lccr ioope4.,eniro qefpcro 6Le.oldpevocndr1venrcpdverc:rotogtoOereiozrlxl.og. MnopotipLee:riorlgvo.cgrdooupemo (610ofiord)'ro1lo.1La5valevr,teupdvo6gripo, 6norgaurdvror X1.29-11a.Xq 0do1rouoToLleior-rdl4 yoviaperalrjd/nclB efvcL/, o- n6tt B.dt=BdtcosO. Andro oXtjpodlorpe6rldLcosQ= r d0,6nord0titel 1 1r'tv[cperlv onoiorpo.tvrrcrto d/andq Odoqrol cyroyorl,ror r eivar1 ofidmoolror d,olrdTovo1co.1ti.Enopevtug A),),tild0 e(varon)"c6g1 ^yr-rivianol oopcfuerolonr5r1vmtLvlxrjcr6oraorlr perali clrrt- 1of rat dl lord r1 blclgcrqrjo1,6r),1pourouzi.elorori6gtipor-r,E1),c6rj22,oldre $, o,=u,,. I u"l QB.dl= 7; Qnr) | | u^t u"t In t . ), _ | !-L t-ra _ : | )a 1 n r ' 4 v t - ) - l u v 817 1o (b) 29-11 (a)To err).op"?ril,rc ol,ortr{poporooB unoloy(ercr xctd prjrogrkLorot 6p<ipounou r€QLr].€i€LTovpcriiQi,€ueriyQotrlo, QeuuqroqdQoaloyd. H lcreiouvol Tou Q€i[dro;1€ivqLrgoSxov ovcyvciml. (b) A!"rdEo 6ad[oE ol,ozirjqorolE6evnepL ,eiertov ql{rlo. (2e-18) Aurrlro cnord).eopc1rcro enrropn{}.loo}'ozirigtopa6eveloprdrorandro oXrjgo.rou bpdpourjcn6r1 06o11rolofppurogo5npogctrdv.Avro gsipcrrouorlppotogdXeLcwi Oeqcpopdondezeivlror.rofiporoE,ro o).orl.rjpotpcc ,tileLnqdorlpo.Av nfl,l o 6pri- pog6elnepLx),eielro ougpc(X1.29-11b),r6re1 o),r,zrjpercpohjrou0xardrq 6rcypcqrj ol<5nLr1gor-rrou6p6poleivalprl8dvro jd0 e(varpr166vow(2n,xatrc elLxapmj),r.oo).o- rl,rjptupapqSev(eraL. AgunoOdoorrpetc6pct6t ntEoodrepottou elriEer0riypoppoLc1,o1o(pelil,otrprj- zor.rE6la:repvo{vl1v emcpdvelcrot :regLd,eieror.anrlrov6pdpoo},oz},rjgoor1g.Too}"rtri palv4rutrinebio-Boeld0e olpLelotol 8qdpoleivctro 8r.cwuoporlxdd0qoLopcrov re- 6iovnol 6rlpLouqlodvroro16rolg e:lpLdgouEcIllodg. Enopdvtr.rE,ro enrxcpn{}.too}.o- z.irjgcopaton o),Lxorine6iorrB eilsr i,oop,tputnirc d,rytBEx6d.9porcparulvqelpdrov. fta vo op(olpe rc ngriorlpatov peupcircovlpeLcldpcmedvcvevro(ozovrivo.AEuno- 0fooupre6n dXere{611en dleLrr1cpogrio),onlrjqoolgxorcipr]xoErol 6gripol.llgooo-
- 15. 818 KEOA.,I.AIO29 NHTEE MAINHTIKOY NEAIOY voxo),iorero 6d?rrll,arou 8tiroi ocExeplorjdrot c6meva 8eilvorJvrrQoErl cpopdo1,o- xl,.rjproorlg:rol enlldlcre. O awiXsLqdgocgttite op(et q 0enr.njcpopti1lc tc perigara. 'Ooo prtlpcno flolv cu{ r4 cpopcieivcr 0enxd tioc dXowl1v avr[0eri1cpopdefvalap- v4txci. 'Evcg dtrtroErp6noE^4cvc :roipe ro [6Lonptllpo e(r,aLo e!{g: Kotrcilre r4v e:rt- cpciverczcl en 'd[te 14cpoqdo]'or],{pcoolEovri0ero orlv xivloq rov 6etrrc6vrou .oo)'o- 1rori. 'Ooa Beriparo6tcnepvotivt4v entcpcivelctpexore 0uvotlnpogeorigeivoL0erLtd,d- ou c:ro;rcxpLivotrorulo roLiEtrvrucpvqrrzu. Av o 6pcipogo)'or).rjptoo4E3svrtprptiil'el rdnoro orryxex.oLp6vogeupcrogopoa- yto.7d,ro enrxcpnii,lool.ox),rjprr;potol ne6iol B 11.'cutdv rov ctltold eivcr 916dvenetbri r1ouvoLLmjlarvfcoriQrDorlEvordqv o]"oz]'rjgoorleivarp16dv,avrilLa 22. O),olot ct'1c'r- .7oIrou 6evneplr],.eiovrsron6'rovoryrezpLpdvo6pdpopnopsivct6Xolvpr1pl6evtnrj orrv€rorpopdoro fisbioB oezd0e ol[sio dpog,10rnrxapn "Loo7or").tjpapLarcovre6(c'rv rougrord prjxogtol xlaroroi 6pdpol eivor,p16dv. Xlpnepaopcrnrd,m4 .TevLnd'reqr1reqinrolol cpzei vc cvtLxarom{ootpe to / qg E!. (29-18)pe1.,,.,,to cl.yepputdclOqoropnci),ovriov.oalpdrllvnorsittpu).aowaL curoto't 6pdpoo),oz),riparorl_<XplorpLonor,ivtcE1lc rov unoLo.Tropdrol aOpoiopcrogrov )ttrvovo npoo{gcornoulreqryQdqrlx€rT[oirdvtD.H levLxtjpogcp{rol vtipourou Ampire trvcr (291e) Anobeilape q o1dor1curri privo1tc qv er6rxrj:reg(:rroiotlfis6iov :ror 6lprorQ- i,orlwcLar6 peputoigpeyd).oUpjzotlg,euoflqcppouE,nopdl'lll'olg nlirtlotiE. OptoE,1 EE.(29-19)toyjrt yw c,,noro6flnoreo1{pc cltoloi rj 6pdpot'o}'oz}'tjgtioqE.H levrz{ c- nci6erlr1cxol.orOefl1v ibra roqe(c dnLlgcurrj itto rcivurUtivonou I Yt(,lpsrQioY[Yslor nlo ro?'inl.ozr1. Orov rolier qB . (Ll= 0, ourd dei,olpo(:veLc'tayxcta^t"x(t6rt"B = 0 o€ dlc ra ol- peic xutd prjzoErou 6gdpou'mrlci xct ptlvoorlpLciveLcirtro o).rzdgeipc nor 8rcnegvtl onorc0{nort trrcptivelrrnouneplxieietcr onrjrov 6gdpoo}'ox}'rjpololgeivorprlbdv. 'Etor dntogbLatrrncir0rlxe,o vcigogrol Ampdre LoXfetpdvo1ra mo0egd pe{pctc xar.TropalvqrLrd rEbic norr6evpetoprll'lovrorperov 1qdvo.Ito 86. 29-9 0c 8orlperr1 lerixelorj rol xct 1lrrre6ic rou percpclLl,ovrarperov lgcivo. {o.n, =u,,",,. 2{+-:7 E ,.1!'.,!.Pirl dlrj- E :, T il .' -{ ]'riii: l-, i'l ii O v6LroErotrAmpdreeivcllprjorpoEdroreprogoripevu erpera)'),eldpcoteq ouprpe- 'rpiarol rgophjpctogmovlrotroyropdror enLrcpn{ltolo)'or}'rlpc6pctogtol B.Ano- ),ol0ot1vpepLrdncgnbeiy1rurc.AqoIper"c,r0eidrLq otqcr11,tx(e;ri)"uo1Erpopi.lptdrov notrolvrmdrore6t6ei:vnLeueldEcwtitroylue(vr1ErouE6.23-31rctrE€qoQtroytqTou vripoutol GaussEivclxc),tjvc encvc)'tipsresztivrl11otqcqllxrj r6pc nnlttt ourlz.oi- veretLg6io pe0d6olg. 'l'{-l i' r, ir ili (-}Y ITPATHIIKH ETIIAYEHE IIPOBAHMATON O vdpog tou AmpBre 1.To fiQc6xoftipq €ilvarva enrl,6leterov 6p<ipoo}'oxl,tjgr- orlgnou0o lg4or,porol{oerepetov vrjpoto! Ampere.Av 0dlerelo trnol,o'yioereTolroyvlrr,]idri€6fooerdtror,oou' prerpqrdvoorlpeio,o SpcipoE0orpdrel vcrtl€evd016cur6. 2. O oqcipogo?.orc1'rjpcoo4E6evlpeltilerouvc tou,(etor,pe rdrioroeuorr66e[o.:!aio('q, €ivorprq,{(Ieoedy€(t)perQF lri xogrd},l progeivc 6r.cttgdlertov lev6 1c6po{ r<cinolo o'repecioc6pc,rilct tc 6do. 3. o opdpog oLorl.{poolg ripdnrI vo €ivcr o,elae'86.oultpE- xQLx6g6a$ q x(J9totd 6!vor<j rov r-rnol,o'yloprirou o),o- r)"IQ6prdlog.Av ro [6r.oro rpdBl.lpo loporc,lp(etor ond nu)"rv6prrriorpperpio, o 6p<ipogol'ottrtipoolE efor ouvi- eolEx{r},oE pe ro rdwpo rol ncivcootov tilovtr rou xll(v- 6gou. 4. Av ro B eedfirerol mlv ?tcpr[{]"I olot].{p(l)olg xo! Xd- porc,qgilercu cnti ro f6r,opiiQo B o€ rld0€ oqpeio, rdre ro
- 16. €m'.qpntil,lool,oxliQ(opq€ivql aqop€B erf ro plirogxlg 6ua6poprjE. 5.Av ro B €i1,c&}ido€roorov6p6pooexdo€olp€io,osdl"o tou ro UixoEri oerprjpoaurori.I cvrrmorxrlouvrrogoeci oto o)"otl"rjpcopcreivolpq6rvr,xrj. 6. To B roo ol.oxl.qpc6poroEf -a. d/ <rvrr,orotletnov,ote 29_7 EOAPMOTETTOYNOMOYTOYAMPIiRE 819 o'cooAm6r,t6io oe*i0e olpeio tou 6p6poo.f€v[]id, ro n€- 6io ur,rci6I$rouQyarrcrrcv peperqno Qr0uqrs '[ou,rrQr- ll.eiovror, rrn<irov Spdpo rior Evp6per,on<ipeiipora dlro n- tr6 dlrdv. Axd[I ]rcr cv to o],rld neprx].er,6pevoperitrroei- t'at p46iv,ro ntdo ora 6rdgoeq oI[€iG rou 6p6pol 6ev lgelcilerat vo eivoLprl6dv.Er€fvo no! eivor lqidv oe orrnj qv :tepirrtoo4 eivol ro $ B . d/. To :rebioarri eu0rjyqdp.poo?o')dp€yriluouprixoug O TQdrxoExlol cptdoopemovvtiprorouAmpdrerrroE6.29-6, pq( €rr['[e6r[€Lvc cvl.oxQdq,oupEToxlQ6p],1polal vo rov lploLporoujooupLe1Lcvc $goripero ne6io evdseuOiyQa[- pou oyc,rlorlpeyci),ouprjrouE,61),c6rjr4v EE. (29-9). H olppetpio rol nqropLrjputoqeirr,$til,),er"va enrl,dlolpe cog 6ptipo oi.oxl"rjpcoolgxixi"o arrivtrg r, xde€ro mov oyc,ly6 pero rdwErorou nrivo or clrrTdv.To B egdnretaLorov x{- r),o oexcloeoqpeio,r.lcrrI EE.(29 19)yfvercr I I B l l - 2 n B = u " l . H EE.(29-9) €i1/orrcirponpogcvrjE. To ae0io prdooor xul"rvbqlxri ayroy<ipeyrilou prixoug lLo vn lno)"olioorrps 10 [cl1v!rr].idrre6iooro eooreplxtl xuLlv6plzorlcycolorjor<lir,c[ER o€qfidorooqr crd rov dlo- vd ro!, drcDs6eaxvetrc 2y.29-12, ert),d1oupeoE 6Qd[oo- l.onLrjpcrroqEoroLov6rinorenrlz),ocrriv(rE r. A6ycDo!p[E- rpr('(.roB fXfl Toi6lo UrrQoo€zLi0€ol[tio ourou(ouxi- %]"orJric! €qdrr€ror oe o!t<iv.Apn ro entn<rpmjLr,ool,ozl,rj- pogn eirr (,aopnB(2rr). fLd va uroloyfqo![e ro Q€tpc 1.n.'nor neplx),eiercIcrld roa 6pdpo,noporrlgoripecirrr1 nuzv<it4rcpefpcroE"I(Q€fpodvcipovti6c enrpciver,ag)ei- vatJ = IltrR', €ropdvoE1.".r= tQrr2)= Ir2lR2.-l ,txd,o vdpoErou AmpCre6a!rr !,,1r1 L"rrB= f , it .:l I. .r-Ii .., , 1;,i t ii .,- 2,:-11'r--9 I . - - "ffi 111, tr .i, ! E ! | ! !, 2g-4)t !,1 t B =; F (.2e-20) flproorlrr orr1rc r'= R.b4).cbrj:rdvworlv rntgcivrrLl rolJolo)r/otj,4 El. (29-9) (nou cnobeipqxe 1rr r > R) noL n Eq. (29-20)(nouono6ei101ze1urr < R) <rupninrolv.To X1.29 13oeipeLq 1.oc9r"xr]ncpdorcrolxo! B oov ouvde- rrlol rou r, rdoo oro eooreplxtitioo rcll mo €Eor€Qlx6rorJ a1co1od. B . l 2"R T-- 2n R' J,. 29-12 To Q€i$aFdoocr,-rdr1vzcirlLq enrcpciveureivcL(rrlfi:)I. fic vcrrno),oyioou[€To[oyvlxritdlirbio mo o!l€io P,eqoppriiouperov vd$oxo! AmpdremornrilLonot reprzLeierqv xdit)atvl€rtqidv€ro. 29-13 To pfrporou pnTvlTutor.iirebaoumo €o!J1cgu16nauro €qorEQrzdErd!FoxQrof, rueJlQcluBo!zri,Lv6przorioyolori c,rxavaE R rorr SrtrppdercrLcrndpeipcr1. To ne6io oe 6vc oorl"qvoerbiE nryr(o 'E'trr od"nvoetlg qnotel.eirc! ond prn <ruppdrLv4ei"r,roe16{neqr,d}"rlr1yripo ofid xi}'Lv6Qo,ouv{0cog)rux),Lr{E6ro.ropL{E.Kcrvovr,xdl- rciplouv ezcrovrti6egcoE1ll,rti.6egoneipeg,trioo ttovtri 4 frs [r€rnv d]"],1tiore vo prrope(1 xoe€prcivo 0€oQq0ei oX€6dvorrvrdl.€roExrlr),oE.:l1vci I leprd)'rf1 yfvetnr oe mp6potct.fro elxo).fq,xo:I. 29-14(osl..820)6eilver dvo oco),lvoetOdEpel,i1eE[6vo orrsfQ€E. -O],€c Sroppdowcrolci to i6Loperip<r1,zol ro ()),[?16r€6fo B o€ xt10eo4peioeivcr, ro 6!cv1'o!rcr!rdd0Qolopqr.ov[s6i0]vJrou6lpr,ouplorivrc{ ((nd1!<er(rIdQouEofl€aOrg.To oxiLro6eilveL6uvaplzdg lgcrjgdg oro enine6ary wl xz. An6 't emopeqeigurol.oi,L- olroi! dler FQ€0€idrr os dvc mrxvtiotol,rlvoet6dgp,eycil.ou prjxoug,trrci rr,g6lvoLrLrrdEyQo1rIdErol 6rcrirepvoivpr<r x€vrQlrlixo! 6rorol,rlj,pcivovol plodgeEdqlowcrtclci rn cr- vor1rdrou tixpct,evcior di"i"egprodg "6tcge{1olv" orti ra r).ciyrc,ovdpeooorr<irLEoreipeE. Av ro prjrog ror-roo)"qvoetborjgei:vorp€./cil"oo€ of- yzQrol F€rI olcipetpor4g 6rcrop{g rol, ro eoa)x€e%'nE- bio novt<imo rdvrpro€ivqr ox€6dyopol,evdgoe ti),1qv d- zrcol rq_<dloropujErcrrrroQdl"l,l),omov cifovc, evciro e- l<orcExtinebbtovrd mo zdvrpoeivcrno7,!pr)iQd.(|IaQc- nl0lm€ orroro >X.2q l4 or buvuprxd<ygcru[i( xovrci(no lidvrQo€ivor xord rpoodyyroll napcil,Lrl),egrcrr,opor,rlpop- 9(I %(I1cv€pIpeveE.) MroQorip€vo lprlor,pLonorrjoo!Fsxov ldpo rorJ
- 17. 820 KEOAAAIO 29 IIHTEE MATNHTIKOY NEAIOY 29-14 OLlgappdgrol trlc.1vrylxoire6iouroodqplooplo{rrolard xoQ€{fqo€dvqoco}.rlvo€1668.flc eljrQfvelc,[6vo].iyEEo,reiQe! 9(rwowormooll[c. Ampereyrq va pporigero rEbiooro xr'vrQoxor xowo or ourd. QE6Q6poo),olihiQooIg e:nl'dyoupero oQooy6vro abcd'cou21q.29-15.H xtj'Ee6.ab piliolE , sivor rroQdLLl- 11n.oogtov dlovo tor ool,1voel6oriE.Or nLerprdgbcxor da 0€oQoilro[ 6Tr€ivor,pe^y<i]"ougrircorE,on6rs rl xr]"€!Qcicd ppioxeror poxplri o.n6to ool"1voel6dg,xcl to r.E|daxqxd 1ui?ioEcrrxrig€ivc! cp€lqr6o. Ady(ooul.rp€rQiqE,ro re6io B ?rord[iroE rIE r[],erQdE a6 e(varrapdl.),1},ooe our{ xqr oro0rQ6,6q}.o6rjyra r1v nleup<ia6 lo$el B =Bnar, I lB dt= BL. J o€€oocpooooooo 29-15 EqoQpollirou!dpo! lou AmpdreyLaiov ro0oQro$6iou ploylr1rlxo{r€6io! xowri oro zdwpo or.oLqvoel6orlEpeyril,or p{noug xcr lruxvrjErepf l,(r19. r APAEtl lA 29-lO Kcrd p{xog rorv rlerpfv bc xat da, wfier, B = 0 ener,6riro fiebio eivor.r.idosrooe oudE. Kcrri prjr,togqg n}eupdgcd B = 0 eneroriI = 0. Enopdvrogro olrodrrig<opc$I . d/ xa- rd p{xog proEn}'{pouErleum{E 6rc6popnigrcna}'{yer vcr eivnuioo peBl. 'Eo[o drr I r[eQrd],r[1nepr6leuz antipegaud.povd.6a pijxoug. O a.woLux6gapl0p6Eonel.oc6voe p{rog I eivoL rdre rl. Kq0rprd ar[6arrdg x[€Qvdpdoo0,:16ro oQ0ol,61,Lo abcdp.iagop6.xat 6LoQQ6ersr0J[6Q€{po1,drlo! 1 efvorro Q€dpoctlrEofteiQeE.Aqc ro oi,r,xdperipanor neqrx),eie,cL cnd to op0oyc6vloeivor 1"n"'= rLI, And rov v<iporol Ampdredxoup€, 67 = ponLl, B = ponl (yuaaot|qvoer6dE). /r0_)1 Aeoopdvou<ifl4 rl'elpd ab 6evou[riffisr qvqyxomrxd [s tov rilovo rou oo|lvoer6orjg,o nogondvrouo),oyLop6gn- no6elri,r,feu<irLro ne6io o'roxdvrpo €fvo[ oloysvdg oe d].rl t1v 6zrao1r4Ebroroprjg. f[c{ oqL[Eaardvo o'rovdlovo, ro re6io roiQvsI rI [e- lcAdrep( rou tlp( oro zdwqo rol or.rl),1voer6or1Exor perc3- verq[ ].!owdmo dxQo.flo oco].1voel6rj peyt 'ou p{xouEoe o{ylaQrorlpsrI brdperQdroug,ro pd,Erorou ne6iouotc ri- 1.tQo€ivol oxQ[p6Eioo pero ploti exeivoumo rdl"rgo.fur rivo.oorl"1voeuOdgplxgor!prjnougrcl pelcilqg 6lapdrpol 1 filo fldv0roxdol €ivar neQLoo6reQor[o].{r},o1{n.To >X. 29-166€ixv€rrI ./Qserxl noQdc[qorlrou B ouvoqrjoertou .rrdvo orov tilova ev6gorol,lvoeL6orlgpLrQo{[ixouE. F-44______? F V'tVV 2a -4a 1a -2a -a O a 2a 3a 4a 29-16 To pdtporou polvl(ro{ fl€8iourdlo oeoqpeiarorrdlovcr €ldEool.lroE[60{Erro!ro prjrogrou eivot4a,6q},c6!terportrriolo q( u)rrivoErouc. H lrFrirou FcrQouoio airQoFrvar:repr;rour1urd €rEfalEororid,"tQo.(trrlxgive,epero IX. 29-9lou 6eipelro ae6io on<iN lruxl,lxd_<oneipeg). To reEfo oe dvo 8oxtolroer6dE oorl'qvoer.66g(aqvio) 'fo >X.29-17a |eiryet €,taaxru)"toetddEot ,4uoe66g(nr1- vio o€ oxlpo tor,i"ofQo.E)6110!ro o{Qpc r1g repLd}"ul4g 6roqqdrrorcnd qrUprcI.:rnv nQqypqtxdrlrq.or oJr€rQ€E eivornoi,{ rol'r<i petcrldrolg. Ol pcrfpegzcpnd},eEoro 21. 29-17b rapr,ordvolv roug 6gril.lougotroxlfproolg nou 0c XQ€Lqorotpeorlv €poQpo./irou 16po! rou Ampdre.AE ndpoupenpciro.11 6ro6poprj1. 'Eoxo drr ro nlvio 61pr- oljeyEirdloro re6io oq, rlsQroxlid!ri. Ariycooupperpiog r6Te,0o 'Ipti'I€1,vo €fuoleEamdpevoae 6lcrrcroqpeiqrou 6pripou,xor ro EB dl 0q etctliqo pero llvdtrlevorot I e- ni qv neqlqdper,o/ = 2zr r4g Dlcrbpoprig. 'Opcug, ro olrxri qetpo nouneEruxl.eietcucnrj rov 6p<jpoe(vcrupq66v,xl eno- pdvtoEoripgrovo;retov vdpotou Ampdrero ne6ioB ng6ner vo tivcr pq6fv rawoU onlv reptopj o.ur{. Ewel.6g cvril,o1o,cv ro rqvio 6qprougl,e(xdroro re- 6io orc orlper'arou 6pcipou3.0c lpdrer enio4;vo eivotr- qcnrdpevorou Opdpouoe d),crou ra o4peio.Kd0e Q€6[q <ipcog0Lcnepvdrqv neglrtreldpevl 016 rov 6OdFo€r[red- yEL(r61iocpoQfeo€ q.vrao€r€EroreuEitae6. Apu.r,oo)"md perjpo.,nou nepuxl,eieralqr6 Tov6Q6poo.rtt5eivo.r"p16dv, ?r,rerop6voEB = 0 o€ 6l,0rorl rq olpeio..)upndgcopc: ?o ne6[oroo 6axntAne6oig oa)"qtoet6oiE(ittvlou) iteQrcQi- lerat ano .tLoztxd.orouyt6porou repm).eiouvot orrtiQ€E. Mropo{pe vcr6odgero 6ari,Tu},loeu6dgr4vio oov dvooro},1- voeLOdE[€ydlo! prir.lougrorr dx€rxqpq0€i perfroro rQ6no c6o'revc o14pcr(er rixl,o. Tdl,oE,osoQoiperov 6Q6po2, d,o?rlirLodxxfvcEr. H oupperpicrenlBdl,l,e[]icLfici],[oro B vq scpcinrerolrol 6pd- pouxor ro$ 'R.d/ 6ivet2nrB.H xdBEonEipcr4Erepr"d),rl1E
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- 20. 29-8 MATNHTIKA YAIKA IlcqcpuyvqtropriE Xe6vcrfuopo,ol neploodrepeEonritr.g8Lriqogegpc^yvrpr,xdEgon6ELrilorrtprqoptig! onlvrclvll.exrqoviovlou dlouvouvloro.pdralpr166v.Xepeqlx6ErepunoioerEdproE,ro ri- topo6la0drelouvr,otopdqpoprlrlxrjpomiqg rdftg roupr. 'Orov dvct6tolou)'rx<jre- Oeipdoaoepra'yv1nx6ne6[o,oexci0epalvrlrlnr]ponr{ooxeirclcn6to re6[oplc qonrj notr,xmrirqvE!. (28-25),sivcr.(or1VEt = lt x B. Orpondgcurdgrefvorvvc euou1pcp,- plootrvrlg pa.lvrylxdggondgpeto ne6io,tiote vc e],clloronoleirau1 6trvop,r.nrjtolE e- vdg'yeLc,tinoEei6cpeoroE6.2&7.Xq Odoqctlrj o ngoocvcrol.top6Erov plnpoolorl- u6v Bgdlovqeiparogeivcr.rdrouogc6orero 8qpr,olqloripevoold ornodEre0[ovo ezt- tpomi9eratmo eltmeplrtiegappo!6pevopclvlruxdne6io. To nptioOerone6ioI nou61ploupye(rc.ucn6 cutoriEtotE pr.tpootorlxotigppti- lorEqeripcrognqonr.irrel6rr,eivor.cvri)'oyoqg oltxtjgpclvwr,trjgqonriEp,",ovtipovdOa 6pou Zoro ul,r,xd.T1 8rowopotunrjcr-rniloodnpc ovoptiloupepayrTitr,o4tol rLr"xo{, xalq ouppolGorpeu.eM: 823 To enlnl6ovpclvrplxd :rs6[onor nqoxak(tcl orri 14pcyn{noqrouu}.lro{ ano6ewWe- ro.rdrr g[vc[(oop"epoM,6notpotttcl 1 i6r.oorcOeprirou eppcvfletcloTorgvdttouE Biofsavart,xo.[Ampdre.Av dvar.rl,r.ndneprprillelrele(ogdvcvo1o1ti,to oh.xrjpa1v1- tt,xr5ne6(oB pdocorou),r.trjeivor. B = Bo+ttoM. (29J7) drou-Boe[vc.r,ro re6[oro oqel].dpevooqv xarovoprjrov elaneqlxrivgei.rpriro.rv. 'Eva trl.lx6nor.roupregr,cpdqercuoripeorvdl.r€rylvrrdQdJrdvat:rtglygcg{ tr6ptt5n e(vcr.ragapalv4turri.To anordl'sopaeirordn ro pclvrplxrine6ioot xrioeolpe(oevdE rdrolol ullxorieirraraufup6voxcrd rovncqd'yowaK. (ri4,),oeoulttquolpt to re6(o notr0cun{q1eexefcv o cll^yriEpplonrirovorotev6.H oro.OeqdK.ovopd(ercroletwri Draregatdrqtarouu),lxori,rcu1 tr.prjqE Ouaqdqeucn6ul,unrioethx6'1lc ouvrjOlro- gapaywplrdoreqedrjulpd rLr.xd,osOegpoxgaoia6orpcr(ou,ol loponqpr.onxdEtupdg ror K. eivuran61,00001og1,003. Ol,egor,e[lo6oelgoeourrito reqd].clonol ouv8douvpclvqntd fieOfou,enEnl- 16Erougpnopouvva npoocppoo0otivoTqvneqinroolnouo clco'ytiEreglpriLLetclcntl nopapcpryntd u),r,x6,cpxe(vc cvrrxcrconiooupencr.'rodro4opero K, 40.Toltv6pevo ffiJrdouvi0ogoup0ol.(ero,lp.eptol ovopdlercr,Olanegatritr;tarouul,lxor.l: tt = K. Po. (2e-28) O ouppolrcprigonl o{6oqcunj propeirqclporltti vc o61^yrjoeuoenagcvo{oe4enelbrj 61ouperj6qlgrlolpono(oelro4 liorTrdfll pdyvrFn{qon{.Efvclo{vq0eEvoXglorpo- nolefrclto 4 xcl llc rq 6rionoorinlreg,1r.'or-rtdlpeuilercLnpoooltiolo e!{EtitcvBld- nerero4, va pepcu6veoreandrc ouvqqcldpevoovnprinelrcl1tcilcnepcrciqrcrj1lc pdTvnrrxliQon{. Toroo6 ncrrizoonofo11olenxrjblcnegor6qroureppa[veuq povri8covoprile- rarpalvrp*ri enrEextwdrrltc,xo,loupBo),(etoupeX,: x. =(. - 1. (29:29) Kor,or66onoodrqreE,I(xclX., elvcuc8urlotctap.e^yd0q.Or,rlp6Erou1. yla 6rdgogcr.r- l',rntl6(vowa.r,orovIlfuaxa 29-1. lqv rdoqrrovcropuxc6vpayqrmr6vponcbvvc rqoocvctotr(owur.nqogro po1v1- rr,nrire6[o(6nol4 8uva{uxrjrougevdpleloe}.alLoronole[tcl)cvrurfoercl1rulafc 0egpl- xrjrlvloq, nor reiveuvc tcrovdperrouEnpoocvaro]'lopotjErougxordruxdiotQdfio.H paplrlxrj enl6exrundqrael.crr6verolpearillol t1g0egpongaoicE.Xenol,l6gnegr,- rnc6oe4 eivcr.cl'norpdgrrrEovrfl,,oy1qg c:rriLulg0eqpoxqaoiogZ,xal1 payfi1ta1M pnoqeivolqc,qre(peq poQcptl n"-.! "'- - T' H oldoq artrj o,to1t&l*.atN6pogtoo Curie,cLn6to 6tto;rcrou PierreCurie(KtooQ[, 1859-1906)rourqvovdxdLuQ€.H oro0sQdCovoy(lnat ma9tpriCurfexol6rcpdperc- r<iul.rxrioetrl.Drd. u.-. M=i. l)o_)A (2e-30) MNAKA' 29-T Ma1,vrp&ri €nr0€ritlrdtlta yrc buigoqo rogog.ol.vr;tutri *or bropoyvqtuad ulutd orouE20'C Ylurri X.=I(.-l
- 21. 824 KEOAAAIO 29 IIHTEE MATNHTIKOY IIEAIOY r IIAPA^EII'M ^ 29-II Xqv E[. (29-27),6eileredl. oul.rovd6egsivoroupprpqordE. AYIH H pap{u,ol M elvcr papqux{ pon{ cvri povriOo 61rou. H povriboqg proyrlruxfEpornjgeivor qedpaeni e- nugciveuc(A . m2),enopdv<ogq povclOarqg prcprjruoqgeG voL(A . m2)/m3= A,/m.)ro E6.29-1oiveror6fl orpovd6eg yrorol0 ril,cuT . nL/A.Apo1 povdocroupoMeivar (r ' m/A)(AJm)= T, 61irc6rji6ucperq povriOcryrcrro 8. I IIAPAAEITMA 29_12 To povolelOuorou olrritou (NO) e(vourogopor7vrltlxdu].u- xd rou onoiou rd0e pdpr,o6ra0drel poplruxrj pomj p(og pdyall6vnE ro! Bohr. 'Otav ro p6glo ppioxercnp6oc oe payvqruadr€6io 8 = 1,5T, ouylcQav€r€Trlv evdp^yexrcr)')'q- )'eni6gcro4Epercld pcyrlfl1i1(E pomig xor ne6iou perrl p6- ol xrv1rLlii €vdQy€rqrou FoQio!).dy(')[€rqgoprxrfEl(v4- oqgoe 0eqporpcoicr300K. AYEH >ro E6. 28-7 cro6efinpe 6tl 1 Ouvcrprx{evdpleua pucEpcprpr.xrigponfg pdocoene6ioB efuctrU = -p ,B = -pB cos0. (Aurd ro I s[vor paTqfl1ir1 eomj.) H p{r.or'4 <r- fidLljrrl rqrri rrlE €vdqleucgor4v reqirtcuol ouni, rreayFq- lonor€(rcl, dlqv cosd = :1 ?iqr€ildr IJ^* = pr. B = (9,27x 10'4J/TX1,5T) = 1,4x 10-uJ = 8,7x 1fs eV. H pdonliwlpxi evdqrlercK ).610lpercaogrmjgxiqoqg 6i- vercrlqrd ro 0eoiqqpar.ooxcrcvopli6xIE tvdQytlaE (E0. 16-4): g = )tcr= 3(1,38x 1o-ryKx3ooK) = 6,2x 10-2'J = 0,039eV. >rn o€QlrorQao(aIov 300K I svdQysuorlE poy..rFu1iiEal.- i'11'en[6qoo4ge(vcuro]:ti pmq6zep4 on6 qv xr.rrpuxrlevdq- lera 7.dyodraxIls 1(ivnolg,&r€ropdvoEo.vdpdv€ro!cv€- rofoOrpq euftryqdppro4. AurdE €(varo ]rtiyognou or rcgc- pcprprxdg eru0exrlr<irrpegong ouv{0eug0epporqo,o(eg eivcuxcrd xcv6vc nol,rl plxp6g. I (c)Ioppdru6io + 29-19 TooIdolo0urdnQodQIflq! 0Jt6p€y€0uFdvleoroyQqqia r4nlorcl-Llnoovnel'(ol,xcr,6ei;gvel perd[o nlv xo,edOwo1trlE pawifl,olE[doaort4pqvrfrrds reQlqldE. 'Orov €qaQpdEeroudvq eloxeputr5poyvrpwr5re6io,ol fi€oloxdEnouq polllinoi rouEeircr, rcgrilJ.ql,lorom6(oreivouvvo livou! l.re/q),{roQ€8. ArcpcyvqtropdE Xerdnolo r-rl,u,r,riq oi'llrl poprpuuj Qorni1td0€ordtrourou nQoltol€itorard rouEftopr- rodgBQdXouEQrdporo5,€fvdrtr16&sgdoov6evur[dQ1orvrEffieQr]tdpoyvrlrrlidn€6[o. A*dpqrol ol.rrcitc u?,,[r(ddtiosepgw(olv [d1vrpr.]idEr6dqreE,yrdr(dvorEoreprr6 paw!1r&6fieofoUJroQs(rc rQononorioerqv x(rlol xor n].€r(TQov(ovpdocorc ritopa' dror8lpLouqloriwarrQ6oesrorpQd?(orQsdpaxoskar rnaydpsvoEpayqxr?{6EQondE,os nl{Qn dv&ororx(apefi. efi(ll6pe1vo,rxro,zd 6(no},arou €q€rdoapeoroE6.25-5.tqv nEQ(rfiooldulri,ro npdooerone6[ocrncivrov pqdIov QsfpffioE61elrdwme xaredouv- o dwlquq an6''jxEiqtol eloteqlxoi ne6[or.r.(O],t5^yog1l' clrd €fvoro vdpoErrls €rrd- yolriErouFaraday,no! 0apsiu€riool)pso-roKeg.30.To enoldpevoQelipdi€(verfidfio- re!q eEor6ereQ0iverqpsrdpoiiro4jneaionrouro nporril,eoe.) TdtorouiulxtiovopdlovrclErcpaprprxd.H enlbennxtinlrdrougr[va[ fidfims op- vlxrffi (pi!.llfvffio 29-1)mr 1 o;ernr{ roog6Lcneqardqrc e}.apEigprxprhqq r1E1to- vd6og,ouv{Oorgc:r60,99990trrg0,99999rsplnou,Trdo"rrQ€d]rdr,qpd. Ol 6r,cpc1vr1rr.xdg erl6eulxdnpeEe[vcr,osnokj rd{ rrQood1ryr,oq,cvelrip,nprEqE OeqpoxqcolcE. ErbqgopapqtroptiE Y:tdq1el plc rpiq mqlopic r.rLr,xr6v,nol ovopdEovidr.olhlQopayvqrurri.2e orndrc l- lur.nd,ol cLlqluun8grioelgpetalri novoropruxrivpcprpr,ncivpontrl,,eir,or,rrioorcryugdEri- oreprogotivva euOulpcpp(ol'rauperclrilolrEoe10lt1165evciopegrou ovoprilol,rcupa. T1qflxdgn€Qro?(dg,ordpq{ar IoQiSrnvrroQouofosEmeQrrc6vre6(rrw.To)1. 29-196e[- IverdvarraQd6€ry.1oqE 6opiExovpoyvrllui6vrr0QroIc6v.MdocoexdoerdroLoreprc- Xli,ortor.oonxddL€Eorl.rdyvp)i6EQondEe[vcr.rcqri]"],q].eE. XoQ(Sr,avdvo.eEo[epLxdrs6[o,oLpcyvqrloelgnov:reqLolriv61or.rvrulc(o rgooc- vcroLuopd. 'Orcv eqaQpd!€xarrdroro fie8forefvouvvc nqoocvcro]'Lororivncqd].J"q].c psauxd.&r[olE, xd6gn pera$j pcyvrplrriv raglop6v prrcxlvodwcl oLneqLol6Eercf- veEror,r1 pcyvrinorirouEouppaivelva e(vclnagri)'?uql1oro ne6(opeyai*rivouv,ev6ol undl,outeEoupqrxvrivowcr..Enelbri1 ol,lrrlpoyvrltu*riqorniproEreQro1liEUJToQe[vo ei- vcl nol),dE1uh,ri6egpclvltdveEtou Bohr,or.QordgorQdli1gnoure[volvvc rr,EerOt.r- (a) Xoe(ErE6io (b) Ao0wd< n€6fo +
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- 25. 828 KEOAAAIO 29 IIHTEI MAINIITIKOY IIEAIOY prjxogqg negr.pdpengroutttx'Lrn:2nr,xorefitlb{ iD= ic ngoxfnrer,rur<irovvtiporouAmpdre,drr 6ooqopr(ercl o mzvtr.n{E, f ' = lln1tr, U., Ip - t 9 1 ; " - )o P'''' /to_tK To unor6?"eopaarrri npopl.6ner,&r mo r,iqo percfi{rov orluoprivro -Beivcr,pr16dvrd- vr,rorovdlovc nc.rcl[dver lpcpprrri peqv nn6orcoqcrd rovti(ovc.llcqdpologuno- lolropdgOeilver<irttfarcprudrcr ytitpouperclrlrox onl"loptiv,ro B efvurereivonou 0c [o1:eavol a1o'yoirjrcvouvele[gxor6evrnrjplcvxa06].or-rorllopof. Av xrivoupepn p&p1oq paytryuxorine8fotroec.urjrqvnegr.opj,0c pgo{pedrl 6- vroEr-rrdplerrs6(oxm drl cxolouOsio.xqlp6gr1vE!. (29-36).Awd enclrlOerjelo:rer- Oe(cgrovgdlorol qeiipcroEpercr6nr,oqgr.oEnrlyiEpc^yql.xorjnebiou. 'Eror rL6ov.live- rcr.cblcptploBrjqrocnobexrdrfuro peipapsrcr6nlolgaroreleIpuc0epetrrc601olr6q- ra n1g@o1Exar6eve[vcrxo0d].otr0eoqlrr,xdrd1vco1.ro.H cvaxriluryqrol Maxwellrj- ravnpoirirrprcEordvrcgetrquiaE.Ilgrilpcn, rinoE0aborjpscqldrepo,ro peripcperotri- nuoqErjrcvo xqfxoEnol 6].suneoqv a]rtrof8or1gllexrpopcyvTlrlfiiEo€oQ(os,rou 064- rploerov Marwellno,r,ril)"o!goqv xorcvdlol rc'rvll.errpopalvllTrxc6vrupdfiov. Ounolol.olrrignor o6ripoeorqvE!. (29-36)noporord[eLpeltll.qopor,ciqrcpLee- xefvorol Ilago6.29-8(E6.29-7),drouXQ1orporrouioopetovvr5potol Ampdre^yLcvc ppo{pero pclvlrlxd ne6(ooro eoorepur6ev6Erru}.rv8prxorjdyoryoripe'yd}.or-rprjxolg. Anripuatinorg pnoporipeva 8oriperov16poperclritulva^y6y,pcovon),ropurvocv tvc xl),lvbprt6u.7to1'd.Asvwdpleuxcpuittivlol npolpcrLxo!qoqtlol :rouvc.ouvlordqe{- 1.rccltoyr,pdrqrcg,urriqleutiptrrgro geripcpercrdnrqg.Aev0c dnpene,l"ondvvc er.t- nl{ooerclxcve(gdn orE!. (29-36)xcl (29-20)efvorrpd.TpottornriolpeE. Aio reLrnrioldl.ra:Ilpcfrov,1.levrxelp6v1poqqrjrotrvdpolrouAmpdre,1 E!. (29-34),naqapdveloeloyl rcl oroeooxeqLrtievdgpclvlrr,xorjtrlnorj,per1vngoii:rd- 0eo16rr,11pc^yrnirLoqefvclcvriloyl rou elrrnepr,xorire6(ounol cil.ol'rma0lororjpero po pr ro 4. Aefrepov,o vripoEtou Ampdrelofeu cxripqxtn orovxev6p6podror 6evr- ndqler,rcv6vcqe{pcc1o1lp<iqrcE.To^yelovdgcurriflel nold ooBcpegenrnrurorrg' peralrj ti),.lorv,olpcfvel rjfl rjrsvra trebia.Exal B perc$ri].].olrorperov xprivo,o],]',qtro- ouv8riowcr.Xu^yxelprpdva,6vapsrcpcl.l.6pevolLexrpr,x6re6(ooexdnor,creguofirou ytipouendslupayt'qzrzdne6[oo16lelrovr,xdEneqr,oldg,ardprlxcr.rftcvo Xuipogcutrig 6evnep .cp$dveroutefl,1 oursqeriparao'yaryrpdqtcg.A.u[oTpopa,0c6o{peoroerd- pevoxepdl.crodr,r,dvaperopcl,ldpevopctywltmdnebir l,enoupyeiaw nqyilrfl.exrpLxod ne6[ol.Oro1doe6clr6E,nou1lc nqc6qpoqri6uorun601xavoen].r{p1popqrjon6tov Maxwellro 1865,avoilorvro 8qripopa q 0etogrpr.xrjxcravrilol t1gllextgopa'yv1ru- xrjEotrr,vopol(cgxalrouqantiErogplcger.Sr,xrjEnegfurorlg owrjEn1gomlvoBo)'(oE.Oo encvdl.ootrpeoro06puaurtioroKeq.33. IYNOWH {a.ar=zn,a . To tio1vrll.xdne6ioB nor-r6qprotrqle(ralard qopnfo4 xr,vo{pevopezapiqrc o e[- v(It B=f qa4r. +1t l' i/rO-) 6rour efvalro buiwopounrito orlpelonr11ig(0dor'lrouq) ogro olpe[onoQoriQ1- o1gP,xcl i e(vor,ro povc8niobldvuol.lcnqogouri qv xareriOuvol.H aplj t1ge- ncllll.(cg l61er.dtr.:To ol,r,xdre6ioB nor.rblproupyefrarandro].].rixr.voripevcqop- Tfo€ivoLro6rowollcnx6ri0poropcttrtvne8lrovtov erupdqotrgqop,r(ov. . N6poErov Biotxol Savart:To pclvqrlx<ine6(odBnouElplougleircr,cndro oTol-
- 26. IYNOIYH 829 Xeaod,dyoyorjpoQeiipcl eivcr, an=* Idt!i- 4n 12 . Q94) To ne6[onoudr;g.loupryefrclar6 c1trryc1nenepcopdvoop{roug e(vcrro o}.ox}'{qopa aunjgqE oldoqErcrri plrog roucloyor!. . OLyQoppdEroupayr'1rwoire6(or6evreppar(olv nordoeolpeio,xcrro enlqc- veLan6oi'onhigrrrpototrB oeoroloO{norex}.e1fitjenrydvelceivo.unrfiTote pr;6dv: OllpcppdEroupclvrpLrorinedfoueivclopoclovr.no[mjr]'or,perifiovcro oippc xcr. or*creu0rivoe6rouEdivowcl an6rovxcvdvarou6elr,orjlepuori. o H 8rivcpl cl)'l]'en[6qcoqg,avri povti6oprjtor-r5,perc!6 Erioncgrilll].tov oyoyriv peldlouprjrougpr grripcrc/ ncr/'. iXetpdrgo F poII' L ZJIT (29-1,r) O oploprigrouampdrepco(ercr.oectmi q oldoq. . To powlTu{dneOlonor.r8qplorqyeitclondttttl.lxri cltfltpo Bpr51ootr[vcEa nor.r blappdercla:rriqeripcI oean6orcoq.rar6 to ndwporor xotd pixogxoudEovdxou, 4er pftQo (2e-10) To anor6l.eopccwri arorelueiro ;rc,lvplrcdovti).oyorouv6pourot Gaussxotuo61- l.6ver,6rr,6evr.rndqlowpepovtopdvolpclwlrlxo(n<i]'ol. . To pcp'rFr,n6re6(oB oecndorcoqr onrietr&ilpcppoouppcpeyil'ol prjlolg nou 6ucqg6ercr,ord qeripc1d1elpdrqo I u ^ =0 (yr.coroLo8rlroren)*Lonfrnrqtiver,a). a = ff GrutooppoorlqpcpeyilrooprinouE). t,= ## (xun).lxrigPp61oE). f n-at=u,r,"",. zlf 11- (2e-e) (zvrs) (2e-17) ft.a N pqr51ouE,1 6ngqcol cur( rolrlonl,cor,rilercueri N. Ito x6r.Tpotot.tpptllou 6- nour =0, B,=!# (mo*ivrQoNPQdrov). . O vdpoErouAmpdre)udyeltirr,ro enlxcpni),tooloxfiqopator B xal6.y(1xogxdlz xi'elorod6p6poueivol ioopepoeniro ol,r.nriqerlp,anol 8r,urepvriqv neqLrler.tiper.rl urd rovEpr5poenlgdven: (2e-1e) H 0erlrrigoprirouperiparoEog(ercl on6tovncvrjvotol OelLori1epror1. . To pawrlrrxdfi€6(ooro eocneqlxdev6Exu)'lv6qLxoticyroyoripeyilou prjxor.rgnar, cxrfvcgRnouElcgqderolondpeiipcI 61elpdrqo Q9:n) .To pawnflrd fi€6foorondwqooarl.qvoer,8origpeTi),,or.rprjtougpen olelpegcvti po- vri6c prjaouEncl peripcI e(vcr, KTPIOI OPOI B = 4onl (orollvocr,6dg). (2e-2r)
- 27. 830 KEOAAAIO 29 IIIITEI MA|NHTIKOY TIEAIOY Topclvrplnrine6(ooroeororepmd6cxml.rcer.6o{Eorll}.1voeL6oiE(n1v(ou)peN onei- pegxcLpe{pcI oecndnrcolr mrdrovdlovclrol, e(var . )rc pclvlnxd ll.Lxri,1 pclvrjrtoqroulLLxotl6lptoug1e(pr.o.rpdoOeqouverogopri oroB. fLa rogc;rclvrylxtixcl blupc1vryrxrilh.xri,orr.Eoldoetgpmralipayv4tlrfrr ;.le1e06vto 4ocvrr,xcO(orcrclcntiro p = (pn, rinol4 1 bLanepardqrorol ul.rlorj xcr l(, 1 olerutrj6r.cnegor6r1to.H pcyvrlrlxrjenlbexrrxtifllrcX. opi(ercrogX, = rK,- 1.Orpo^yvpndgenrbexnrdqregrov nagutrrclv4tLxr6vlLxrrivefvaLpLlpoiOen- kofdQr0poi€rtf sEr0r! 6LopoTvqnxtivlhxc6vefvcr,pLxgoIoqv4rLxofapL0poi.)ro o16lgopoplrlxri utrrxd,ro rK.e(valno).ripelchlteqomrd11povri6oxor 6eve(vor otoOepti.Opropdvoo16lpopayvltlzriuhxd eivaLptivlpolpclvrjreg,6llc6rj 6raq- porivq payvrjtrorjrougcx6pqxcrpetdrovpqbevlopriroueloreqlxor.lpalvltxori nr- 6[or-r. o To Qeripsperm6rlolEio).er,roug1,eiogn11j pclvqnrorire6[oucxguprnEcirrlExor ro qeipcaycopprir4rog.Op(eroronriq o1dor1 U',NI B = i; (Doxrulroer6dEoo)"1voer6dE). , - -d@u " o - . d t (2e-22) /rq_l1 (2e-34) (xaucvtll.roq) tolv r1l"e- O vdpoErol AmpEre,oupnegcpBavopdvotrxcl rol pe{pcroEperorrjnLorlE,eivol fn.ar=p"1i,+i,5. To perjpapercrrinlorlEnc(el orlpcvrlx<ip6lo m1v{rcplrl lrrQop0yvlTt)r6vxupdror'. ATKHI,EIX Ebrirpro29-1 Mayvqtlxti n€bao?irvorjp€vouqoet(ou 29-1 OerLr<io4pelqrdqoQrfoq = 3,00pCdxer.rqxljrrlrsu = (8,00x 106mh)i.TI orlypi rrouro eoQriobrdplercu.o:rdrqvog- X{rov oltivcovuotroyimenorceivolTodlovuogarlxd;lolvryrrld ru6ioB orsordl'ouooo4peio:a);r= 0,500m,1= 0,2= 0 b)r = 0,) = _0,500m,? = 0. c):r= Q,y= 9,7= +0,500m d)x = 0, / = -0,500m,z = +0,500m. 29-2 Lvo0eru6,orlpelonriqoprioq xor4' xrvo{wolroEirgogd- vovrcrpo,qp4nioroP,drrDEqqfu€rororo>X.29-24.a)l7one( vorrlxareiOuvo4qg Orivopqgrol corciToq'oroq; b)flolc eivor 11xmerl0woqrr1gdrivctrrqgrou coaeiro 4 oroq'; c) A'tu = v' = 7,00x 106m/s,noloE€ivoLo trrilog.rorvpdrpovqq [q/vryrz{E6i" voprlgngog'qOrivopqCoulombpercfunov6riogopriov; 29-3 Arloorlpercx<ipopric4 = +5,00pCxcu.4' = -l,QQpg,x1- vou!.rcLonuicbFixvrrroIX. 20-25.T1oulxrxprprv4cur{ nrr1p11. roLoeivcrrropirgolnr 'roroq xclret0uvolrouBnor blprou.oleircl oTry c(Qi rov crEdvov;@ctoQrioredrr"u = u' = 6,00x 1(}m/s. EXHTtrA29_25 E66rpto29-2 Mal,vqtrntifiebfoororlrroibouErr7oyo{ 29-4 Eu0rjlqoggogaloyig peycil,or,rprjnotgnol 6tcrppde,oLcr- ndpedgo200A, 6rdpleroLulroxuBlrd!t)"r,r,olt|3cirlopdorocvory- pcirovoroxdwpa6tocndvcwLr).euqc6v()1.29 26).TopjxoEqg oxpqErivnr20.0cm.Orc',p4orrevuororlriorol cloyoripryoug,XHl]iIA 29-24
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- 29. 832 KXOA AIO 29 IIHTEE MAINHTIKOY NEAIOY TodvqoiQFomo dl,l,o€ir/or6,00x 10'N/m, rcr €ivorar0loruti. Av ro petpcorodvao"J,opcreivc[2,00A, a)rLpeiipooLopgderro d,.loofQpq;b) 'E1ouv r1vi6Lorlcrwf0€qqoQdro 6{0Q€igsro; 29-14 Tpic rapc 'trr1trcorjqporc6rcppdor,rqlqrTdQ€ipa1xo xoodvq,dr[o_(bEixvrrxo)X.29-31.Av1 ordmcroqcrcipeoctoe1eL- rovLzcio[ppc-rceilcld, uno]"oyimero pdrpozcl rcrei0uvoqrouo- ).tzoiponqnroi nediouovtigovci6crprjzouEo€xdO€qiQpq. rouprrlvqnrotiirebiouoedvooqpeioorotdwporqEtlrorolujg'qE leprdlLlqEcircwororeiqeg6rcrgpdoworcrti peipo0,300A. 29-20 )cohlvoer6dgprjroug20,0cmxcu,crttrivog3,00cmeivor ruwd neprelrlpdvope200oreigegoilpporogrotrbLappdowoLcnd p€r1lcr6,00A. Yro)"oyiorero pcryrrprxdrebio o€oql.r€i]oxo.[doro ldvrporouoolqvoe16or.lg. 29-21 )co).r1voer6dEtrixouE50,0cmrqr oltrilvsg3,00cmeivor ntreouopdvovc blplouQleioroxdaporouflEbio0,140T. To pdY|,- oropedporou plopeirc oLogpderro ouppnro! €ivor10,0A. a) noro! silvcrro €ldxrorogcplopriEoneq6r crvd[ovd6aLdtouEfiou rpd:rerva dlerro otol,4voer6dg;b) Iltiooeivu ro oLndpt'jxoErou 0lQpqroE; 29-22 To lui'fd"toeLbdgoo).1voer6dgrou2y.29-77dyet"eortxt pr,u,rjbr<iperqor, = 0,200m xcreEcoreQr,xrjr, = 0,280m.'E1e1300 oneipeglol drcppdoworcrd ge go3,50A. Ynoloyior€10pdxQo ToupcrnryritorireoioUoexooeprdcndrq o].id)'ou0€Eoromdo€lE cndrordwporouryvior: a)0,150mb)0,240mc)0,350m. 29-23 Opoalouxd xol,6Ero. hprcyjg rulrv0gLlt6Eo- yrolclgori,.rivaga reqlpd),Lerorord povtrinrdxul,Lv6puldmqipllgo uxr(vova xcLb,rol penl oeprirou:repl$till"ercrlcnriulc6yLgore- piBllpncrxrivcwb xarc,rircoEbei;verro 11.29-33.Av o)i€rrQftdE crlroyrigxalro a1c61gompip),1po6roppdowclc:rdro i0lopeiipcl or cwroercgri,.rrru0uvotrc.ppcrrrlrrcoXiorl.7rtrro pdrporoupcr- yvrlrLxotre6iotr a)oeoilpe(arou cndlouvcrd ro xdlrgo ondcno- oI r,dnoua <r<b b)oeo4peiad[corurdro ouo'qpo(r > c). xxHMA 29-33 29-24 E-twnL1lltrE1lv dorilq 29-23OetopriwoE<irrro pefpo ccoveocrxepr,zdcrlcoltis(!o[1r,orov€EcfirQlxd1r,xcrdxoxrvn]vG 6rcqopd. Er5dqro29-8 Iai,vrlrrzd ul,rxti * 29-25 O v61togtou Curie. Aivovrctorrcpnxdrconerqo- UdrxrETrUiEyrurlv Uc,lvqrrxqrrrbeznxcirlroTISoruJrrr'(IEou- oicrgnounepldXeloi61polal apptrivLo.Aro6c6nrelpoqlxciql e- itipqoq rol i/1. cr6 qv nldtrw10eppoxpoois.Itc{vororeirou- )'wdcurdrovv<igorouCu e;Avvqt,fiotqtfvcr1 mo0eptiCurie; r('c) x, 1 2 9 x 1 0 4 19,4x 104 9 , 7 x 1 0 4 6,5x 10-a * 29-26 Lw;luL'r,eLbigorolrlvoeL0igpe500oup[dxrvsEorr€iQ€-( [doIEolxfvag0,0800n 6ro.ppdetcr,ard pei;rc0,400A. H ol€xr]ii bLcrepc,d'qroTol nuQ{voEivq[120, a)lldoo €ilorxo[oyvlrD{d nE6io[dooorovrluQ]ivcqb)T! FdQo(xoupolvl, rao rediouotpeG tr€IcllmI Ict1,,lir[olTouu]'Lxof; I , ,| 4 v1 - EXHMA 29-31 29-15 OprlcirttooupgolB pe1ritrouprjnougelvorrono0erlpd- von<ivooedvcrpcldll. 'Evo beftepoouppoCDptjlouE0,400m Bpioxrrolrtivcocrrciro rprfto rapr 'Lr1Lop€or'rdxor€[vo!€]'t{- 0€Qovool,roOoi!€LXdprloe6io drqrpoug,xcrordQugou!,tr€xq]'h- roig aloyorjECncllD (:X.29 32).To 6io oup[oroeivorouv6ebe- pldrqldoc,llul1niE€rrotprjErcLbrcppdowctrcld peipa40,0A. To ouppaCDdlerlpcpprx! nuzvtirryopri[crg5,00x 10'kg/m.le rL riuo_(l?eq rqoQQonioeLro oippoCD,rrvulo06ooupedI[ t1pcyr'1- rr,rr]6rivc1t1ror colei:rcLoecurdocpe,etclo,lorluonxd mopet- lli pdoorou.4B; TXHMA 29_32 Ur)dtpro29-5 hIa'vrlttrij nebd$HirHirxolillQ{ilou 29-16 Klz,lrrd:r4vioarrivcg5,00cmrar mryvri-cregri)'tlr1E 200oneLgt6v6lcpqderaroxrdQ€i[c 0,300A. floLoeivaLro gdrpo rorrpolv4rLitoire6iou a)mo rdwQorourlvio!; b) oroolprio rol ir[ovcrou:qviounor n:rd1el10,0cmondro xd]xQoxo!; 29-17 Illvio pemnvrjrepr,dl,r,!16r.cpdtpou18,0cm6Lopqderor crrtiperlpcr2,50A. Ilio€Eorr€iQ€E8lqedt€tto rqvioovro pcryvlrt- xdrebfomordwQorou€iv(l[4,19x 10rT; F.{i.t6tt 29-{t O vtil.i*q ,f{}u Alnpi!'e 29-18 KleLolj zcrlLnd)"r1irepLxl.eieLpegLxo{Esj,oryoiE.To €r[- xo[nriiLootroztrrjptopcQB d/ rrivroorlv no[ri),q biv€r3,75x 10' T m.llolo eivcLro o)'lz,cigeiipororrdurqqdelrougoytoyotig; Iliriit ?:i--7 lll nrlplrldg riili a{;llrlti r(}rJAmpire 29-19 E{trrvobcrruiroer6dqrtrnioro,pdorlg6rcpi'rpou0,180m, €alc'|nuzid ir€Qr1Uir./[dvo[€ 500oireiQeE.Yxro],oyiorEro pdrQo I - r13
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