Khoa cng ngh thng tincng ho x hi ch ngha vit nam B mn in t vin thngc lp - T do - Hnh phc

THI S 1Mn: L thuyt trng in tThi gian : 90 phtHnh thc thi : VitCu 1 : (3 im)Trnh by phng trnh 1 v 2 ca Maxwell v ngha vt l ca chng.Cu 2 : (3 im)Trinh bay v khai nim v mi trng khng ng hngCu 3 : (2 im)Cho mt hinh cu tich in ban kinh laa. Giasin tich phn phu trn bmt cua novi mt in tich mt s = Q/4a2. Tinh cng in trng tai nhng im ngoai va trong hinh cuCu 4 : (2 im)t kh co) / 1 ( / 10 , 430m m Ci . Hay tim gii han theo bc song to xem t kh la dn in va in mi.p n:Cu 1 : (3 im)1.Phng trnh Maxwell th nht.Bng cch b sung thnh phn dng in dch vo v phi ca biu thc nh lut dng ton phn cng vi dng in dn phng trnh th nht nh sau:S dtDS d J l d HS S l + (1)Phng trnh (1.1.31) m t mi quan h gia cc vect ca trng in t (D H ,) trong mt vng kn bt k cc dng in dn chy qua n, m t n trong khng gian:S dtDS Jd S d H rot l d HS S S l + (2)V mt S l tu nn ta nhn c phng trnh Maxwell th nht dng vi phn nh sau:dcJ JtDJ H rot + + (3)(1 im)Nu mi trng c dn in ring =0 thE J =>0 Jnn phng trnh c dng:dcoJtEH rot0 (4)Phng trnh ch ra : Dng in dich hay in trng bin thin cng to ra t trng xoy tng ng dng in dn2. Phng trnh Maxwell th hai:Maxwell cho rng biu thc ca nh lut cm ng in t p dng khng ch chomt vngdydnknmmcnngchobt k mt vngkn no( khng nht thit dn in) trong khng gian. Trong trng hp tng qut vng kn ny c th mt phn nm trong trn khng, phn khc nm trong in mi hay trong kim loi. Ta nhn c phng trnh sau:S dtBl d ES l (5)(2 im)Nu p dng nh l Grin Stc cho v tri vi S l tu nhn c phng trnh sau:tBE rot (6)Vy t trng bin thin to ra in trng xoy3. ngha vt l ca phng trnh th nht v th hai ca Maxwell:Bt k s bin thin no ca in trng u gy nn t trng xoy(ng sc khp kn) v ngc li. in trng v t trng bin thin khng th tn ti c lp vi nhau, chng lun lin h mt thit vi nhau v lin tc chuyn t dng ny sang dng khc to nn sng in t truyn lan vi vn tc nh sng.(3 im)Cu 2 : (3 im)Mi trng ng hng lami trng matinh cht cu a nomoi im lanh nhau. Trong cac mi trng nay ca c vec t B H,vaD E,lasong song vi nhau tng i: E D H B . , Nu chiu cac phng trinh ve c t trn xung ca c truc toa ta c cac phng trinh v hng:'z zy yx xH BH BH B'z zy yx xE DE DE D(1 im)i vi cac mi trng bt ng hng mi quan h gia cac vec t trn c xac inh qua cac phng trinh:'+ + + + + + z z z y z y x z x zz y z y y y x y x yz x z y x y x x x xH H H BH H H BH H H B '+ + + + + + z z z y z y x z x zz y z y y y x y x yz x z y x y x x x xE E E DE E E DE E E D Cac hng s , co th c vit di dang nh sau:111]1

zz zy zxyz yy yxxz xy xx H B 111]1

zz zy zxyz yy yxxz xy xx E D (2 im)goi la tenx t thm goi la tenx in thmTrong thc t khng tn tai ca c mi trng ma ca va u mang tinh tenx.Mi trng bt ng hng cotenx tthm in hinh lapherit c tho a bi ttrng khng i; con mi trng cotenx in thm in hinh lami trng ion hoa( mi trng plasma).(3 im)Cu 3 : (2 im)Ap dung phng trinh 3 cu a Maxwell dang tich phn:q S d DSLy S la mt cu ban kinh a. Do tinh cht i xng nn D tai moi im trn hinh cu la nh nhau24 . r D S d DS (1 im)a) Xet trng hp thnht: im M ngoai hinh cu(r>a)Ta co: q = QD.4 r2 = Q = S.4 a2D = S.(a2/r2)b) Trng hp th hai: im M trong hinh c u(r haythi t co tinh cht cu a cht in mi- Nu ) 1 ( > < haythi t co tinh cht dn in.(1 im)Gii han theo b c song to xem t kh la dn in hay in mila: 1 hay140 hayMa 6001460 310 . 151151 = (2/3).102(m)cang ln thit cang co tinh dn in hnTy ta co th kt lun la:- Vi > (2/3).102 m thi t co tinh dn in.- Vi < (2/3).102 m thi t co tinh in mi.(2 im)Khoa cng ngh thng tincng ho x hi ch ngha vit nam B mn in t vin thngc lp - T do - Hnh phc

THI S 2Mn: L thuyt trng in tThi gian : 90 phtHnh thc thi : VitCu 1 : (3 im)Trnh by phng trnh 3 v 4 ca Maxwell v ngha vt l ca chng.Cu 2 : (3 im)Hy trinh by v s phn cc cu a song in tCu 3 : (2 im)Mt in tich dong Q phn b u theo th tich quacu coban kinh la a, vi mi in thm t trong khng khi. Hay tim cng in trng E trong va ngoai qua cu oCu 4 : (2 im)Song phng truyn trong mi trng in mi ng nht ng hng rng v han co tham s = 40; 0 ;0 ; bin cng in trng cu a song Em= 10-3 (V/m) va f = 106Hz. Lp biu thc gia tritc thi cng ttrng cua song va mt dong cng sut trung binh.p n:Cu 1 : (3 im)Maxwell coi nh lut Gauss v nguyn l lin tc ca t thng p dng choctrnghpintrngvttrngltnh, khngi cngnhvi trng hp tng qut ca in t trng bin thin theo thi gian. Ta c:Q dV S d DV S (1)0 dV B divV (2)V th tch V l tu nn nhn c cc phng trnh Maxwell th 3 v th 4 nh sau: Ddiv (3)0 B div (4)(1 im) tin cho vic theo di, ta vit thnh hai dng sau:Dng tch phn:0tBtDSS + S d BQ dV l d DS d l d ES d S d J l d HSV SlS l (5)Dng vi phn:0 B divD + divtBE rottDJ H rot(6) (2 im) ngha vt l ca phng trnh 3 v 4 ca Maxwell: DDiv 0: ta thy ng sc ca in trng l nhng ng cong khng khp kn m c im u ti in tch +q, im cui ti q. DDiv = 0: in trng sinh ra ch do s bin thin ca t trng. ng sc ca n hoc khp kn hoc tin ra v cc. 0 B Div ng sc ca t trng va khp kn va tin xa v cc.(3 im)Cu 2 : (3 im)Ta c cc loi sng phn cc c bn c s dng :- Pht hnh : Sng phn cc ngang- Pht thanh: Sng phn cc ng hoc ngang- Sng ngn : Sng phn cc ngang- Sng FM: Sng phn ng hoc ngangS ph thuc hng ca vect E vo thi gian v khng gian gi l sphn cc phn cc.Sng in t khi truyn lan vect cng in trng v t trng c th thay i c v ch s v hng. V vy khi sng truyn lan nu quan st im cui ca vect E th ta thy n v ln mt qu o no Xt ti mt im c nh trong khng gian cng vi thi gian im cui ca vect E thc hin mt chuyn ng tnh tin dc theo mt ng thng th ta ni sng in t phn cc thng(phn cc tuyn tnh). Tng t nu im cui ca vect E v nn mt hnh elip ta c phn cc elip, cn v nn ng trn ta c phn cc trn. Nu nhn theo hng truyn sng vect E quay theo chiu kim ng h ta c phn cc trn quay phi, ngc li c phn cc trn quay tri.Gi s c hai sng phng phn cc tuyn tinh vung gc vi nhau ta c:) cos() cos(0 20 1 + z t E y Ez t E x Emymx(1 im) y Emx, v Emy l bin cc sng thnh phn, l gc lch pha ban u ca hai sng phngSuy ra 2 2 12221sin cosE E2

,_

+

,_

my mx my mxE EEEEEPhng trinhny biu din mt hnh elip(2 im)Elip c trc ln lam mt gc vi trc ox cos222 2my mxmy mxE EE Etg ; vi Emx > Emy- Khi Emx =Emy; = /2 thi phn c c luc nay l phn cc trn.- Khi = n (n = 1, 2,...) thi la phn cc thng. Nh vy khi t thay i vec t E se quay cung v phi a ngc chiu kim ng h, vi chu ky: 2 T, u nut cu a no vach thanh ng elip. Chiu quay cua Ela chiu quay v phia thanh phn trng chm pha.(3 im)Cu 3 : (2 im)Ap dung phng trinh 3 cu a Maxwell dang tich phn:q S d DSLy S la mt cu ban kinh a. Do tinh cht i xng nn D tai moi im trn hinh cu la nh nhauq r D S d DS 24 . a) Xet trng hp thnht: im M ngoai hinh cu(r>a)Ta co: q = QD.4 r2 = Q 24rQDMi trng la khng khi nn = 0Ma D = .E = 24rQE = 24 rQ(1 im)b) Trng hp th hai: im M trong hinh c u(r> . Ty ta suy ra c t co tinh dn in tt.Vy vi song cc dai = 104 105 m thi t co tinh dn in tt.- Vi = 10 m 4 06 , 0 10 . 10 . 60 603 b.p n:Cu 1 : (3 im) xt iu kin b i vi E1n v Hn ta xt hnh tr c y S1v S2 nh v cao h .- i vi En Ta xt phng trnh Maxwell dng vi phn sau y: V SdV dS D c th vit nh sau vi v tri ca phng trnh: + + SxqxqS S SdS D dS D dS D dS D122211 Khi h 0 ta c :12 0 2121 12 21210) ( ) (limdS n D D S d D D dS DS S Sh (1)S12* l giao tuyn gia mt phn cch v hnh tr (1 im)T v phi ca biu thc (1) ta c :12 0120limS d n dVSSVh t ta c t v tri v v phi ta c biu thc sau y:D1n - D2n =s1E1n - 2E2n =ss l mt in tch mt Nh vy thnh phn php tuyn ca vect in cm D khi chuyn quab mt phn cch 2 mi trng thay i mt lng bng mt in tch mt s.(2 im)- iu kin b i vi HnXt phng trnh Maxwell n n n nSB B B B S d B2 1 2 10 0 1H1n - 2H2n=0Nh vy thnh phn php tuyn ca vect t cm Bn lin tc khi i qua b mt phn cch hai mi trng.(3 im)Cu 2 : (3 im)Ta khao st sng phng jkzme E EDang phu thuc vao thi gian(dang tc thi) nh sau: ) cos( kz t E Em Trong mi trng in mi l tng = 0 thi k l s thc: kPhng trinh mt ng pha cu a song:. const kz t x yE H(3.5)Suy ra: z = 1/k(t cosnt)(1 im) mi thi im t mt ng pha cua song la mt phng z = const.Vn tc pha la vn tc di chuyn cu a mt ng pha, ky hiu la 1 k dtdzvphaTrong khng gian t do: c vpha 1Va cmzkz tE EH ). cos((2 im)(3 im)Cu 3 : (2 im)Mt dong in dich chay qua hai ban tu la: tEtEJch Di0 Ma dUE . Ty ta suy ra c:t UdJm ch Di cos0Mat Udrr J S J Im ch di ch di ch di cos . * *21 0 21 1 Ap dung inh lut dong in toan phn cua AmpeLI l d H(1 im)Ly L la chu vi cua ng tron ban kinh r = 1cm. Do tinh cht i xng nn Htai moi im trn ng cong L la nh nhau. I r H 2 .Con tng ai s cac dong in xuyn qua ng cong L la: S J Ich di. (S la din tich cua ng tron ban kinh r).I2bI2. r J Ich di t rUdrJrr JHmch di ch di cos2.2 2.02 (2 im)Cu 4 : (2 im)Ap dung inh lut dong in toan phn cua AmpeniiLI l d H1Xet L la ng tron co tm nm trn truc cua cap ng truc ban kinh r. L vung go c vi truc cu a cap.Do tinh cht i xng cua cap nn H tai moi im trn L la nh nhau:niiI r H12 . (1 im)- Trng hp r>b thi0 01 H I I Inii- Trng hp a r b thi I Inii 1rIH I r H22 . (2 im)Khoa cng ngh thng tincng ho x hi ch ngha vit nam B mn in t vin thngc lp - T do - Hnh phc

THI S 5Mn: L thuyt trng in tThi gian : 90 phtHnh thc thi : VitCu 1 : (3 im)Hy chng minh v pht biu inh lut bao toan nng lng i vi trng in t. Vec t Poynting.Cu 2 : (3 im)Hy trnh by v hiu ng b mt vt dn.Cu 3 : (2 im)Codong in khng i I chay theo dy dn hinh trutrong ban kinh a. Hay tim cng trng tai im bt ky cach truc dy dn 1 khoang r cho hai trng hp r>a va r 0 la mi trng dn in, cu th la kim loai ng co dn in ring 0 0 07; ); / 1 ( 10 . 8 , 5 m, theo phng truc z truyn mt song thng ng nht vi tn s f = 105Hz. Hay xac inh vn tc pha, bc song, tr khang song, h s suy giam va thm su cu a trng() trong kim loai ng cua song. Bin cng trng se giam i bao nhiu ln so vi b mt kim loai khi song i su vao c mt khoang d = 1mm.p n:Cu 1 : (3 im)Trng in t l mt dng c bit ca vt cht, nn n cng tun theo nh lut bo ton nng lng.T vt l nng lng in t trong mt n v th tch :dVH EV)2 2( W2 2 + H v E thay i theo thi gian v khng gian, suy ra W cng thay ip dng phng trnh 1 v 2 c Maxwell :tDJ H rotd+ ;tHE rot e dJtEJ H rot ++ (1 im)Vy ta c : tHH E+ ++ e dJtEE E J E rot H H rot E + dJ H rot Ta c ] . [ H E div E rot H H rot E tEtEE221 tH221tHH E Jd E )2 2( ] . [22 2 eJ EH EtH E div + + + Ly tch phn theo th tch V 2 v ri p dng nh lut L tstrgratski Gauss.[ ] + + + VeV V SdV E J dV E dVH EtS d H E 22 2)2 2( . (1)[ ] + + VeV SdV E J dV E S d H E 2tW. (2)(2 im)Xt ngha:dV EV2 l cng sut tiu hao di dng nhit trong th tch V k hiu Pt VedV E J l Cng sut do ngun ngoi sinh ra trong th tch V k hiu PetW l tc bin thin nng lng in t trong V[ ] S d H ES . l cng sut chy ngoi V qua din tch S.Tm li: Cng sut do ngun ngoi sinh ra trong th tch V bng tng cng sut tiu hao di tc dng nhit trong V, cng sut chy ra ngoi V qua din tch S v cng sut lm thay i in t trng trong V. chnh l nh lut bo ton nng lng i vi trng in t.(3 im)Cu 2 : (3 im)Trong vt dn in tt( >>1) ta c :2 (1)Khi rt ln th cng rt ln dn n suy gim cng nhiu, ta thy bin cng trng suy gim rt nhanh khi truyn vo trong vt dn. Ngha l sng in t ch tn ti mt lp rt mng st b mt ca vt dn in tt. Khi cho dng in cao tn chy trong vt dn in tt ngi ta cng thy dng in ny ch tn ti trn mt lp theo nh lut m.Jd = Ei vi dng kho st: E=Eme-ze-jzJd = Eme-ze-jz =J0e-ze-jz(2)J0 l mt dng chn b mt vt cht J0 = Em (1 im)Mt dng in s gim dn khi i vo su trong vt dn theo quy lut ging nh bin cng in trngHin tng sng in t hay sng in cao tn khi truyn trong vt dn in tt ch tp chung mt lp rt mng trn b mt ca n gi l hiu ng b mt, hay hiu ng Skin c trng cho hiu ng b mt ngita a vo khai nim thm su ca trng hay su thm nhp ca trng , l khong cch m ng vi n bin cng trng suy gim i e ln: e 2,718Ta c : ee Ee Ezmzm + ) ( e = esuy ra = 1/ 2 1 (2 im)Hiu ng b mt c p dng trong thc t (m vng, bc), khi lm gim tiu hao khi truyn sng in t ngi ta ch m mt lp mng vng hoc bc ln b mt kim loi.Khi tnh ton cc bi ton ngi ta thy khi nim tr khng mt ca kim loi: ZS = RS + XSRS l tr c trng cho cng sut tiu hao 2SRXS l cm khng ca mt ring ZSVn tc pha: 2 pVpha(3 im)Cu 3 : (2 im)Ap dung inh lut dong in toan phn cua AmpeniiLI l d H1Ly L la chu vi cua ng tron ban kinh r. Do tinh cht i xng nn Htai moi im trn ng cong L la nh nhau. niiLI r H l d H12 .(1 im)- Trng hp r>a: I Inii 1rIH 2- Trng hp r0 la mi trng dn in, cu th la kim loai ng co dn in ring 0 0 07; ); / 1 ( 10 . 8 , 5 m, theo phng truc z truyn mt song thng ng nht vi tn s f = 105Hz. Hay xac inh vn tc pha, bc song, tr khang song, h s suy giam va thm su cu a trng() trong kim loai ng cua song. Bin cng trng se giam i bao nhiu ln so vi b mt kim loai khi song i su vao c mt khoang d = 1mm.p n:Cu 1 : (3 im)- Tphng trinh 1 cua Maxwell dang bin phc: ngm m mmJ J E j H rot+ + .0Va ta co m m E J . ngm m mmJ E E j H rot + + . .0 ngm mmJ E j j H rot + ) (0 ngm m pmJ E J H rot + . Trong o : j p la hng s in mi phc tuyt i cua mi trng jpp 0la hng s in mi phc tng i cua mi trng.fcf jp ; 2 ( 60Co th chng minh rng ty s gia phn a o va phn thc cu a p la : la ty s in dn va in di ch, no c trng cho tiu hao trong mi trng in mi.t tg=; la goc tiu hao in miNu la cht in mi: tg< 0,001Dn in: tg> 100Ban dn 0,01 < tga)Ta co: q = QD.4 r2 = Q 24rQDMi trng la khng khi nn = 0Ma D = .E = 24rQE = 24 rQ(1 im)d) Trng hp th hai: im M trong hinh c u(rb.p n:Cu 1 : (3 im)Noi chung khi giai ca c bai toan vin ttrng lamt cng vic phc tap. Vivy trong mt strng hp giai cac bai toan mt ca ch n gian vanhanh chong hn ngi ta ap dung mt s nguyn ly c ban cua trng in t.1. Nguyn ly xp chngi vi mi trng tuyn tinh phng trinh vi phn vit cho cac vec t in t trng cung la tuyn tinh. Tgiao trinh toan ho c ta a bit tng ca c nghim ring cua bt ky phng trinh vi phn tuyn tinh nao cung la nghim ring cu a phng trinh nay. Do o ta co th thy rng: trng do mt s ngun nao o selatng vec t cac trng cua tng ngun. y chinh la ni dung cua nguyn ly xp chng. Nhng c mt iu l nguyn l ny khng c ap dung i vi cng sut hoc nng lng.Thi du : Gia s co n ngun dongn J J J ,..., , 21Goi11, H Ela trng do 1Jgy ra khi0 ,..., 32 n J J JTng t:11, H Ela trng do 2Jgy ra khi0 ,..., 31 n J J JnnH E , la trng do 1Jgy ra khi0 ,..., 1 1 nnJ J JTy ta suy ra trng Edon J J J ,..., , 21 gy ra la: ). ( ... ) ( ) ( ) ,..., , ( 2 2 1 1 2 1 n n n J E J E J E J J J E + + + ). ( ... ) ( ) ( ) ,..., , ( 2 2 1 1 2 1 n n n J H J H J H J J J H + + + (1 im)2. Nguyn ly i lna, Nguyn lyi ln c suy ra t tinh cht i xng cu a cac phng trinh Maxwell. Xet phng trinh Maxwell o khng co ngun ngoai.(a) '0 H d i vtEH r o t (b) ' 0 E d i vtEE r o t Nu iu kin phep i ln: . ; H E thih(a) trthanh h(b) vangc lai. iu nay conghi a la: Nu nh cohai bai toan in ng matt caca c iu kin i vi H(hocE) cua bai toan nay setrthanh cac iu kin i viE(ho c) H cua bai toan kia. Khi thc hin phep i ln thinu bit nghim cua bai toan thnht ta co th suy ra c nghim cua bai toan th 2.(2 im)Thidu : Nu nh ta tim c cac biu thc i vi cac hstich phn c xac inh tiu kin thanh phn tip tuyn cu a vec t E= 0. Trn bmt bin gii cua 2 mi trng thikhi thc hin phep i ln: . ; H E ta sec biu thc i vi H mathanh phn tip tuyn cua Hcung bng khng trn bmt phn cach.b, Nguyn lyi ln cung ap dung c i vi khng gian ocongun in t trng. Luc nay h phng trinh Maxwell co dang:) (a' D d i vtHE r o t) (b'+0 B d i vJtEH r o t ) (ava ) (bi xng ta phai a vao cac ai lng quy c MM J ,M J: mt dong tM : mt khi t tich.- Cac ai lng MM J ,trong tnhin khng co , ta a vao chinhm muc ich lam cho hphng trinh Maxwell i xng vi E,H. Do ocothap dung nguyn lyi ln: ; H E; M MJ J ; H phng trinh Maxwell la:' D d i vJtHE r o tM'+MB d i vJtEH r o t(3 im)Cu 2 : (3 im)Mun timH,E ta phai giai cac phng trinh song almbe. So sanh vi cac phng trinh almbe ta thy chung u codang ging nhau. Do vy, chicn tim nghim cua 1 phng trinh co dang sau:gt 22. (1)Trong o: ai din cho m m e eA A , , ,g ai din cho phng trinh v phai cu a cac phng trinh song.Co th tim c nghim cua phng trinh song almbe(1) co dang nh sau:dVrvrt gVt) (41) ((3)(1 im)V: la th tich cha ngunr: la khoang ca ch t im tinh trng M ti ca c im ngun(vi phn th ti ch dV):1 vla vn tc truyn song trong mi trngT phngtrinh (3) tathyrngtrng tai imkhaosat thiim t c xac inh khng phai bi giatringun tai thi im t mac xac inh bi giatricu a ngun thi im sm hn t mt khoang thi gian lavt1 ,tchinh lakhoang thi gian truyn tngun n im quan sat vi vn tc v hu han. Nh vy trng im quan sat chm pha so vi ngun mt khoang thi giant. Do o nghim (3) ung la th chm cu a trng in t.(2 im)Nu trng la iu ho a thi:jkr jkr t jmvrt jme t g e e g e gvrt g ). ( . . ) () (Vi vk: la s song trong mi trng.Do o th chm cu a trng in tco dang:dVre t gVjkrt). (41) ( (4)I2bITrng tai im khao sa t chm pha so vi trng tai im ngun mt lng la kr.(3 im)Cu 3 : (2 im)Ap dung phng trinh 3 cu a Maxwell dang tich phn:q S d DSLy S la mt cu ban kinh a. Do tinh cht i xng nn D tai moi im trn hinh cu la nh nhau24 . r D S d DS (1 im)c) Xet trng hp thnht: im M ngoai hinh cu(r>a)Ta co: q = QD.4 r2 = Q = S.4 a2D = S.(a2/r2)d) Trng hp th hai: im M trong hinh c u(rb thi0 01 H I I Inii- Trng hp a r b thi I Inii 1rIH I r H22 . (2 im)Khoa cng ngh thng tincng ho x hi ch ngha vit nam B mn in t vin thngc lp - T do - Hnh phc

THI S 9Mn: L thuyt trng in tThi gian : 90 phtHnh thc thi : VitCu 1 : (3 im)Hy xc nh iu kin bi vi thanh phn phap tuyn cua vec t cng in trng va ttrng trn b mt phn cach gia hai mi trng Cu 2 : (3 im)Hay trinh bay v song in t phng trong mi trng dn inCu 3 : (2 im)Codong in khng i I chay theo dy dn hinh trutrong ban kinh a. Hay tim cng trng tai im bt ky cach truc dy dn 1 khoang r cho hai trng hp r>a va r a: I Inii 1rIH 2- Trng hp r haythi t co tinh cht cu a cht in mi- Nu ) 1 ( > < haythi t co tinh cht dn in.(1 im)Gii han theo b c song to xem t kh la dn in hay in mila: 1 hay140 hayMa 6001460 310 . 151151 = (2/3).102(m)cang ln thit cang co tinh dn in hnTy ta co th kt lun la:- Vi > (2/3).102 m thi t co tinh dn in.- Vi < (2/3).102 m thi t co tinh in mi.(2 im)Khoa cng ngh thng tincng ho x hi ch ngha vit nam B mn in t vin thngc lp - T do - Hnh phc

THI S 10Mn: L thuyt trng in tThi gian : 90 phtHnh thc thi : VitCu 1 : (3 im)Hy trnh by v nh lut bo ton in tch.Cu 2 : (3 im)Hy trinh bay v trng tinh in.Cu 3 : (2 im)Co1 tuphng khng khitao thanh thai ban tron ban kinh r1 =2cm, vakhoang cach gia chung d = 0,5 cm. Tuin nay lamt phn cua mach dong in. Trn hai ban tu co mt in ap bin i um =sint; Um = 500V; = (2/7).106 rad/s. Hay tim dong in dich toan phn chay qua hai ban tu vi ban kinh r = 1cm.Cu 4 : (2 im)Cho tham s in cua t kh:Hng s in mi tng i 4 dn in ring = 10-31/m.Chng to rng i vi song c c dai( = 104 105 m) thi mt t co tinh dn in tt hn, con i vi song c c ngn( = 10-3 10 m)thimt t co tinh dn in kem.p n:Cu 1 : (3 im)in tch c th phn b gin on hay lin tc. N khng t nhin sinh ra v cng khng t nhin mt i. in tch tun theo nh lut bo ton. nh lut bo ton in tch (do Faray tm ra qua thc nghim nm 1843) c pht biu nh sau:Lng in tch i ra khi mt mt kn S bao quanh th tch V trong mt khong thi gian no bng lng in tch trong th tch ny b gim i trong khong thi gian y.i xc nh dng ton hc ca nh lut:Gi s trong th tch V ty ca mi trng vt cht c bao bi mt kn S ti thi im t cha mi lng in tch l Q vi mt khi :VdV Q (1) (1 im)Sau mt khong thi giandtlng intchtrong thtchVgimi1 lng l dQ. Theo nh lut bo ton in tch lng in tch gim i trong V bng lng in tch i ra khi V qua mt S trong khong thi gian dt to ra dng in dn I. VdVdtdI (2)V th tch V ng yn nn chng ta c hn thc sau y:dVtS d JS (3)(2 im)nh lut trn l dng tch phn, nu p dng biu thc nh l tstrogratski Gauss cho v tri ta c:dVtdV J div S d JV V S (4)V th tch V l ty nn suy ra:0 +tJ div (5)Biu thc trn y l dng vi phn ca nh lut bo ton in tch hay gi l phng trnh lin tc.(3 im)Cu 2 : (3 im)Trng tinh in latrng c tao ra bi cac in tich ng yn vakhng i theo thi gian.Hay J = 0; 0 t'E DD d i vE r o t.0 (1)Trng tinh in la 1 trng th ngoai co0 E rot nn co th biu din qua 1 bin mi tl grad E 0(2) ( vi th0 ) ( grad rot E rot ).Th cu a trng in tinh theo (2) co th xac inh bng biu thc: l d E (3)(1 im)Cng A cua trng tinh in theo 1.18 c thc hin khi di chuyn 1 in tich im(+) q = 1C tim M1 n im M2 la:) ( ) (2 12121M MMMMMl d E l d F A (4)Trong o) ( ) (2 1,M M la th cua trng tinh in tai M1, M2.11) (MMl d E ; 22) (MMl d E ; 0 l d E ( Tich phn theo ng cong L khep kin)Ta co: divgrad E div D div (5)Ta co: 2; v v div grad (6)Phng trinh (6) goi laphng trinh Poison. Phng trinh nay lin hthva in tich tai mt im bt ky cua trng.- Tai nhng im maomt in trng bng khng thita co02 , phng trinh (6) tr thanh phng trinh Laplas.Giai phng trinh Poison co nghim: dVrV) (41 (7)r la khoang cach tim tinh trng n vi phn th tich dV.(2 im)- i vi in tich im ta co:rq. . 4 (8)Ta co:dVrgrad grad EV 41dVrgrad EV14 3 2021 1rrrrgradrr rgrad Ta c:VdV rrE341 (9)Trng hp in tich im ta co:qrrE .43 (10)Nu a vao trng cua in tich q mt in tich th q1, ta co:rrqqE q F3114 (11)Biu thc (11) chinh lainh lut Culng. Vivy inh lut Culng lahqua cu a phng trinh Maxwell i vi trng tinh in.(3 im)Cu 3 : (2 im)Mt dong in dich chay qua hai ban tu la: tEtEJch Di0 Ma dUE . Ty ta suy ra c:t UdJm ch Di cos0Mat Udrr J S J Im ch di ch di ch di cos . * *21 0 21 1 Ap dung inh lut dong in toan phn cua AmpeLI l d H(1 im)Ly L la chu vi cua ng tron ban kinh r = 1cm. Do tinh cht i xng nn Htai moi im trn ng cong L la nh nhau. I r H 2 .Con tng ai s cac dong in xuyn qua ng cong L la: S J Ich di. (S la din tich cua ng tron ban kinh r).2. r J Ich di t rUdrJrr JHmch di ch di cos2.2 2.02 (2 im)Cu 4 : (2 im)Ta co hng s in mi phc tng i cua t c biu din nh sau: 60 jp c trng cho tinh cht in mi 60c trng cho tinh cht dn in.Ta thycang ln thi t cang co tinh dn in hn.(1 im)- Vi = 104m thi 4 600 10 . 10 . 60 603 4 >> . Ty ta suy ra c t co tinh dn in tt.Vy vi song cc dai = 104 105 m thi t co tinh dn in tt.- Vi = 10 m 4 06 , 0 10 . 10 . 60 603 a: I Inii 1rIH 2- Trng hp rb thi0 01 H I I Inii- Trng hp a r b thi I Inii 1rIH I r H22 . (2 im)Khoa cng ngh thng tincng ho x hi ch ngha vit nam B mn in t vin thngc lp - T do - Hnh phc

THI S 14Mn: L thuyt trng in tThi gian : 90 phtHnh thc thi : VitCu 1 : (3 im)Trnh by v hng sin mi phc vago c tiu hao in mi trong trng iu ho a.Cu 2 : (3 im)Hy trnh by v hiu ng b mt vt dn.Cu 3 : (2 im)Cho mt hinh cu tich in ban kinh laa. Giasin tich phn phu trn bmt cua novi mt in tich mt s = Q/4a2. Tinh cng in trng tai nhng im ngoai va trong hinh cu.Cu 4 : (2 im)Cho tham s in cua t kh:Hng s in mi tng i 4 dn in ring = 10-31/m.Chng to rng i vi song c c dai( = 104 105 m) thi mt t co tinh dn in tt hn, con i vi song c c ngn( = 10-3 10 m)thimt t co tinh dn in kem.p n:Cu 1 : (3 im)- Tphng trinh 1 cua Maxwell dang bin phc: ngm m mmJ J E j H rot+ + .0Va ta co m m E J . ngm m mmJ E E j H rot + + . .0 ngm mmJ E j j H rot + ) (0 ngm m pmJ E J H rot + . Trong o : j p la hng s in mi phc tuyt i cua mi trng jpp 0la hng s in mi phc tng i cua mi trng.fcf jp ; 2 ( 60Co th chng minh rng ty s gia phn a o va phn thc cu a p la : la ty s in dn va in di ch, no c trng cho tiu hao trong mi trng in mi.t tg=; la goc tiu hao in mi Nu la cht in mi: tg< 0,001 Dn in: tg> 100 Ban dn 0,01 < tg>1) ta c :2 (1)Khi rt ln th cng rt ln dn n suy gim cng nhiu, ta thy bin cng trng suy gim rt nhanh khi truyn vo trong vt dn. Ngha l sng in t ch tn ti mt lp rt mng st b mt ca vt dn in tt. Khi cho dng in cao tn chy trong vt dn in tt ngi ta cng thy dng in ny ch tn ti trn mt lp theo nh lut m.Jd = Ei vi dng kho st:E=Eme-ze-jzJd = Eme-ze-jz =J0e-ze-jz(2)J0 l mt dng chn b mt vt cht J0 = Em (1 im)Mt dng in s gim dn khi i vo su trong vt dn theo quy lut ging nh bin cng in trngHin tng sng in t hay sng in cao tn khi truyn trong vt dn in tt ch tp chung mt lp rt mng trn b mt ca n gi l hiu ng b mt, hay hiu ng Skin c trng cho hiu ng b mt ngita a vo khai nim thm su ca trng hay su thm nhp ca trng , l khong cch m ng vi n bin cng trng suy gim i e ln: e 2,718Ta c : ee Ee Ezmzm + ) ( e = esuy ra = 1/ 2 1 (2 im)Hiu ng b mt c p dng trong thc t (m vng, bc), khi lm gim tiu hao khi truyn sng in t ngi ta ch m mt lp mng vng hoc bc ln b mt kim loi.Khi tnh ton cc bi ton ngi ta thy khi nim tr khng mt ca kim loi: ZS = RS + XSRS l tr c trng cho cng sut tiu hao 2SRXS l cm khng ca mt ring ZSVn tc pha: 2 pVpha(3 im)Cu 3 : (2 im)Ap dung phng trinh 3 cu a Maxwell dang tich phn:q S d DSLy S la mt cu ban kinh a. Do tinh cht i xng nn D tai moi im trn hinh cu la nh nhau24 . r D S d DS (1 im)a) Xet trng hp thnht: im M ngoai hinh cu(r>a)Ta co: q = QD.4 r2 = Q = S.4 a2D = S.(a2/r2)b) Trng hp th hai: im M trong hinh c u(r> . Ty ta suy ra c t co tinh dn in tt.Vy vi song cc dai = 104 105 m thi t co tinh dn in tt.- Vi = 10 m 4 06 , 0 10 . 10 . 60 603 0 la mi trng dn in, cu th la kim loai ng co dn in ring 0 0 07; ); / 1 ( 10 . 8 , 5 m, theo phng truc z truyn mt song thng ng nht vi tn s f = 105Hz. Hay xac inh vn tc pha, bc song, tr khang song, h s suy giam va thm su cu a trng() trong kim loai ng cua song. Bin cng trng se giam i bao nhiu ln so vi b mt kim loai khi song i su vao c mt khoang d = 1mm.p n:Cu 1 : (3 im)Maxwell coi nh lut Gauss v nguyn l lin tc ca t thng p dng choctrnghpintrngvttrngltnh, khngi cngnhvi trng hp tng qut ca in t trng bin thin theo thi gian. Ta c:Q dV S d DV S (1)0 dV B divV (2)V th tch V l tu nn nhn c cc phng trnh Maxwell th 3 v th 4 nh sau: Ddiv (3)0 B div (4)(1 im) tin cho vic theo di, ta vit phng trnh Maxwell thnh hai dng sau:Dng tch phn:0tBtDSS + S d BQ dV l d DS d l d ES d S d J l d HSV SlS l (5)Dng vi phn:0 B divD + divtBE rottDJ H rot(6)(2 im) ngha vt l ca phng trnh 3 v 4 ca Maxwell: DDiv 0: ta thy ng sc ca in trng l nhng ng cong khng khp kn m c im u ti in tch +q, im cui ti q. DDiv = 0: in trng sinh ra ch do s bin thin ca t trng. ng sc ca n hoc khp kn hoc tin ra v cc. 0 B Div ng sc ca t trng va khp kn va tin xa v cc.(3 im)Cu 2 : (3 im)Trang thai ring quan trong th 2 la t trng do dong in khng i tao ra. y la trang thai dng cu a trng in t: J 0, 0 t'E DD d i vE r o t.0 (1)'H BB d i vJ H r o t0 (2)Tng tnh trng tinh in, i vi trng dng ta cung conhng nhn xet sau:- in trng va ttrng dng khng c lp vi nhau na ma lin tuc vi nhau thng quaJ .- Trng dng co0 E rot nn in trng dng la mt trng th co tht lgrad E - Ttrng dng co tinh cht xoay vi) 0 ( J H rotnn khng th dung thmva co th biu din qua bin mi m A rot B (3)Vi0 m A divrot B div trong o m A la vec t th, ta co:m m m A A graddiv J A rotrot2 xacinhm Antri thi tathmmt iukintuyy. ngiantaly 0 m A div J Am 2(4). Biuthc(4)goila phngtrinhPoisoncho m A. Phng trinh vec t nay tng ng vi (5) phng trinh sau:' zzyyxxJ AJ AJ A222(5) (1 im)Nghim cu a phng trinh (5) la dVrJAVz y xz y mx, ,, ,4(6)Dang ve c t cu a no la: dVrJAVm4 (7)Biu thc xac inh BvaH la:dVrJrot BV4(8)dVrJrot HV 41(9)Trng hp dong in chay trong dy dn co thit din ngang nho co th boqua so vi chiu dai dy dn vakhoang cach tdy n im quan sa t. Ve c t th luc nay co dang: l S l S lmrl d Is d Jrl dl d s drJA4 4 4(10)Va lrl drotIH 4 (11) hay lrl drotIH 4(12)(2 im)Ap dung hng ng thc vec t:[ ] v rot v grad rotv + . ly l d vr ;1 ta co:l rotdrl drgradrl drot1.1+1]1

Bi vitrng c tinh im quan sat M vi to a x, y, z ma l d khng phuthuc vao im M nn0 l rotd 1]1

l drgradrl drot .1, va20 1rrrgrad thay vao biu thc (12) ta co:[ ]lrr l d IH20 .4(10)Biu thc (10) labiu thc dang ti ch phn cu a inh lut Bixava. Con dang vi phn nh sau:[ ]20 ..4 rr l d IH d (11)Kt lun: inh lut Bixava lahquacua phng trinh Maxwell i vi trng dng.(3 im)Cu 3 : (2 im)Ap dung phng trinh 3 cu a Maxwell dang tich phn:q S d DSLy S la hinh tru thng dai v han D tai moi im trn din tich xung quanh(Sxq) cu a hinh tru nh nhau.Ta co: Sxq = 2r.l (l ) va q = L.l D.Sxq = q vaD.2rl = L.l rDL2Ma D = E rEL2(1 im)Th tai im ca ch truc mt khoang r la: drrr d EMLM 2Tng ttai im cach truc mt khoang x:in trng:xEL2Th: dxxx d ErLr + 2 CrxLrL+ + 1ln2ln2 (2 im)Cu 4 : (2 im)Ta c ln nn7 , 4782210 . 8 , 5 . 10 . 4 . 227 7 fVn tc pha: 4 , 5607 , 112010 . 2 25 fvphaMa 3510 . 604 , 5104 , 560 fvphaVa 12000 CZ47 710 . 09 , 210 . 8 , 5 . 10 . 4 . 22 f(1 im)Ta co : ) cos( . z t e E Ezm (1) ma trn b mt thi z = 0 nn bin cua phng trinh (1) la Em.Khi song i su mt oan d = 1mm, luc o bin cua phng trinh (1) ladm e E.bin song suy giam: 119.. 103 e n l ee E Eddmmln(2 im)