Direct current regimes in the linear electric circuits according to the relativistic circuit theory

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ISSN: 63-316X (Ol OI: 1.9114/av.vol.ss1.

1 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: c c gms h la lcc ccs accodg o h lavsc cc ho ml Ivaov Paov 1 1 Tchcal Uvs of Vaa, pam of Thocal lccal gg ad Ismao, 91, 1 Sdsa S, Vaa, lgaa Cospodg aho coac: paov@ahoo.com Absac. Th pap s ddcad o a mssg chap of h cc ho, whch s cocd wh h spcal ho of lav. I s cocd wh h dc c gms h la lcc ccs, whch a movg wh spds small ha h spd of lgh o clos o. I a ss of basc sos, cocd wh h lavsc foms of h fdamal laws fo h lcc ccs (Kchhoff s c law, Kchhoff s volag law, Ohm s law, Jol s law, h g cosvao law, a obsvd. Th lavsc foms of h basc as of h lcc ccs (cs, volags, pows ad h lavsc laos of h basc paams of h ccs (ssacs, codcacs, capacacs, dcacs a psd, oo. Ths fomlas a acd sp b sp b h hlp of Mawll--s ssm of basc aos of h lcomagc fld, whch s appld o fas movg obcs (la lcc ccs wh aba vlocs lss ha h spd of lgh o v clos o. Th fal sls a llsad b h hlp of som smpl ampls abo fas movg la lcc ccs. Th aalss a psd sp b sp od o show h vald of h cvd laos. Kwods: lavsc cc ho, spcal ho of lav, lavsc laws fo h lcc ccs, lavsc paams, lavsc as 1 Iodco Th cao of h Mawll s ho of h lcomagc (M fld had a omos flc o h dvlopm of h mod phscs (Mawll, I was h ma bass fo h appaac of h Spcal Tho of Rlav (STR of Alb s (s, 195, 198, (Fma, 1964a, (Kl, 1963, whch fomd h mod vws o h sodg wold. O of s ma coscs was h lavsc coco of h Mawll- s of aos of h M fld fo movg mda (Fma, 1964b, (Pcll, 1965, (Smo, 1964 ad h sl was h appaac of h Mawll--s ssm of basc aos of h M fld. Th cao of h Roa Tho (RT of h M fld bogh w cocos ha s of aos b h hlp of h mhod of moms (Paov, 15, 17a, 17b. A h sam m Cc Tho (CT, bg a cosc of h Mawll s M ho ad s complma ho, s o v wll posd lavsc fom, a fac whch ca b dcd v asl h chcal la,.. s abs Th aso s cocd mab wh h fac ha h a som scss, who clam dcl ha: Th mpoa coscs (of STR a lad o h sph of phscs, b o o lccal gg (Smo, 1964, p. 75. a h sam m h s aoh gop of scss who pa ao h moogaphs o som lms of h Rlavsc Cc Tho (RCT (whch ca b calld also Spcal Cc Tho (SCT (Pal, 1958, (Movch, 1966, (Polvaov, 198, (Movch, g h las fw as som addoal sachs o ha opc w do, b h a o gald sls owads RCT... Th ma goal of ha pap s o collc h sg fomao abo h basc laws of h lcc ccs lavsc fom (Kchhoff s c law, Kchhoff s volag law, Ohm s law, Jol s law, h g cosvao law, h lavsc cocos of h basc as of h ccs (cs, volags, pows ad h basc paams (ssacs, codcacs, capacacs, dcacs, od o s h bass fo h aalss of dc c (C gms lcc ccs, mod fas movg afcal obcs (l salls o spac shps wh vlocs lss ha h spd of lgh o clos o. Toda h hghs vlocs achd b afcal cosmc obcs a abo 15 m/s ad a Pag 17

2 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: ha spd h lavsc ffcs ca b alad dcd Th basc poblm h sach s cocd wh h fac ha som of h lms of h plod ccs a oad paalll o h dco of movm, ad som of hm a asvsl dsposd, so h volags ad h cs hs movg lms ca b accpd b a sac obsv a dff wa compad wh a obsv, movg ogh wh hs ccs wh h sam spd. Aalss.1 asc laws of h fas movg C la lcc ccs Accodg o h lav pcpl of STR ach al cooda ssm h basc foms of h laws of phscs ms ma h sam (s, 195, (Fma, 1964a, (Kl, I ha lao l s mag a movg la lcc cc wh a fom spd v alog h -as of a sac Casa cooda ssm S (Fg. 1(a. Ad l s mag a movg Casa cooda ssm S wh h sam fom spd v v, whch h cc s sac poso ad h dco of h -as cocds wh h -as of h sac cooda ssm S. Th Mawll s s of aos dffal fom fo a sac coodag ssm S has h followg fom: o (1 o ( dv ρ (3 dv (4 Th Mawll s s of aos dffal fom fo a movg cooda ssm S ( whch h dco of h -as cocds wh h -as of h sac cooda ssm S wh a fom spd v psvs s fom (.. s vaa: o (5 o (6 dv ρ (7 dv (8, ad a h vcos of h magc fld ss, ad a h vcos of h lcc fl dss, ad a h vcos of h lcc fld ss, ad a h vcos of h magc fl dss, ad a h c dss, ρ ad ρ a h volm d- ss of h lcc chags boh cooda ssms S ad S, cospodgl. I mo dald fom h fs s of aos cosss of 8 paal dffal aos: (9 (1 Pag 18

3 OI: /av.vol.ss1.66 Vol Iss 1 (18 ISSN: X (Ol Pblshd: Pag 19 (11 ρ (1 (13 (14 (15 (16 I mo dald fom h scod s of aos cosss of 8 paal dffal aos, oo: (17 (18 (19 ρ ( (1 ( (3 (4 Th compos of h M as of h M fld h movg cooda ssm S, pssd b h compos of h sam as h sac cooda ssm S accodg o STR, a as follows (Movch, 1966, 1987: (5 ( v. (6 ( v. (7 (8

4 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: v. (9 v. (3 (31 ( v. ( v. (3 (33 (34 v. (35 v. (36 ( ρ.v (37 (38 (39 v ρ ρ. (4 c 1 (41 v 1 c s h coffc of lav ad c s h spd of lgh vacm, wh v c. Thfo, hs fomlas pss h Lo asfomaos of h compos of h M as. Th sam sls ma b psd b h asvs ad h logdal compos of h M as accodg o h oaos of s-lab as follows (s, 198: (4 ( v (43 (44 v (45 (46 ( v (47 (48 v (49 ( ρ.v (5 (51 Pag

5 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: v ρ ρ. (5 If w sbs ao (4 o ao (37, havg md ha ρ, w ca cv h followg sl: v. ( ρ v. v. (53 If: s a codco c ds, wh s h covco c ds,.. (54 (55 cov.. v cov. (56 c ( (57 cod. cod. If w accp h oaos of s ad Lab (s, 198 fo h asvs ad h logdal compos of h c dss, h c dss fom aos (37 (39 ad (53 (57 ca b oad as follows: ( cod. (58 cod. cod. cod. Ad f w a o acco h asvs ad h logdal coss-sco aas S ( S, of h codcos of h ccs h cooda ssms cod. S, cod. S ad S (59 (6 S ad S ad S, h w ca ac h laos of h flowg cs h:.s cod..s..s. cod. cod. cod. cod. cod. (61 cod..s..s..s. cod. cod. cod. cod. cod. cod. cod.. (6 Usg h las wo aos w ca fomla h Kchhoff s c law lavsc fom. I h movg cooda ssm o o S wll loo l: I h sac cooda ssm S wll loo l: 1 (63 (64 (65 (66 Pag 1

6 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: o o cod (67 (68 Th lavsc laos amog h las s aos a as follows: ( Th las ao pss Kchhoff s c law lavsc fom. So, h algbac sm of h codco cs flowg hogh a od of a lcc cc h cooda ssm S o h cooda ssm S s alwas al o o. I s o dffcl o ps Kchhoff s c law aoh fom, whch h lcomov cs of h c socs (f h a sch a asfd o h gh had sd of h ao ad all h codco cs, flowg hogh bachs coag o c socs, a psd o h lf had sd. Usg a smla pocd w ca ac h Kchhoff s volag law lavsc fom, oo. Fo ha ppos f w sbs ao (35 o ao (7, havg md ha, w ca cv h followg sl: If: ( v. v. v. (7 cod. (71 s a compo of h lcc fld s casg codco cs, (7 wh v. d. (73 c s h compo of h lcc fld s, casd b h pola dco, h ( cod. (74 cod. If w appl h oaos of s ad Lab (s, 198 fo h asvs ad h logdal compos of h lcc fld ss, h compos of h lcc fld ss aos (5 (7 ad (7 (74 ca b oad as follows: d. (75 ( (76 cod. cod. cod. ( (77 cod. cod. cod. Ad f w a o acco h asvs ad h logdal lghs of h lms h ccs l ad l ( l, l cod., l cod. ad l h cooda ssms S ad S, wh h compos of h lcc fld ss ac po, h w ca ac h laos of h volag dops h: cod. cod.. l. l.. l.. l.. (78 cod. cod.. l. l. l.. l. cod. (79 cod. cod. cod. Pag

7 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: Usg h las wo aos w ca fomla h Kchhoff s volag law lavsc fom. I h movg cooda ssm o o S wll loo l: I h sac cooda ssm S wll loo l: o o 1 1 (8 (81 (8 1 1 (83 (84 (85 Th lavsc laos amog h las s aos a as follows: (86, o s a volag dop, whch cass flowg of a codco c, ad (87 cod. d. cp ha d. s a volag dop casd b h pola dco, bcas of h lav mov- m of h cc h cooda ssm S owads h sac obsv h cooda ssm S. ao (86 pss Kchhoff s volag law lavsc fom. So, h algbac sm of h volag dops a coo of a lcc cc h cooda ssm S o h cooda ssm S s alwas al o o. I s o dffcl o ps Kchhoff s volag law aoh fom, whch h lcomov focs of h volag socs (f h a sch a asfd o h gh had sd of h ao ad all h volag dops acoss h passv lms h coo a psd o h lf had sd. Th cocss of aos (58 - (6 ad (75 - (79 gvg h lavsc laos of h c dss, h cs, h lcc fld ss ad h volag dops boh cooda ssms ca b povd b Jol s law po fom fo a small logdal o asvs lm of a codco wh a c: p.p V. p P V P V.P V..P V.P V. cod. V cod.. cod. V cod... (. (.. cod. cod. V.. cod. cod.. (. (.. cod. cod. V. cod. cod.... cod.. cod. cod. V.p cod. V.p.. cod. cod. (88 (89 Pag 3

8 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: wh p, p a h spcfc pows small lms of h codcos of h plod cc; p, p ad P, P, P ad P a h pows, casd b h codco cs; ad V a h volms of h codcos h cooda ssms h pows a psd (Pal, V, V, V S ad S. Th laos amog. asc laos of h paams of fas movg C la lcc ccs If w s h Ohm s law po fom, h lavsc laos amog h codcvs of h codcos h cooda ssms S ad S ca b acd (Movch, 1966: cod.. σ cod... cod. cod. cod.. σ.. cod. cod. cod. σ. σ. (9 cod. σ σ. (91 cod. wh σ, σ, σ ad σ a h codcvs of h logdal ad h asvs codcos of h plod ccs h cooda ssms S ad S. Fom h las wo aos h followg laos occ: σ.σ (9 σ σ (93 Th cospodg laos of h ssvs of h codcos a as follows: ρ ρ 1 R.1 R σ σ (94 1 ρ ρ (95 R σ. σ Th, sg h las wo aos, h laos amog h ssacs ad h codcacs of h codcos of h plod ccs h cooda ssms R R R S ad S ca b acd: ρ R. l 1 ρr.. l ρr. l R S G.S S G1 ρ R. l 1. ρ R. l ρ R. l 1 R S G.S S G Aoh mpoa laos ca b acd fo h capacacs ( C, C, C, C ad h dcacs ( L, L, L, L of h acv lms of h plod lcc ccs h cooda ssms S ad S : C C L (96 (97 C. C.. C. v. (98 cod. C C. C.. C C. v. (99 cod. cod. C C (1 C C (11 Ψ L. L.. Ψ L. v. (1 Ψ L L. cod. L L.. Ψ L. v. (13 L Pag 4

9 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: , C, C, C ad L L (14 L L (15 C a h lcc chags of h capacos; Ψ L, Ψ L, Ψ L ad a h magc fl lags of h cols h cooda ssms S ad S. Th sam sls ca b cvd f w am h sod g of a chagd capaco ( W, W C, W C, W C ad a col wh a c ( W L, W L, W C. W C. W L C. C Ψ.. C C C Ψ L C. L L. C C. C. C C. C.. L L L. ( C W L, W. W L.(. C C.( ( C. W. C L (.C C.(.( L. W. C L (. L L.( (. L L Ψ Ψ L C boh cooda ssms. C C L C C L (16 (17 (18 Ψ L. L... L L ΨL L W L W. L L (19. (. L ΨL. L L.( L.. So, h lavsc laos, whch w psd b aos (1, (11, (14 ad (15 ca b asl acd fom h las fo aos. Th lavsc laos of h pows h cooda ssms S ad S a psd (Pal, Nmc ampls ampl 1: Gv a C lcc cc a Casa cooda ssm S whch s movg wh a vloc v 6 m/s owads a sac Casa cooda ssm S (Fg. 1., h lcomov foc of h volag soc h cooda ssm S s V ad h ssacs of h ssos a R R 1Ω. All as ad paams h cooda ssm S a od wh a pm (Fg. 1(a ad hs h cooda ssm S a o (Fg. 1(b. Fd h as ad h paams boh cooda ssms. Pag 5

10 OI: /av.vol.ss1.66 Vol Iss 1 (18 ISSN: X (Ol Pblshd: S S R R O O v (a (a R (a R (b Fg. 1. A movg lcc cc wh a fom spd v owads a sac Casa cooda ssm S. Solo: Th coffc of lav hs cas s:. I h cooda ssm a vald: cod. V cod. cod. (Kchhoff s volag law fo h loop of h cc Fg. 1(a; cod. cod. cod. R R (Kchhoff s c law fo od (a Fg. 1(a; (Pow of h hooal sso Fg. 1(a; (Pow of h vcal sso Fg. 1(a. Th balac of pows s as follows: R cod. cod. cod. P. 1V.1A 1W R P. 1V.1A 1W 1V 1V V 1A 1Ω 1Ω. R R P. V.1A P P 1W 1W W I h cooda ssm S h followg sls a vald: cod. V 1V 1V,5V 1V,5V 1V,5V,5V (Kchhoff s volag law fo h loop of h cc Fg. 1(b; 1A,5A 1A,5A 1V S h followg sls Pag 6

11 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: (Kchhoff s c law fo od (a Fg. 1(b; PR.,5V.,5A,5W (Pow of h hooal sso Fg. 1(b; P.,5V.,5A,5W R (Pow of h vcal sso Fg. 1(b. Th balac of pows s as follows: P. 1V.,5A P Th ssacs of h ssos a: R P R 1 R R 1Ω ; R R Ω.,5W,5W,5W ampl : Aal h C lcc ccs psd Fg., whch a smla o hs h pvos Fg. 1, wh h ol dffc s cocd wh h fac ha h volag soc s dsposd hooall ad s lcomov foc s V. Th ssacs of h ssos a R R 1Ω ad h vloc of h lcc cc owads h cooda ssm S s v 6 m/s. S S R R O O v (a (a R (a R (b Fg.. A movg lcc cc wh a fom spd v owads a sac Casa cooda ssm S. Solo: Th mc sls h cooda ssms S ad S a h sam as h pvos ampl. Th coffc of lav hs cas s:. I h cooda ssm S h followg sls a vald: V 1V 1V cod. cod. cod. cod. (Kchhoff s volag law fo h loop of h cc Fg. (a; cod. cod. cod. R R (Kchhoff s c law fo od (a Fg. (a; (Pow of h hooal sso Fg. (a; (Pow of h vcal sso Fg. (a. Th balac of pows s as follows: R cod. cod. P. 1V.1A 1W R P. 1V.1A 1W R V 1A 1Ω 1Ω R P. V.1A P P 1W 1W I h cooda ssm S h followg sls a vald: W. Pag 7

12 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: cod. cod. V / 1V 1V,5V 1V,5V 1V,5V,5V (Kchhoff s volag law fo h loop of h cc Fg. (b; 1A,5A 1A,5A (Kchhoff s c law fo od (a Fg. (b; PR.,5V.,5A,5W (Pow of h hooal sso Fg. (b; P.,5V.,5A,5W R (Pow of h vcal sso Fg. (b. Th balac of pows s as follows: P. 1V.,5A P Th ssacs of h ssos a: R P R R R 1Ω ; R R 1Ω. 1V,5W,5W,5W 3 Coclsos As a sl of h sach h basc laws (Kchhoff s c law, Kchhoff s volag law, Ohm s law ad Jol s law lavsc fom fo fas movg lcc ccs wog C gms w acd. A gop of lavsc laos fo h as (codco cs, volags, pows, lcc chags ad magc fl lags ad h paams (ssacs, codcacs, capacacs, ad dcacs of hs ccs a psd, oo. Som laos abo h pows (h balac of pows as a cosc of h g cosvao law a show addoall h mc ampls. Two mc ampls wh fas movg la lcc ccs llsa mos of h acd laos, oo. All h ca b v sg o h lccal gs who d o l STR od o b abl o dm h as ad h paams of fas movg ccs. I hs wa RCT s also wh op wa o., h ploaos cov a small pa of RCT, cocd ol wh h C gms la lcc ccs. Th ma as s o sp h cos of h sachs abo h fas movg lcc ccs, bcas h lavsc ffcs s aod s oda. I hs wa RCT ca b v sfl fo pdco ad plaao of w M pocsss, phoma ad ffcs fas movg lcc cc Rfcs s, A. (195. Z lodam bwg öp. Aal d Phs, 17, ( Gma Pag 8

13 ISSN: X (Ol OI: /av.vol.ss1.66 Vol Iss 1 (18 Pblshd: s, A., Lab, J. (198. Üb d lomagsch gdglhg fü bwg öp. Aal d Phs, 331(8, ( Gma Fma, R., Lgho, R., Sads, M. (1964a. Th Fma lcs o phscs. vol. 1, Addso Wsl Pblshg os, Ic. Fma, R., Lgho, R., Sads, M. (1964b. Th Fma lcs o phscs. vol., Addso Wsl Pblshg os, Ic. Kl, C., Kgh, W.., Rdma M. A. (1963. Mchacs, l phscs cos. vol. I, N. Y., McGaw-ll oo Co. Mawll, J. C. (1873. A as o lcc ad magm. vol. I, vol., Macmlla ad co., Lodo, Ud Kgdom. Movch,. A. (1966. Mhods of h Rlavsc lcodamcs lccal gg. Moscow, ga. ( Rssa Movch,. A., Movch,.. (1987. Mhods of h Rlavsc lcodamcs lccal gg ad lccal Phscs. Moscow, goaomda. ( Rssa Paov,. I. (15. Roa ho of h magc fld, bascs, cocps, mhods ad modls. (Moogaph, 148 p., LAP Lamb Acadmc Pblshg, Gma. ISN Paov,. I. (17a. O h lcodamcs of movg bods accodg o h oa ho. Pocdgs of h Scod Iaoal Scfc Cofc Illg Ifomao Tchologs fo Ids (TI 17, Advacs Illg Ssms ad Compg 68,, Vaa, lgaa, Spg, (SCOPUS, ISSN , ISSN (lcoc, ISN , ISN (oo, do:1.17/ _31 Paov,. I. (17b. O aoh poof of h fomla m.c accodg o h oa ho, Aal Joal of h Tchcal Uvs of Vaa, 1(1, 13-. ISSN (Ol, do:1.9114/adv.vol1.ss1. Pal, W. J. (1958. Tho of lav. Lodo, Pgamo Pss. Polvaov, K. M. (198. lcodamcs of Movg ods. Moscow, goda. ( Rssa Pcll,. M. (1965. lcc ad magsm, l phscs cos. vol., McGaw-ll oo Co., N. Y. Smo, K. (1964. Thocal lccal gg. Moscow, M. ( Rssa Pag 9

k of the incident wave) will be greater t is too small to satisfy the required kinematics boundary condition, (19)

k of the incident wave) will be greater t is too small to satisfy the required kinematics boundary condition, (19) TOTAL INTRNAL RFLTION Kmacs pops Sc h vcos a coplaa, l s cosd h cd pla cocds wh h X pla; hc 0. y y y osd h cas whch h lgh s cd fom h mdum of hgh dx of faco >. Fo cd agls ga ha h ccal agl s 1 ( /, h hooal