# Chapter 1 Electromagnetic Field Theory

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1 hpe ecgeic Fie The - ecic Fie ecic Dipe Gu w f : S iegece he ε = 6 fee pce. F q fie pi q q 9 F/ i he. ue e f icee chge: qk k k k ue uce ρ Sufce uce ρ S ie uce ρ qq qq g. Shw h u w F whee. q Pf F q S q q q q F g. Deeie he eecic fie iei f ifiie g ie chge f uif ei ρ i i. S. S

2 g. Deeie he eecic fie iei f ifiie p chge wih uif ufce chge ei ρ. A S. S S A A g. A ie chge f uif ei ρ i fee pce f eicice f iu. Deeie he giue ieci f he eecic fie iei he cee f he eicice. [ 高考 ] S. i i g. Deeie he eecic fie cue pheic cu f eec wih ue chge ei ρ=-ρ f h ρ e piie ρ= f >. [ 交大電子物理所 ] S. S S S S i i g. A chge i pu hi pheic he f iu. Deeie he eecic fie iei i pi iie he he. [ 台大電研 ] S. S S S S c c c c

3 ecic ipe: A pi f equ u ppie chge wih epi. ] [ ] [ ] [ ] [ / / / ] [ P P q q c i c p p p p p i c p g. A wh ue f θ e he eecic fie iei f -iece ipe he -cpe. S. i c p i c N -cpe i i c c θ=5.7 5.

4 - Sic ecic Pei p ecic pei ue pi chge: p q q q p p ecic pei ue icee chge: qk k k ecic pei ue eecic ipe: q f << we he c c c c q c p q p p c i Sc eecic pei ue iu chge iiui: ue uce ρ. Sufce uce ρ S ie uce ρ Ne:. i c u i ec.. i i i he ic M fie.

5 g. Oi fu f eecic fie iei g he i f uif ie chge f egh. The uif ie-chge ei i ρ. [ 高考 ] S. / / / / / g. A fiie ie chge f egh cig uif ie chge ei ρ i cicie wih he -i. Deeie i he pe iecig he ie chge. S. / / / / g. A chge i iiue uif e que pe. Deeie pi he i pepeicu he pe hugh i cee. S. / /

6 g. A piie pi chge i he cee f pheic cucig he f ie iu i ue iu. Deeie fuci f he i ice. [ 高考 ] S. > S i << < i i i g. A chge i iiue uif e he w f cicu ue f iu heigh h. Deeie i i pi uie he ue pi iie he ue. S. h h h h h h i h h

7 g. ie w pheic cuc wih ii > h e cece wie. The ice ewee he cuc i e ge i cpi h chge pheic cuc e ciee uif iiue. A chge i epie he phee. Fi he chge he w phee he eecic fie ieiie he phee ufce? S. g. Oi fu f he eecic fie iei he i f cicu ik f iu h cie uif ufce chge ei ρ. [ 高考 ] S. / / / / A >> / g. Mke w-iei kech f he equipei ie he eecic fie ie f eecic ipe. S. F eecic ipe c q =c c c k whee k i c. k i i c i i c

8 - Mgeic Fie Mgeic fie: H M whee μ =π -7 A/ i he fee pce. Mgeic fu ei: Apee w f H : H H M M H M H H M H H whee Gu w f : S A fufi A S A A A he A A Ne: i c Pi equi A W/ S A S A W Mgeic fu: i-s w: S S A f G f G f G A

9 Ne: he g. A iec cue fw i igh wie f egh. Fi he geic fu ei pi ce ice f he wie i he iecig pe. S. g. Fi he geic fu ei he cee f que p wih ie w cig iec cue. S. w w i hi ce w w w w w g. Fi he geic fu ei pi he i f cicu p f iu h iec cue. S. ẑ. ce f = g. Deeie he geic fu ei pi he i f ei wih iu egh wih cue i i N u f ce wu ci. ] [ N S. N N

10 Apee w f : whee μ=μ i he fee pce. c g. A ifiie g igh cuc wih cicu c eci f iu cie e cue. Deeie he geic fu ei h iie uie he cuc. [ 交大光電所 ] S. ie he cuc : Ouie he cuc: => g. A g ie cig cue f ck wih eicicu e f iu. Deeie geic fu ei he cee pi P f he e. [ 高考 ] S. whee g. A cue fw i he ie cuc f ifiie g ci ie eu i he ue cuc. The iu f he ie cuc i he ie ue ii f he ue cuc e c epecie. Fi he geic fu ei f egi p eu. [ 高考電機技師 ] S. c c c g. Deeie he geic fu ei iie ifiie g ei wih i ce hig ce wu u pe ui egh cig cue. S. =>

11 g. The figue hw ifiie g ei wih i ce hig ce wu u pe ui egh. The wiig e e ge α c cue. Deeie he geic fu ei h iie uie he ei. S. i i c g. Deeie he geic fu ei iie ce wu i ci wih i ce hig N u cig cue. The i h e iu he iu f ech u i. S. N N -<<+ f <- >+ g. cei epeie i i eie he egi f c geic fu ei. Thi c e cee i ff-cee ciic ci. The uif i cue ei i. Fi he giue ieci f i he ciic ci whe i i ipce f h f he cucig p ice. [ 台大電研 清大電研 中原電機 ] S. e ei f h F - i he he pi A

12 - ecgeic Fce e fce equi: q F ecic fce:. Mgeic fce: q F e q F g. A eec i ijece wih iii eci i egi whee h eecic fie geic fie ei. Decie he i f he eec if. Dicu he effec f he eie giue f he eec ph i p. S. e e e e ; i c c i c c c c c f Mgeic fce ue : q q F q F F g. Deeie he fce pe ui egh ewee w ifiie g pe cucig wie cig cue i he e ieci. The wie e epe ice. [ 清大電研 ] S. F F

13 g. cue he fce pe ui egh ech f hee equii ifiie g pe wie p ech cig cue f i he e ieci. Specif he ieci f he fce. S. c f g. The AA ee cucig ph f he cue i w e g pe ie. The ie he iu e pce ice p. Fi he ieci he giue f he geic fce he. [ 中山物理所 ] S. F F F Appici f he eecic fce: The e-ppe

14 Sc eecic pei fuci: ec geic pei fuci: A ee pei: / A

15 -5 F w Mgeic Dipe F w: S S A A A A fufi A Ne: ic fie: u i ie-ig fie: f:. Mgeic fu: S S Mi ef: F q F q S S g. A cicu p f N u f cucig wie ie i he -pe wih i cee he igi f geic fie pecifie c i whee i he iu f he p ω i he gu fequec. Fi he ef iuce i he p. 8 S. [ c i ] [ ] i N 8N c g. A e ie e pi f cucig i i uif geic fie wih c eci. Deeie he pe-cicui ge h ppe c ei. Auig h eice i cece ewee he w ei fi he eecic pwe iipe i. Negec he eecic eice f he e f he cucig i. [ 交大電子物理所 ] S. h

16 h h W P e g. The cicui i Fig. i iue i geic fie μt. Auig =5Ω fi he cue i. [ 中山物理所 ] S. c [c5.6 c5 ] i 7.76i5. 7 c5 g. A cucig iig cie e w pe cucig i i iui ig geic fie 5c T. The pii f he iig i gie =.5-cω he i e eie i eice =. Ω. Fi i. S. 5c..7 =.5-cω i i.75 i c g. The F ik gee ci f cicu e ik ig wih c gu eci ω i uif c geic fie f fu ei h i pe he i f i. uh cc e he pe-cicui ge f he gee if he iu f he ik i. S. [ ]

17 Mgeic ipe e: = S whee S i he e f he p h cie =S. ec pei f geic ipe: A whee A c i g. F he ecgu p wih ie h cie cue. Fi he ec geic pei A i pi P. A eeie he geic fu ei A. [ 交大光電所 ] S. A whee = A c i Mgeii ec: M k i k A/ whee k i he geic ipe e f. M A M M M M M A F F S M M S Mgeii ue cue ei: M A/ Mgeii ufce cue ei: M â A/ quie Mgeii hge Deiie: Ne: P P S M M S S Defie he geii ufce chge ei M he geii ue chge ei M

18 g. A cicu f geic ei wih peeii μ i iee ci i he g ei. The iu f he i e h he ie iu f he ei. The ei wiig h u pe ui egh cie cue. Fi he ue f H M iie he ei f < f <<. Wh e he equie geii cue eiie f he geie? [ 清大電研 ] S. < : H M H < < : M H M M g. A fegeic phee f iu i uif geie wih geii M M. Deeie he equie geii cue eiie. Deeie he geic fu ei he cee f he phee. [ 台大電研 ] S. M c i M M i i M i M i M. g. Deeie he geic fu ei he i f uif geie cicu cie f geic ei. The cie h iu egh i geii M M. [ 台大物研 ] S. M M M M M M

19 g. A ciic ge f iu egh h uif geii M M g i i. Ue he equie geii chge ei ccep eeie he geic fu ei i i pi. [ 交大電子所 ] S. M M p M ρ = i he iei egi iew q q M A M c M T c whee M T M q c M T c i T ie ifiie g ei wih u pe ui egh u cee geic fie; ge = i iuce ui egh which ppe he cue chge. Pwe P =- pe ui egh u e uppie ece hi iuce ge i e icee he cue. The wk pe ui ue equie puce fi geic fu ei f i W = H. f

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