Lí thuyết trường điện từ

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    18-Dec-2014

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  • 1. Nguyn Cng Phng L thuyt trng in tL thuyt trng in t Dng in & vt dn
  • 2. Ni dung 1. Gii thiu 2. Gii tch vct 3. Lut Coulomb & cng in trng 4. Dch chuyn in, lut Gauss & ive 5. Nng lng & in th 6. Dng in & vt dn 7. in mi & in dungg 8. Cc phng trnh Poisson & Laplace 9. T trng dng 10. Lc t & in cm 11. Trng bin thin & h phng trnh Maxwell 12. Sng phng 13. Phn x & tn x sng phng Dng in & vt dn 2 13. Phn x & tn x sng phng 14. Dn sng & bc x
  • 3. Dng in & vt dn Dng in & mt dng inDng in & mt dng in Vt dn kim loi Tnh cht vt dn & iu kin b Tnh cht vt dn & iu kin b Phng php soi gng Bn dn Bn dn Dng in & vt dn 3
  • 4. Dng in & mt dng in (1) Cc ht in tch chuyn ng to thnh dng inCc ht in tch chuyn ng to thnh dng in dQ I dt n v A (ampre) Dng in l dng chuyn ng ca cc ht mang in dt Dng in l dng chuyn ng ca cc ht mang in tch dng Dng in & vt dn 4
  • 5. Dng in & mt dng in (2) Dng in: bin thin in tch (theo thi gian) qua mtDng in: bin thin in tch (theo thi gian) qua mt mt, n v A Mt dng in: J (A/m2) g ( ) Gia s ca dng in qua mt vi phn mt vung gc vi mt dng in: g I = JNS Nu mt dng in khng vung gc vi mt:u d g g vu g gc v : I = J.S Dng tng: J SI d Dng in & vt dn 5 Dng tng: J. S S I d
  • 6. Dng in & mt dng in (3) vQ v z Q v S L S vQ v v S L vQ S x S L x y x vQ Q I t v x I S t xt v xSv x v xJ v xI J S x v x J v Dng in & vt dn 6 J vv
  • 7. Dng in & mt dng in (4) Cho J = 102za 4cos2a mA/m2 Tnh dng V d 1 z z = 2 J SI d J Sd Cho J 10 za 4cos a mA/m . Tnh dng in tng chy ra khi mt ng ca hnh tr. = 3 z = 1 J. S S I d 3 J . S S d z d 2 2 3 10.3 4.3cosJ a az x y = 3 z+dz d dz 3 2 90 12cosa az 3S a ad d d d d 0 z dz z3S a ad d dz d dz Dng in & vt dn 7 x +d +d d
  • 8. Dng in & mt dng in (4)V d 1 Cho J = 102za 4cos2a mA/m2 Tnh dng z z = 2 J SI d J Sd Cho J 10 za 4cos a mA/m . Tnh dng in tng chy ra khi mt ng ca hnh tr. = 3 z = 1 J. S S I d 3 J . S S d 2 2 3 10.3 4.3cosJ a az x y = 3 3 2 90 12cosa az 3 270J . Sd zd dz 3S a ad d d d d 3 2 2 270 z I zd dz 2 2 270 z zdz 2 54A 3S a ad d dz d dz Dng in & vt dn 8 1 0 270 z I zd dz 1 2 .270 z zdz 2,54A
  • 9. Dng in & mt dng in (5) J. S S I d Dng in chy ra khi mt mt kn: in tch dng trong mt kn: Qin tch dng trong mt kn: Qi nh lut bo ton in tch J. S i S dQ I d dt dt Trong l thuyt mch, I = dQ/dt v l dng chy vo Dng in & vt dn 9 Trong l thuyt trng, I = dQ/dt v l dng chy ra
  • 10. Dng in & mt dng in (6) J S idQ I d J. S i S dQ I d dt ( . ) i V dQ dv dt J ( )d dv J S J (nh l ive) i vV Q dv ( . ) S V d dv J. S J (nh l ive) ( . ) vV V d dv dv dt J v V dv t ( ) v v v t .J v t .J Dng in & vt dn 10 t t
  • 11. Dng in & mt dng in (7)V d 2 t e t e Kho st mt dng in A/m2.r e r J a 1 2 (4 ) 4 t r e I J S r re r 1 1 s, 5 m 4 5 23,1 At r I e 1 4 6 27 7 AI e 1 s, 6 m 4 6 27,7 At r I e Dng in & vt dn 11
  • 12. Dng in & mt dng in (8)V d 2 Kh d i A/ 2 t e J t e v J Kho st mt dng in A/m2.r r J a r r . av t .J 2 2 1 1 1 . ( ) (sin )r D r D D D 2 ( ) ( ) sin sin r r r r r 2 2 2 1 t t v e e r t 2 2 ( ) ( ) t t v e e dt K r K r 2 2 t r r r r t e 2 2v r r Gi s v 0 khi t , khi K(r) = 0 t t J e e Dng in & vt dn 12 3 2 C/ mv e r 2 m/sr r v J e e v r r r
  • 13. Dng in & vt dn Dng in & mt dng inDng in & mt dng in Vt dn kim loi Tnh cht vt dn & iu kin b Tnh cht vt dn & iu kin b Phng php soi gng Bn dn Bn dn Dng in & vt dn 13
  • 14. Vt dn kim loi (1) Thuyt lng tThuyt lng t Di ho tr, di dn, khe nng lng Vt dn kim loi: di ho tr tip xc vi di dn trng Vt dn kim loi: di ho tr tip xc vi di dn, trng bn ngoi c th to thnh mt dng in t Trong vt dn kim loi:Trong vt dn kim loi: F = eE Dng in & vt dn 14
  • 15. Vt dn kim loi (2) F = eEF eE Trong chn khng, vn tc ca in t s tng lin tc Trong vt dn vn tc ny s tin n mt gi tr trung Trong vt dn, vn tc ny s tin n mt gi tr trung bnh hng s: vd = Evd eE e: c ng ca in t, n v m2/Vs, lun dng VD: Al: 0 0012; Cu: 0 0032; Ag: 0 0056 VD: Al: 0,0012; Cu: 0,0032; Ag: 0,0056 J = vv J = E Dng in & vt dn 15 J = e eE
  • 16. Vt dn kim loi (3) J = EJ e eE e : mt in t t do, c gi tr m J lun cng hng vi E J lun cng hng vi E J = EJ = E d i /i d t ( ) S/ : dn in/in dn sut, (), n v S/m VD: Al: 3,82.107; Cu: 5,80.107; Ag: 6,17.107 Dng in & vt dn 16 = e e
  • 17. Vt dn kim loi (4) S E J E khng i I J. S S I d JS E L a V d L J khng i I J S .E Lab b V d .E L a b d V I L V I L S S b E.L E.Lba ab V EL V L S S L R S V RI (lut Ohm) V EL J E V J L S a ab b dV R E. L Dng in & vt dn 17 . S I d E S
  • 18. Dng in & vt dn Dng in & mt dng inDng in & mt dng in Vt dn kim loi Tnh cht vt dn & iu kin b Tnh cht vt dn & iu kin b Phng php soi gng Bn dn Bn dn Dng in & vt dn 18
  • 19. Tnh cht vt dn & iu kin b (1) Gi s c mt s in t xut hin bn trong vt dnGi s c mt s in t xut hin bn trong vt dn Cc in t s tch xa ra khi nhau, cho n khi chng ti b mt ca vt dn Tnh cht 1: mt in tch bn trong vt dn bng zero, b mt vt dn c mt in tch mt, Bn trong vt dn khng c in tch khng c dng in cng in trng bng zero (theo nh lut Ohm) Tnh cht 2: cng in trng bn trong vt dn Dng in & vt dn 19 bng zero
  • 20. Tnh cht vt dn & iu kin b (2) D S h h h w EN E a b 0E. Ld b d DN Dtt Vt dn h h w Ettcd 0 b c d a a b c d ,tai ,tai0 0 2 2 tt N b N a h h E w E E E = 0Ebn trong vt dn = 0 0h 0ttE w 0ttE 0 0tt ttD E 0tt ttD E D. S S d Q trn bncanhdi Q D S 0 0 N SD S Q S Dng in & vt dn 20 trn ;ND S 0; di bncanh 0 0N S ND E
  • 21. Tnh cht vt dn & iu kin b (3) 0tt ttD E D S h h h w EN E a b 0tt ttD E 0N N SD E DN Dtt Vt dn h h w Ettcd . 0 x xy y V d E L Tnh cht ca vt dn trong in trng tnh: 1. Cng in trng tnh trong vt dn bng zeroC g g g g 2. Cng in trng tnh ti b mt ca vt dn vung gc vi b mt ti mi im Dng in & vt dn 21 g 3. B mt ca vt dn c tnh ng th
  • 22. Tnh cht vt dn & iu kin b (4)V d Cho V = 100(x2 y2) V & P(2 1 3) nm trn bin gii vt dn khngCho V 100(x y ) V & P(2, 1, 3) nm trn bin gii vt dn khng kh. Tnh V, E, D, S ti P; lp phng trnh ca mt dn. 2 2 100[2 ( 1) ] 300 VPV 2 2 300 100( )x y 2 2 3 x y [ ( ) ]P ( )y V E y 200 200x yx y a a2 2 100 ( )x y 200 200 400 200 V/E 2, 1, 3 200 200 400 200 V/mP x y x y x y z x y E a a a a 12 2 0 8,854.10 ( 400 200 ) 3,54 1,77 nC/ mP P x y x y D E a a a a0 , ( ) , ,P P x y x y ,S P ND 2 3,96 nC/ mS P Dng in & vt dn 22 2 2 2 , 3,54 1,77 3,96 nC/ mN P PD D , ,S P