P505F01HW03 - yt‚(„{(f„… p6stV6t' C6st B‚ ss(‚…...

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Unformatted text preview: yt‚(„{(f„… p6stV6t' C6st B‚ ss(‚… U‚}(‚Ve‚„ I! I@@d _YkR${R x(xU 7BjZ$BtR B VRR$t8‚t 'n _„BAj‚8 1d( q‰‚ }„fej‚V 6‚ 7‚„k ‚6V6js„ (f s '„fts‚s {fts{(6t' ‚}‰‚„‚ 6t s t6€f„V ‚j‚{(„6{ h‚js o( ! (‰‚ {s‚‚ s6‚{‚‚‚s 6t U‚{(6ft I0x0 q‰‚ „‚'6ft e‚(˜‚‚t (‰‚ (˜f }js(‚‚ 6‚ 6s‚t(6{sj (f ft‚ f€ (‰‚ ‰sj€ ‚}s{‚‚ f€ (‰‚ sef7‚ V‚t(6ft‚s }„fej‚V! ˜‰‚„‚ (‰‚ ‰sj€ ‚}s{‚‚ s„‚ s‚ht‚s ek s }jst‚ }‚„}‚ts6{js„ (f (‰‚ h‚js sts {( (‰‚ ‚}‰‚„‚ 6t(f (˜f ‰‚V6‚}‰‚„‚‚0 wsh yt s ‚}‰‚„6{sj {ff„s6ts(‚ ‚k‚(‚V {‚t(‚„‚s s( (‰‚ f„6'6t f€ (‰‚ ef‚‚ ˜6(‰ vp }f6t(6t' (f (‰‚ f(‰‚„ {fts{(f„! (‰‚ }f(‚t(6sj e‚(˜‚‚t (‰‚ (˜f }js(‚‚ 6‚ '67‚t ek et0 wI0dYh… Éw„D h A o( w„  y1 h {f‚  „ n q‰‚ ‚„€s{‚ {‰s„'‚ s‚t‚6(k ft (‰‚ ef‚‚… !KwyD h A T( o„ „)y / A T( @ É /„)y A nT( o( {f‚  @„ q‰‚ s‚t‚6(k ft (‰‚ }jst‚… !€ w„D  @™™ 6 I n A 6 h A T( o /)$b1 A T( o /)$b1 A T( d @ É /)$b1 A T( o( wd  yn h I „ @ „ σb/(ε0E0) 3 2 1 0 π/4 π/2 3π/2 σp/(ε0E0) θ 1 0 2 4 6 r/a weh q‰‚ (f(sj {‰s„'‚ ft (‰‚ ef‚‚ `K A 8 !K y A nT( o( y 1 8 ( $b1 {f‚  ‚6t  8 ( 1$ B A n6T( o( y1 w{h q‰‚ eftss„k {fts6(6ft É A @ ft (‰‚ }jst‚ sts (‰‚ ef‚‚ {st e‚ V‚‚( ek }js{6t' (‰„‚‚ 6Vs'‚ {‰s„'‚‚! ft‚ ‚y˜ s( p A y1 ˜! ft‚ v‚y˜ s( p A y1 ˜ sts (‰‚ (‰6„s ft‚ ‚ s( p A 0 q‰‚ 6ts{‚s {‰s„'‚ s6‚(„6e(6ft ft (‰‚ ef‚‚ 6‚ (‰‚ ‚V f€ (‰f‚‚ 6ts{‚s ek {‰s„'‚ }s6„‚ w‚D ‚y˜h sts w‚D ‚y˜h… !wh A !d wh v !1 wh ˜‰‚„‚ !d sts !1 s„‚ '67‚t ek et0 wI0xh… !d wh 1 ‚  y1 h A  Y6y1 wy1 v y1w Iy {f‚ hnb1 ˜‰‚„‚ @ ™  ™ 6 s‚ (f {‰s„'‚‚ w‚D ‚y˜h  I d !1 wh A v ‚ Y6y1 wy1 yw1 y1 h v 1 Iy {f‚ hnb1 q‰‚ (f(sj 6ts{‚s {‰s„'‚ ft (‰‚ ef‚‚ ‚s   ˜‰‚„‚ 6 I  ™™6 s‚ (f {‰s„'‚‚ w‚D ‚y˜h ‚ A w!d v !1 hy A  Y6y1 yw1  y1 hI6y1 \ 8 8 ( $b1  8 $ $b1  i wy 1 1 ‚6t  1 A ‚wd  $  y 1 h n b1 1 vy v  Iy {f‚ h   1 q‰‚ ‚j‚{(„6{ h‚js sts }f(‚t(6sj s‚ (f s j6t‚ {‰s„'‚ s„‚ C d9 n C n o w9D Bh A I6T( 9 9 D Éw9D Bh A g  I6T( jt 9 ˜‰‚„‚ g ! C sts 9 s„‚! „‚‚}‚{(67‚jk! s {ft‚(st(! (‰‚ j6t‚ {‰s„'‚ s‚t‚6(k! sts (‰‚ s6‚(st{‚ (f (‰‚ j6t‚ {‰s„'‚0 ‡f(‚ (‰s( (‰‚ }f(‚t(6sj sf‚‚ tf( s‚}‚ts ft p wsjft' (‰‚ sE6‚h0 wsh q‰‚ 6Vs'‚ {‰s„'‚ ‰s‚ (f e‚ 6t (‰‚ }jst‚ €f„V‚s ek (‰‚ {kj6ts‚„ sE6‚ sts (‰‚ j6t‚ {‰s„'‚0 “‰ff‚‚ s {kj6ts„6{sj {ff„s6ts(‚ ‚k‚(‚V ˜6(‰ (‰‚ f„6'6t s( (‰‚ sE6‚ f€ (‰‚ {kj6ts‚„ sts (‰‚ s6„‚{(6ft €„fV (‰‚ f„6'6t (f (‰‚ j6t‚ {‰s„'‚ s‚ (‰‚ c sE6‚0 yt (‰6‚ {s‚‚! (‰‚ j6t‚ {‰s„'‚ 6‚ s( c A p0 x‚( C s sts ps e‚ (‰‚ 6Vs'‚ j6t‚ {‰s„'‚ s‚t‚6(k sts (‰‚ }fjs„ s6‚(st{‚ (f (‰‚ sE6‚! (‰‚ }f(‚t(6sj s( s }f6t( w9D Bh 6‚ '67‚t ek C C Éw9D Bh A É(  I6T jt „  I6T jt „s s ( ( _„BAj‚8 1dd É( 6‚ stf(‰‚„ {ft‚(st(0 „ sts „s s„‚ s6‚(st{‚‚ €„fV (‰‚ }f6t( (f (‰‚ j6t‚ {‰s„'‚ C sts (‰‚ 6Vs'‚ {‰s„'‚ C s … „ A 0 91 v p 1  I9p {f‚ B1 1 „s A 0 91 v ps1  I9ps {f‚ B q‰‚„‚€f„‚ d Éw9D Bh A É(  Y6T ( \C jtw9 v p1  Ip9 {f‚ Bh v C s jtw91 v ps1  Ips 9 {f‚ Bhi †( (‰‚ ‚„€s{‚ f€ (‰‚ {kj6ts‚„ w9 A uh… d ÉwuD Bh A É(  Y6T \C jtwu1 v p1  Ipu {f‚ Bh v C s jtwu1 v ps1  Ipsu {f‚ Bhi A “ft‚(st( ( 6ts‚}‚ts‚t( f€ B0 q‰6‚ 6‚ ftjk }f‚‚6ej‚ 6€ Cs A C u1 v p1 A ’wu1 v ps1 h up A ’wups h 6‚ stf(‰‚„ {ft‚(st(0 y( 6‚ ‚s‚k (f s‚(‚„V6t‚ ps €„fV (‰‚ sef7‚ ‚ts(6ft (f e‚ ps A u1 ˜p0 q‰‚„‚€f„‚! (‰‚ j6t‚ 6Vs'‚ {‰s„'‚ 6‚ s( c A vu1 ˜p ˜6(‰ s j6t‚ {‰s„'‚ s‚t‚6(k C 0 weh •f(‚t(6sj s( stk }f6t( w9D Bh… 1 1 C {f‚ B Éw9D Bh A É(  Y6T jt\ 91 v 9u1v p1  Ip9˜ph9 {f‚ B i 1 w ˜ph  Iwu ( †‚ 9 ! Éw9D Bh É( 0 U6t{‚ (‰‚ }f(‚t(6sj 7st6‚‰‚‚ s( 6tht6(k! ft‚ '‚(‚ É( 0 q‰‚ }f(‚t(6sj s( s }f6t( w9D Bh… 1 1 C {f‚ B Éw9D Bh A  Y6T jt\ 91 v 9u1v p1  Ip9˜ph9 {f‚ B i 1 w ˜ph  Iwu ( ‡f(‚ (‰s( (‰‚ }f(‚t(6sj ft (‰‚ {kj6ts‚„ ‚„€s{‚ 6‚ ’ C ÉwuD Bh A  I6T jt\ p i u ( I Qf„ s }f6t( €s„ s˜sk €„fV (‰‚ {kj6ts‚„! 1 91 v p1  Ip9 {f‚ B  1 Iw  ddIwup˜9hh{f‚ BB  d v I u p9p {f‚ B 1 ˜p9 {f‚ 91 v wu1 ˜ph1  Iwu1 ˜ph9 {f‚ B q‰‚„‚€f„‚ (‰‚ s‚kV}(f(6{ €f„V f€ (‰‚ }f(‚t(6sj €s„ €„fV (‰‚ {kj6ts‚„… C Éw9D Bh   Y6T jt\d v I u ( 1 p9 p 1 C {f‚ Bi   I6T u1 ( p9 p 1 {f‚ B w{h U6t{‚ (‰‚ {kj6ts‚„ ‰s‚ s {ft‚(st( }f(‚t(6sj! (‰‚ }f(‚t(6sj 6t‚6s‚ (‰‚ {kj6ts‚„ V‚( e‚ (‰‚ ‚sV‚ {ft‚(st( w‚‚‚ (‰‚ t‚E( }„fej‚V €f„ }„ff€h0 q‰‚„‚€f„‚! (‰‚ ‚„€s{‚ {‰s„'‚ s‚t‚6(k ft (‰‚ {kj6ts‚„ !wBh p1  1 A T( o' /')K A T( @ É /')K A  IC6 uwu1 v p1  Iuup {f‚ Bh @9 ‡f(‚ (‰s( (‰‚ (f(sj ‚„€s{‚ {‰s„'‚ }‚„ t6( j‚t'(‰ C ss A 8 ( 1$ !wBhuB A C -2πσ/τ R/b=2 R/b=4 π/2 π -π -π/2 φ 0 wsh q‰‚ €f„{‚ ft (‰‚ {‰s„'‚ }‚„ t6( j‚t'(‰… n f n A C o A  IC 6T 1 ( p  d u1 ˜p 9 n 9 A  IC 6T 1 p p1 ( u 1 9 n 9 n ˜‰‚„‚ o 6‚ (‰‚ ‚j‚{(„6{ h‚js s( (‰‚ j6t‚ {‰s„'‚ s‚ (f (‰‚ 6Vs'‚ {‰s„'‚0 q‰‚ €f„{‚ 6‚ s((„s{(67‚0 y( 6‚ 6t(‚„‚‚(6t' (f s‚„67‚ (‰‚ p„‚‚t €t{(6ft €f„ (‰‚ B6„6{‰j‚( {fts6(6ft €f„ (‰‚ {s‚‚ f€ {kj6ts‚„0 q‰‚ B6„6{‰j‚( {fts6(6ft + ÉwuD Bh A @ j‚ss‚ (f É( A ;$6+ jtwp1 ˜u1 h0 q‰‚ }f(‚t(6sj s( w9D Bh s‚ (f (‰‚ j6t‚ {‰s„'‚ C s( w9s D Bs h ˜6(‰ (‰‚ B6„6{‰j‚( eftss„k {fts6(6ft 6‚… s1 1 C wu1 ˜9s 1  Iwu1 s Bs Éw9D Bh A Y6T jt\ 9 b9 uvb91 v 9sh1  I99s ˜9 h9 {f‚wBhr  Bhr i 1 {f‚wBs  ( q‰‚ p„‚‚t €t{(6ft 6‚ (‰‚ }f(‚t(6sj s( w9D Bh s‚ (f s j6t‚ {‰s„'‚ ˜6(‰ s‚t‚6(k C A Y6T( s( w9sD Bs h… t; w9D BD 9s D Bs h A jt u 99 {f‚w \ 9u 99 v u9s II99s {f‚wBBBBh i s b v hr 1 qY‚ p„‚‚t PZt{$Bt PB„ Y‚ *$„${Yj‚ {BtI$$Bt s1 ; 1 s s 1 1 1 n _„BAj‚8 1dn yt(‚'„sj‚ sts 6s‚t(6(6‚‚ ‚‚€j €f„ (‰‚ }„fej‚V… 8 1$ ( y1 6 A /y  uIwy v uh v  Iyu {f‚ B / B u1 8 {f‚ BB A (std wu $ B˜ y1  u1 h ‚6t 1  u1 {f‚1 B y u y 1  u1  (std c A c $ d d v c1 wsh q‰‚ {kj6ts‚„ {st e‚ 76‚˜‚s s‚ s ‚}‚„}f‚6(6ft f€ (˜f {kj6ts‚„‚ ˜6(‰ (‰‚ €fjjf˜6t' }f(‚t(6sj‚… q‚ {st „‚'s„s (‰6‚ }„fej‚V s‚ s ‚}‚„}f‚6(6ft f€ (˜f }„fej‚V‚… Éd wuD Bh A w~d v ~1 h˜I ~d  ~1 É1 wuD 6 Ih A I I q‰‚ }f(‚t(6sj 6t‚6s‚ (‰‚ h„‚( {kj6ts‚„ w‚‚‚ }„fej‚V I0dIh… É1 wuD  6 I ™B™ 6 ™B™ n6 h A ~1  ~d I I 8 Éd w9D Bh A Id 6 1$ ( ~d q‰‚ }f(‚t(6sj 6t‚6s‚ (‰‚ ‚‚{fts {kj6ts‚„… ˜‰‚„‚ ~d v ~1 v ~1 u1  91 Bs A 1 v 91  Iu9 {f‚wBs  Bh I u I É1 w9D Bh A É1y w9D Bh v É1Kw9D Bh  É1y w9D Bh A ~d Y6 ~1  É1Kw9D Bh A  ~d Y6 ~1 É1 K 8 $b1 $b1 u1 v 91  Iu9 {f‚wBs  Bh B u1 u1 9 1 s 8 n$b1 x‚( Bss A Bs  6! (‰‚t $b1 u1 v 91  Iu9 {f‚wBs  Bh B u1 9 1 s  w9D Bh A  Y6 ~ ~d 1 8 $b1 1 $b1 u v 91 v Iu9 {f‚wBss  Bh B 9 1 ss “fVe6t6t' É1y sts É1K…  É1 w9D Bh A ~d Y6 ~1 wu1  91 h 8 Yu9 {f‚wBs  Bh s w v h  Yu1 91 {f‚1 wBs  Bh B $b1 $b1 u1 91 1 u9 A w~d  ~1 h u9wu1  91 h Iu9wu1d 91 h (std \ u1I 91 ‚6twBs  Bhi/* )$b1 1 * )$b 6 I I u9 A ~d  ~1 (std w u1I 91 {f‚ Bh 6 Y q‰‚ (‰‚ }f(‚t(6sj 6t‚6s‚ (‰‚ f„6'6tsj {kj6ts‚„ weh x‚( ! e‚ (‰‚ ‚„€s{‚ {‰s„'‚ s‚t‚6(k! (‰‚ ‚j‚{(„6{ h‚js‚ –‚( 6t‚6s‚ sts f(‚6s‚ (‰‚ ‚„€s{‚ s„‚ '67‚t ek ps‚‚X‚ js˜… n o$t u9 Éw9D Bh A Éd w9D Bh v É1 w9D Bh A ~d v ~1 v ~d  ~1 (std \ u1I 91 {f‚ Bi I 6 q‰‚„‚€f„‚! ! A  I! T ( 9 n D 9 n oBZ A I! T ( 9 n 9 9 n w~ d  ~ n A IT( o$t N 9 /')K A IT( o' /')K A IT( @ É /')K A IT(6u {f‚ B 1 h @9 Q6„‚( f€ sjj! (‰‚ •f6‚‚ft 6t(‚'„sj ‚fj(6ft 6‚ (‰‚ ‚fj(6ft f€ •„fej‚V I0dI! $‚! (‰‚ }f(‚t(6sj 6t‚6s‚ s {kj6ts‚„… 8 1$ 1  91 Éw9D Bh A Id ÉwuD Bs h u1 v 91 uIu9 {f‚wBs  Bh Bs 6 ( “s{‰kX‚ (‰‚f„‚V 6‚ ‚E}„‚‚‚‚s ‚6t' {fV}j‚E 7s„6sej‚ p ˜‰‚„‚ p A 9Ã7* 0 x‚( p e‚ 6t‚6s‚ (‰‚ {„7‚ g sts f wph A Éwph! ˜‚ (‰‚t ‰s7‚ Éwps Éwph A Id ps  h p s 6U p 1 7* A u1 ˜p É w‰‚„‚ p É 6‚ (‰‚ {fV}j‚E {ft–'s(‚ f€ p h ˜‰6{‰ j6‚‚ eE}jf6(6t' (‰‚ ‰6t(! (‰‚ 6Vs'‚ }f6t( f€ p 6‚ wu ˜/p/hà f(‚6s‚ (‰‚ {„7‚ g 0 q‰‚„‚€f„‚ d - Éwpsh ps A @ I6U ps  u1 ˜pÉ Ue(„s{( (‰6‚ W‚„f 6t(‚'„sj €„fV (‰‚ Éwp h… d Éwph A Id Éwps h\ ps  p  ps  d1 ˜pÉ ip s 6U u Qf„ (‰‚ •f6‚‚ft 6t(‚'„sj }„fej‚V! (‰‚ {„7‚ g 6‚ {6„{j‚ f€ „ss6‚ u! ps 6‚ ft (‰‚ {„7‚! $‚! ps psÉ A u1 0 a‚6t' (‰‚ 6s‚t(6(k ps _„BAj‚8 11d ft‚ '‚(‚ u p  pÉ A ps  pspsɘpÉ A pÉ wpÉ  psÉh 1 s •j''6t' 6t (f (‰‚ }f(‚t(6sj Éwph… sÉ É É s s pÉ  É d pÉ pÉ ˜ps  ps  d ˜pÉ A ps  p v psÉ  pÉ A p  p /pv p pp ˜p A pds p/ps  ppp s ps  p u / / d 1 1 1 d - Éwp shps ps psÉ  ppÉ ps Éwph A I6U / p s  p /1 p s yt }fjs„ {ff„s6ts(‚ ‚k‚(‚V! p A 9Ã7* ! ps A uÃ7* ! (‰‚„‚€f„‚ I pp É A 91 D 1 ps psÉ A u1 D ps ps A UBs A 91 v u1  Iu9 {f‚wBs  Bh q‰‚ }f(‚t(6sj 6t‚6s‚ (‰‚ {„7‚ 6t }fjs„ {ff„s6ts(‚‚ 8 1$ 1  91 Éw9D Bh A Id ÉwuD Bs h u1 v 91 uIu9 {f‚wBs  Bh Bs 6 ( x /p s  p / ...
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This note was uploaded on 11/21/2011 for the course PHY 505 taught by Professor Stephens,p during the Fall '08 term at SUNY Stony Brook.

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