vDt ? ¨ i? b?¥áè? o ? p 7-1 ü9è? è 1 Q¥]B?è?s? ?s B?s ( s?1 o  6B?s ( s? o  P ? ì-W¥ o  ??z·h£μ? ? X?1 o¥é  M" 5.98×l0 24 kg  o¥é  m=7.34×l0 22 kgb  1 p Q ¥Kl′  2 ?Tè? s ¥Dé ??1 p Q¥′b 3  1 ! Qs? q 1 aq 2 ?s? 5iμ 22 21 r Mm G r qq k =  ? 0 4 1 πε =k ' 2 2 21 q kq GMm qqQ +=+= b p′ 7 0'=Q ¤ 01 2 2 =? kq GMm C1069.5 13 2 ×==∴ k GMm q  C1069.5 13 2 1 ×== kq GMm q  C1014.1 14 21 ×=+= qqQ  2 21 q m q M =Q  k GMm qq = 21 k GMm mqmqMq ==∴ 21 2 2 3¤ C1032.6 12 2 2 ×== k Gm q  C1015.5 142 1 ×== m Mq q  C1021.5 14 21 ×=+=∴ qqQ 7-2 ??è  1 –q ¥? è?òbHé1 l ¥ ?H ???¥ ????  è? Q Q# 0b ???¥ ×? b1 P ??μè? s ?1 , Q′?1v$ q? q?q? ll l r Q r r 3 Q?? ?¥  ?1 lr 3 3 =  QD -q¥Mo ? ?1 2 0 1 4 1 r qQ F πε =  ? -qW¥ Mo ? ?1 2 2 0 2 4 1 l q F πε = 5iμ ' 1 0 2 30cos2 FF = 2 0 2 2 0 4 1 300cos 4 1 2 r qQ l q πεπε =× 3¤ qQ 3 3 = è? < 7-3 ?m 7-3 ? U μBé l¥{è%?b  1 è ? ( s? L á1 +λ 5?  e? x)¥Lí dx P ?¥?è? q 0 ¥è? ?1?$ q 0 s¥9è? ?1?$  2 ? è ?L á λ=kx k1?è ?  pP?¥è ? <b q 0 a λ l P x m 7-3 O 3  1L í dx ?{è 1 xq dd λ=  ? q 0 ¥è? ?1 2 0 0 2 0 0 )( d 4 1 )( d 4 1 d xal xq xal qq F ?+ = ?+ = λ πεπε q 0 s¥9è? ? )(4)( d 4 0 0 0 2 0 0 ala lq xal xq F l + = ?+ = ∫ πε λ πε λ 0 0 >q H Z_ £ ü_· H Z_ £ ü_P 0 0 <q 25 vDt ? ¨ i? b?¥áè?  2 x) |Lí dx  ¥è  xkxxq ddd ==λ  ? P? ¥è? <1 2 0 2 0 )( d 4 1 )( d 4 1 d xal xkx xal q E P ?+ = ?+ = πεπε )ln( 4)( d 4 0 0 2 0 al a a lk xal xxk E l P + += ?+ =∴ ∫ πεπε Z_ xà?_b 7-4 B??1 R ¥ '? ???%?  ? ( {è  +q/? (  {è  -q ?m 7-4 ? U p? ???)è? <b 3 y ? ? m ? U¥US"??? V? +q ? -q  O ?è? < x à¥s -?1 ,b |é1 dl ¥Lí   ?{è 1 + + + + R m 7-4 θ π θ π π λ d 2 d 2 d 2 1 dd q R R q l R q lq ====  2 0 d 4 1 d R q E πε =∴ Z_ ? m yZ_¥s  θ επ θ θ πε cos 2 d cos d 4 1 d 2 0 22 0 R q R q E y ?=?= j R q j R q E vvv 2 0 2 2 0 2 0 2 dcos 2 2 επ θθ επ π ?=×?=∴ ∫ 7-5B??1 R¥? o T ( {μè?è? ? á1 σ  p o?)è? <b 3 ? o ?¥?ày ? xà USe?1 o? Ob x R O r  o ?  |??1 ra z1 dl¥ì{  ?m  ?1 θππ d2d2d RrlrS ?==  ?{è? θπσσ d2dd RrSq ??== dq O)á 3¥è? <1 2 3 22 0 2 3 22 0 )( d 2 )( d 4 1 d rx xrR rx qx E + = + = θ ε σ πε θsinRr =Q  θcosRx = θθθ ε σ dcossin 2 d 0 =∴ E y1 o ?  ?μì{ O)á 3¥è? <Z_M] iiE vvv 0 2 0 0 4 dcossin 2 ε σ θθθ ε σ π ==∴ ∫ 7-6 BíKv ( {è üe ?è? á1 σ  üe??μB??1 R ¥? d ?m 7-6 ? Ub p? d ??àL ¥? <s?b  4 U ?¨í kve?? ?¥è?#? <?Fe ? 3 ?¨? êE|? d AT?? ¥?aμè?×?7?'?r1B? σ P R m 7-6 ??¥{èí kv üe?B?è? ? áMQ¥? ??F7?b í kv üe¥è?1 n eE v v 0 1 2ε σ = 26 vDt ? ¨ i? b?¥áè? ? ??¥è?1 n e Rx x E v v )1( 2 22 0 2 + ??= ε σ  ? n e v 1 üe?EL¥?ê O b ? d??àL ¥è? <1 n e Rx x EEE v vvv 22 0 21 2 + =+= ε σ èY  7-7 è? < 1 E v ¥ <è? Z_D??1 R ¥? o ?¥?à ü? ?m 7-7 ? U pYV?? o ?¥è? <Y b 3 T?? 1 R¥ ü ? S’D? o ? S?B?>? w ????>? w ? =íè??ú ?? ? 0ddd '' =?+?=?=Φ ∫∫∫ + SSSS SESESE vvvvvv m 7-7 E v R ERRESESE SS S 22 ' cosdd πππ =??=??=?=Φ∴ ∫∫ vvvv 7-8 BHé 1 a¥ ?Z8??° ?US" ? ?m 7-8 ? UbC bW? μBd (  è? jEikxEE vvv 21 )( ++=  E 1 aE 2 1è  pè? ?Z8òV ?#?? ?Z8V ?¥è? <Y b 3 0= z EQ 0=Φ=Φ∴ DEFGOABC z y x D G F E O C B A ∫∫ ==?++=?=Φ SS ABGF aESEjSjEikxESE 2 2221 )(d])[(d vvvvv ∫∫ ?=??++=?=Φ SS CDEO aEjSjEikxESE 2 221 )d(])[(d vvvvv ∫∫ ?=??+=?=Φ SS AOEF aEiSjEiESE 2 121 )d()(d vvvvv ∫∫ +=?++=?=Φ SS BCDG akaEiSjEikaESE 2 121 )()(d])[(d vvvvv m 7-8 ?? ?Z8V ?¥è? <Y  3 ka i i =Φ=Φ ∑ ú ?? ? 7-9μ ?] ?¥ ( {è o ? =???sY1 R 1 ? R 2  X?? o ?¥è? ? á1 +σ   ? ?ò)¥ è? <? ^ ,b k p  1 = o ? ¥è? ? á  2 ? o ?[ = bW¥è?s?b 3 TB? ?1 r¥]? o ?1ú ? ?b ! = o ? ¥è? ? á1 'σ b  1 )y1? o ??¥è? <))1 ,?ú ?? ?μ 2 Rr > 0)4'4( 11 d 2 1 2 2 00 3 =?+?==? ∑ ∫ RRqSE i i S πσπσ εε vv ¤ σσ 2 1 2 )(' R R ?=  2?ú ? ? ? 0 11 =< ERr v 27 vDt ? ¨ i? b?¥áè? 21 RrR << 2 1 0 2 4' 1 d RSE S πσ ε ?=? ∫ vv ' 2 1 0 2 2 4' 1 4 RrE πσ ε π ?=? 2 0 2 2 2 0 2 12 1 2 2 0 2 1 2 )( 4 4' r R r R R R r R E ε σ ε σ πε πσ ?=??= ? =∴ Z_? _Q_ 7-10 Bí Ké¥ ( {è à°?c =???sY1 R 1 ? R 2 àLZ_?êé¥è sY1 λ 1 ? λ 2 b 1 p ò u× =¥? <s?  2 ? λ 1 " λ 2  f ? ??$?N f?/¥ E j r¥1" wLb 3  1T B??1 raé1 h¥ à?? ?1ú ? ??ú ?? ?μ 0 11 =< ERr v 21 RrR << hSE S 1 0 2 1 d λ ε =? ∫ vv hrhE 1 0 2 1 2 λ ε π =?∴ ¤ r r E ? 2 0 1 2 v v πε λ = E r O 1 R 2 R 2 Rr > hSE S )( 1 d 21 0 3 λλ ε +=? ∫ vv ¤ r r E ? 2 0 21 3 v v πε λλ + =  2 21 λλ ?= H 0 1 =E v  r r E ? 2 0 1 2 v v πε λ =  0 3 =E v 7-11 !?? 1 R¥ o8  è?8 á ρ ═ kr r ≤ R  ? k1è  r1  o?¥  ?b pè?s? i ? E j r¥1" wLb 3 TB? ?1 r¥]? o ?1ú ? ?b? ú ?? ? Rr < 4 0 0 2 00 1 1 d4 1 d 1 d krrrkrVSE r VS π ε π ε ρ ε =?==? ∫∫∫ vv E r O R ' 4 0 2 1 1 4 krrE π ε π =? ¤ r kr E ? 4 0 2 1 v v ε = Rr > 4 0 0 2 0 2 1 d4 1 d kRrrkrSE R S π ε π ε =?=? ∫∫ vv ' 4 0 2 2 1 4 kRrE π ε π =? ¤ r r kR E ? 4 2 0 4 2 v v ε = 7-12B¨ 1 d=0.5cm¥ íKv üe ( {èè?8 á ρ ═ 1.0×10 -4 C/m 3  p  1 üe = ?¥è? s?  2 ) ? üe?[# üe =D V ?M  0.1cm) ¥è? <b 3  1 ! ? ? ü ?1 S 0 b? ??   S 0 )1 x)?1 |  ? (1 S? ¥? ?TB???ú ? ? § ?De ?<° ?m ? U ' § ?¥èY 1 ,b 2 d x < H SxSESE S ??=?=? ∫ ρ ε 2 1 2d 0 11 vv  xE 0 1 ε ρ =∴ 28 vDt ? ¨ i? b?¥áè? S? S? 0 S d x x 2 d x > H S d SESE S ???=?=? ∫ 2 2 1 2d 0 22 ρ ε vv  0 2 ε ρd E =∴  2 üe?  0=x 0 0 =∴E üe = DV ?M  0.1cm) cm15.0=x 4 12 34 0 1069.1 1085.8 105.1100.1 ×= × ××× ==∴ ? ?? ε ρx E V/m 7-13B ? è ?8 á1 ρ è ¥ o8b 1 £ ü o =  o? r )B ?¥è? <1 rE v v 0 3ε ρ =   2 ? o =? ?B?l o ?m 7-13 ? U£ ül o b 8 =¥è? ^ <è? aE v v 0 3ε ρ =  T? a v ^ o?? b 8??¥  ? O b R O O’ a v r v 'r v P £  1T D o8]?¥ o ?1ú ? ?? ú ?? ? ∫∫ =? VS VSE d 1 d 0 ρ ε vv ' 3 0 2 3 4 4 rrE π ε ρ π ?=? rE 0 3ε ρ =∴ O  T rE v v 0 3ε ρ = ¤£  2A E ! b 8?A è? ásY1 ρ? - ρ¥è? o8??è? ásY1 ρ? - ρ¥ v o8?l o8b  8 = ?B? P ?m ? 1¥ 2Tμ v o rE P v v 0 1 3ε ρ =  l o ' 3 0 2 rE P v v ε ρ ?= arrEEE PP vvv vvv 00 21 3 )'( 3 ε ρ ε ρ =?=+= ¤£ áè?¥ì ^? ? 7-14 ?è? ? B?sè?L¥? ^[ O?1??¥]???b£ ü??s ò?¥è? <??D? ? ? O?¥  ??Q1' E 1 r 1 = E 2 r 2 b O θ r 2 r 1 £ TBí ^ abcd ? mb? áè?ì ^? ? 0ddd 221121 =?=?+?=? ∫∫∫ lElElElElE dabc vvvvvv a b c d 1 l 2 l 2 r 1 r θ O ' 2211 lElE = m 7-14 θ 11 rl =Q θ 22 rl =  2211 rErE =∴ ¤£ 29 vDt ? ¨ i? b?¥áè? 7-15 £ ü áè?? Oè?L ? ^ ü?° L¥1Z è? <¥ vlA?) )M?b  4 U ?¨ ì ^? ??ú ?? ? £ !è? Z_ £ ü_·bBè?L  ? | ? 1? 2 T ? ?@l¥?? ? ?mb?ú ?? ? 0ddd 1212 =?????=?+?=? ∫∫∫ ?? SESESESESE SSS vvvvvv E v 12 12 EE =∴ ']Bè? L  ?i ?¥è? <M?b TB ?í ^ abcd  ? abacdD è?L<° bcadaD è?L ü?'μ cbda EEEE ==  E v a b c d ?áè?ì ^? ? ∫∫∫∫∫ ?+?+?+?=? dacdbcab lElElElElE vvvvvvvvvv ddddd ∫∫ ?+?= dabc lElE vvvv dd 0=???= lElE ab ab EE =∴ '?]è ?L  ?i ?¥è? <M?b ?[ 5? ?b è? ?¥??è ] ? 7-16 Hé1 a ¥? ??? , ????  òb? q q ? 2q ¥? è? pN ???×? ¥è ]b|Bè 1 +Q¥?è??íKù)M?×? ? ?S? $ 3 ??? ×?¥  ? ar 3 3 = ×?¥è ]1 a q r q r q r q U 0000 2 3 4 2 44 πεπεπεπε ?= ? + ? += ? ? ?S¥? a qQ QUUUQA 0 00 2 3 )( πε ?==?= ∞? 7-17 ?m 7-17 ? U ? ??è? Q 1 aQ 2 aQ 3 B°L? b? O Q 1 =Q 3 =Q ? ?B?è? ? s? ? (1 ,b p Q 1 aQ 3 %? f ?/  1 Q 2  O? H¥ è ] ?  2| Q 2 V O? w?í kù )? ? ? S ¥?b Q 1 dd O Q 2 Q 3 3  1 Q 1 ? Q 3  O?á 3¥è ]1 d Q d Q d Q U 00 3 0 1 0 244 πεπεπε =+= m 7-17 y1 Q 1 ? s? ?1 ,' 0 )2(44 2 0 31 2 0 21 =+ d QQ d QQ πεπε  3¤ QQQ 4 1 4 1 32 ?==?=  Q 2  O?¥è ] ? d Q QUUQW 0 2 002 84 1 πε ?=?==  2| Q 2 V O?w?í kù)? ? ?S¥? a qQ UQUUQA 0 0202 8 3 )( πε =?=?= ∞? 30 vDt ? ¨ i? b?¥áè? 7-18 B?? 1 R¥íKé{è?  =?¥è? ( s?è?8 á1 ρ b 1 pè?s?  2 ?m 7-18 ? U  ?à_¤ j  ??è ? q 0 ? a? ?? b?5 è? ?S?1 $ 3  1 | é1 la?? 1 r OD{è?]à¥?? ?1ú ? ?b?ú ?? ? Rr < ∫∫∫ ==? VVS rrlVSE d2 1 d 1 d 00 1 πρ ε ρ ε vv R r 2 b a r 1 ' lrrlE 2 0 1 1 2 ρπ ε π =? ¤ rE v v 0 1 2ε ρ = m 7-18 Rr > lRrlE 2 0 2 1 2 ρπ ε π =? ¤ r r R E ? 2 0 2 2 v v ε ρ =  2??M ])¥è ]M? ∫∫∫∫∫ +=?+?=?= 2 1 d 2 d 2 ddd 0 2 0 0 020100 r R R r b R R a b a ab r r R qr r qlEqlEqlEqA ε ρ ε ρ vvvvvv R rRq rR q 2 0 2 02 1 2 0 0 ln 2 )( 4 ε ρ ε ρ +?= è ] 7-195 7-18? ? |?¥V ?1 ,è ] p bW¥è ]s?b 3 |?V ?1 ,è ]' 0= U R Rr < H )( 4 d 2 d 22 00 11 rRr r lEU R r R r ?==?= ∫∫ ε ρ ε ρ r v Rr > H r RR r r R lEU R r r R ln 2 d 2 d 0 2 0 2 22 ∫∫ =?=?= ε ρ ε ρ r v 7-20 ?m 7-20 ? Uè? ? ásY1 +σ ? -σ ¥  voí Kvp ( {è ü? ü ?sYD xàM? ? x 1 = a ? x 2 = a ?b ! USe? O)è ]1 , p bW¥è ]s?b 3   ax ?< 0 1 = E v axa <<? i E v v ε σ 0 2 =  ax > 0 3 = E v b x +σ -σ O -a a ∴ ax ?< alElEU ax 0 0 2 0 1 dd ε σ =?=?= ∫∫ ? vvvv axa <<?  xlElEU x x 00 2 0 22 dd ε σ ?=??=?= ∫∫ vvvv m 7-20 ax > allElEU a ax 00 0 0 2 0 3 ddd ε σ ε σ ?=?=?=?= ∫∫∫ vvvv 31 vDt ? ¨ i? b?¥áè? 7-21 ?? ?sY1 R 1 =3.0×10 -2 m? R 2 =0.10m¥é °]à?? ?{μ? s|¥è? ?¥è ]μ1 450Vb p?? ??êé  ?{è? λ b 3 ?ú ? ? ? V p¤ ? ?W¥è? < r E ε π λ 0 2 = V450ln 2 d 2 d 1 2 00 12 2 1 2 1 ===?=∴ ∫∫ R R r r R R R R lEU πε λ πε λ vv 3¤ mc10 1.2 18 ? ×= ?? λ 7-22 ?m 7-22 ? U¥{è %? è?L á1 λ  ? BCD1 ??1 R¥ ?? AB=DE=R p 1? ? ¥è????? O)á 3¥è ]  2° % ? AB? DE???? O)á 3¥è ]  3 O) ¥9è ]b R O A m 7-22 ED C B 3  1 | è?í lq dd λ=  000 1 444 d ε λ πε λπ πε ===∴ ∫ R R R q U  2 AB   O?1 r) |è?í lq dd λ= 2ln 44 d 4 d 0 2 00 2 πε λ πε λ πε ===∴ ∫∫ R R r r r q U b] ? DE O?á 3¥è ] 2ln 4 0 3 ε π λ = U  3 )2ln2( 4 0 3210 +=++= π ε π λ UUUU 7-23 ??s Y1 R 1 ? R 2 ¥ ?]? o ?sY{μè? q 1 ? q 2 b p  1 ò u×è ]s?i?s? w L  2  o ?Wè ]μ  3 ? R 1 =10cmaR 2 =30cmaq 1 =10 8 Caq 2 =1.5×10 8 C ? o? 20cm? 50 cm )¥è ]1 $ 3  1? ú ?? ? V¤è?s?1 R r 1 <   0 1 = E v R r R 21 <<  e r q E r v v 2 0 1 2 4 ε π =  R r 2 >  e r qq E r v v 2 0 1 2 2 4 ε π + = b è ]s?1 R r 1 <  ∫∫∫∫ ∞∞ ∞ ?+?+?=?= 2 2 1 dddd 3211 R R Rr r lElElElEU vvvvvvrv R q R q R qq RR q 20 2 10 1 20 21 210 1 444 ) 11 ( 4 0 ε π ε π ε π ε π += + +?+= R r R 21 <<  20 2 0 1 322 44 ddd 2 2 R q r q lElElEU R R r r πεπε +=?+?=?= ∫∫∫ ∞ ∞ vvvvrv R r 2 >  r qq lEU r 0 21 33 4 d πε + =?= ∫ ∞ vv 32 vDt ? ¨ i? b?¥áè? (2) ) 11 ( 4 d 210 212 2 1 RR q lEU R R ?=?= ∫ πε vv (3) '  o ?-W cm20=r V900) 3.0 10 5.1 2.0 10 ( 10 9)( 4 1 88 9 2 21 0 20 = × +××=+= ?? R q r q U ε π cm50=r '  o ?-? V450) 5.0 10 5.1 10 ( 10 9)( 4 1 88 921 0 50 = ×+ ××= + = ?? r qq U ε π è? <Dè ]¥1" 7-24X ? B è?¥è ]f ?1 U = 2x 3 +y pè? < E v b 3 x x U E x 2 6?= ? ? ?=  1?= ? ? ?= y U E y  ji x j E i E E yx vvv v v v v ??=+=∴ 2 6  )6()( 2 ji x k z U j y U i x U E vv v vvv +?= ? ? + ? ? + ? ? ?= 7-25 k9 ? ??1 Raè?L á1 λ¥ ( {è%?ìàL ¥è ]s?i?è ]s? pàL ¥ è? <s?b 3 ?ì  ? |BLí{è 1 lQ dd λ=  àL  ?ì??1Qd x?á 3¥è ]1 22 0 0 4 d 4 d d xR l r Q U + == πε λ πε  22 0 22 0 24 2 d xR R xR R UU + = + == ∫ ε λ πε πλ Q 2/322 0 )(2 xR Rx x U E x + = ? ? ?= ε λ  i xR Rx iEE x vvv 2/322 0 )(2 + == ε λ 33