Classical Electrodynamics

Transcription

1 Fist Look t Quntu hysics Cssic Eectoynics Chpte gnetosttics Fy s Lw Qusi-Sttic Fies Cssic Eectoynics of. Y. F. Chen

2 Contents Fist Look t Quntu hysics. The etionship between eectic fie n gnetic fie. iot n Svt w n veto potenti. Diffeenti equtions of gnetosttics n pee s w. Vecto potenti n gnetic inuction fo cicu cuent oop. nogy between eectic ipoe n gnetic ipoe.6 gnetic sc potenti.7 gnetic oent.8 copic equtions bouny conitions on n H.9 ethos of soving bouny-vue pobes in gnetosttics. Unifoy gnetie sphee. Fin ek Cssic Eectoynics of. Y. F. Chen

3 . The etionship between eectic fie n gnetic fie The foce on chge cte by neby conuction wie is: n the ineti coointe the chge epeiences gnetic foce: F qv n the etive coointe whee the obsevtionis pefoe in the coointe of chge it epeiences eectic foce: F qe R net q v Cssic Eectoynics of. Y. F. Chen

4 y t y t With the tnsfotion of coointes in the speci etivity: c v j c v c v c v t t y y c v vt With the Guss s w: R E n the etive coointe: c v v q c v c v j R q qe F Cssic Eectoynics of. Y. F. Chen. The etionship between eectic fie n gnetic fie

5 . The etionship between eectic fie n gnetic fie ut when we consie the sitution in the ineti coointe: F q v qv qv This ens tht by pope tnsfotion of the coointe we cn just e with the eectic foce to sove the eectognetic pobes. Othewise the concept of the gnetic foce ust be intouce. n gene the foce cn be epesse s: F q E v Cssic Eectoynics of. Y. F. Chen

6 The gnetic fie genete by shot segent of wie cying cuent is given by: f f f Whee the vecto potenti is: Cssic Eectoynics of. Y. F. Chen. iot n Svt w n veto potenti

7 . Diffeenti equtions of gnetosttics n pee s w f f f c c c Cssic Eectoynics of. Y. F. Chen

8 s S f f f Cssic Eectoynics of. Y. F. Chen. Diffeenti equtions of gnetosttics n pee s w

9 Fo sttic eectognetics we get the pee s w: Geney the pee s w shou be oifie s the we- pee s w: t E t t t Cssic Eectoynics of. Y. F. Chen. Diffeenti equtions of gnetosttics n pee s w

10 y y y y Cssic Eectoynics of. Y. F. Chen. Vecto potenti n gnetic inuction fo cicu cuent oop

11 Cssic Eectoynics of. Y. F. Chen. Vecto potenti n gnetic inuction fo cicu cuent oop

12 Epn the enointo of with binoi epnsion:... 8 Note...!!! Cssic Eectoynics of. Y. F. Chen. Vecto potenti n gnetic inuction fo cicu cuent oop

13 & ssue et h h h q q q h h h h h h Cssic Eectoynics of. Y. F. Chen. Vecto potenti n gnetic inuction fo cicu cuent oop

14 Eectic ipoe: p n p n E p gnetic ipoe: n n Cssic Eectoynics of. Y. F. Chen. nogy between eectic ipoe n gnetic ipoe

15 . 6 gnetic sc potenti f H in fee spce : To iustte this concept we consie the pobe s foows. Fo the gnetic inuction t the point with coointe pouce by n inceent of cuent t the gnetic inuction cn be epicity epesse s: R R whee the soi nge is: R R Cssic Eectoynics of. Y. F. Chen

16 s n epe fin the gnetic inuction t point on the -is: i Diecty fin gnetic inuction: Cssic Eectoynics of. Y. F. Chen. 6 gnetic sc potenti

17 ii With the concept of the gnetic sc potenti: R R R R Cssic Eectoynics of. Y. F. Chen. 6 gnetic sc potenti

18 iii Since this pobe hs the popety of syety we cn epn the gnetic sc potenti with the hep of the Legene poynoi. esies the gnetic sc potenti t ny point cn be obtine with the knowing the gnetic sc potenti on the -is: Fo < : Epn with the binoi epnsion n note tht the constnt te of the cn be oppe without oss:...!!! 6 Cssic Eectoynics of. Y. F. Chen. 6 gnetic sc potenti

19 Cssic Eectoynics of. Y. F. Chen. 6 gnetic sc potenti

20 b Fo > : Epn with the binoi epnsion n note tht the constnt te of the cn be oppe without oss: !!! Cssic Eectoynics of. Y. F. Chen. 6 gnetic sc potenti

21 The figue beow shows the siution of the gnetic sc potenti viewe fo i is with the petes of =.n =: Cssic Eectoynics of. Y. F. Chen. 6 gnetic sc potenti

22 .7 gnetic oent Fo ocie cuent ensity we cn use Tyo epnsion:... no gnetic onopoe i i Cssic Eectoynics of. Y. F. Chen O

23 n the tet book it is pointe out tht: j j i j i i j j i j i j j i j i t is custoy to efine the gnetic oent: Consequenty the gnetic ipoe vecto potenti is: n the gnetic inuction outsie the ocie souce is: n n Cssic Eectoynics of. Y. F. Chen.7 gnetic oent

24 H gnetition: i N i i With the buk gnetition n opic cuent ensity: S f f f V V s Cssic Eectoynics of. Y. F. Chen.8 copic equtions bouny conitions on n

25 intepet: H f the tei is ine: : ignetic pgnetic : : H ouny conitions: the se iscussion s fo the eectosttics sufce cuent ensity is whee : : K K H H H t t n n Cssic Eectoynics of. Y. F. Chen H.8 copic equtions bouny conitions on n

26 .9 ethos of soving bouny-vue pobes in gnetosttics Geney ppicbe etho of the vecto potenti: if H H choose Couob guge : : oisson eqution gnetic sc potenti H H if H : Lpce eqution Cssic Eectoynics of. Y. F. Chen

27 H feognetic given oisson eqution : n efine H H i n fee spce n no sufce contibution: ii With sufce contibution: n Cssic Eectoynics of. Y. F. Chen.9 ethos of soving bouny-vue pobes in gnetosttics

28 oeove:...* f f f S n f f f Cssic Eectoynics of. Y. F. Chen.9 ethos of soving bouny-vue pobes in gnetosttics

29 Note tht the epession * is geney ppicbe even fo the iit of iscontinuous contibutions gnetic sufce chge ensity: Sufce chge contibution Cssic Eectoynics of. Y. F. Chen.9 ethos of soving bouny-vue pobes in gnetosttics

30 Consie sphee of ius with unifo penent gnetition of gnitue n pe to the -is: - syetyn eebe : n * e Y Y n i Cssic Eectoynics of. Y. F. Chen. Unifoy gnetie sphee

31 y othogonity : - Y nsie the sphee: Outsie the sphee: Cssic Eectoynics of. Y. F. Chen. Unifoy gnetie sphee

32 . Unifoy gnetie sphee The gnetic sc potenti n the ines of n H e shown beow. The ines of e continuousy e pths but those of H teinte on the sufce becuse thee is n effective sufce chge ensity. Cssic Eectoynics of. Y. F. Chen

33 Fin the gnetic ipoe oent of unifoy chge spheic she of ius otting with ngu fequency bout the -is: V q T T q t q We cn use this oe to epin soe gnetie behvio of the toic syste. ẑ e Cssic Eectoynics of. Y. F. Chen. Fin ek