Ch 25C Notes pdf - Che*u 25 Tlnr Had-Ho Fieh‘l We{Mink as...

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Unformatted text preview: Che. *u 25- Tlnr. Had-Ho Fieh‘l We {Mink as am fled-Ht. (Junta: ms SvfroonAi-na «4- The Suki czar-45 a some, on am] 944m (‘Jnau‘ag in We rayon- crea-“vxa an (flu-Arie $.1ch In 4%: rzgfon as SPO‘C‘C 25-1 Ehclrh‘c Fad amé Glee-\rfical Forces (9 The 4mm Pomlwely chm-89,4 Lakes ftpd each 0W9}. The corn, F ovx boaj 3 oak a} a Ais-l-qnm grew: loon A- Thg eleubriufl Sow: F Joes mfl- need MR‘HV 44, be +romsmi+¥e$ :row: A +0 B. In orJer .‘V We “~an 0; L394, A as MOJ:$ M some 2 4- 0: 59“ M Na \I\'ciA{-‘-\/. 1 ‘ Prop r Baal», A lb 54-4 40 cnvse. an mama Skew a,“ Poin+ P. Wkeu has). 3 .‘s locaA'ecl 0.“ P (0" Some. oLL‘er pat-IA“ M Mae VCL'MH-Y o; A) , we 4-qu 44M. foM" as; View 4hr} Mae Q‘elcl “4 P exerLs ‘W‘E Some. on 3, "G'H’W' 4kon um'nkhna a; A as being 44w. chug-A muse a: ~Hne $orce. 2. BOA, A Stk up an ehckrfc View a} a.“ 90“an "n 4'LW r? 3. To 415% $0:- “nu am‘sLenpe a; an deg-Hie geld, yov Place a. oLgrjeJ L:on qulecl a. 4ea¥ charac ad a. 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SRQAA grog“; A‘ We Ac no’r waw“ We -\-e.s¥ charge *0 “RU “at: €18°“"‘"C QB” we are Jcrjin h mea>ore. 5- 15; a.“ e,\e.c.«\rio Sigh! exisk u);+\'\;:\ a wnéua‘or MAP—'4 a Song .‘5 gxuw‘recl on evefj dnar e M -\'\Ae combo-Vow The. mo-Hon 09 Mac gr“; cqugu causeJ L3 We, guru, {a a (Lorre-a4. lO- 1? Mam-e Is vxa curred M o. concludmr ) Hun were Ls no movemen¥ <9“: (Anorae, in Mme conAQrA—or onA “me deg-hub $5ch In 44m condud'or‘ "IV-5+ be {are - k2 u. Examplt FMA 4M3, 9.\u.c\-r-‘r. 9.1% on“ a3§5'\'ov\ce 0S- 1_o m Cram 0. 905(L‘vc Poivfi- chug-3a 0? an = no mo‘” C, Fa 31$: t z) E‘- El: k _ = homo—ID : 9500 U/C. 41% r "v wear” 4T1:(8-85xlo"1)(l~0xlo‘z)i Tke ANN-OLD“ oS E is /"" I . ‘B ‘B ‘1 - E m Mp\£ Two posk'L-‘Va fowl: Charges 05; (It kola.) an; (0‘ 'Q) ‘ gal FMA +5“. e‘co‘m‘b ficalé U.) Fm; +‘AE e,\¢c+r-‘c “chi (an Lem.) 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(“away/z EH ‘ ‘29 5M9 = -20a 4-1150 (0,7-+xl) 41:60 (ak'xas/z = —_- ~ 0 E 1 Eu 4- Eu 41eoxtaL+XLFh 51: 511-2”: “363‘L ——3f_ 411% (a‘ul) " IE\:,E:+E;':__§_‘_W: Q W ‘awmcahx‘P’z 4155. W .4. EX M ‘3 _)} An eta-tron enhrs «Hr-crescon Lehman {woo “Jack‘s P5313) L: 2J3“. 1“; T __ am; A: L0 0M wilc. ch ngm‘hJie 0? HM. an.‘§‘ov-M dean}, field E a .“‘~--‘3E bg¥ween Hue pqu’é \‘5 = 5500 Isl/C. Who." f5 Hag MI'm'MuM valocHy L \‘\ HA3 eled'ron mus’c have. 4-0 escape w§+hou+ L‘H—Lf,‘ We \owgr ‘ “are? 1kg eled'rcm 15 inihalw .50 cm Rom aquA P‘q+fi. 2_&+1.E"=J__I_Ee 2: 1=Y0‘VVoA£+‘é‘avb+ -3 ZMA+ .5 ZTA£ =vaid>ak=i~=g=j d__J.Ee Ll_ , =E¢L1 “° 1 on v, E 2m(7,)'°7‘177,} 3: EEL a) ‘ E - _:9 Va Vo- _"-. L : (500°)Ll.exto ) ( lo)_ 5 e I Md ‘IMA :wluxlymubom) .9 mo M s 15. Examp‘b A unfiom Sign! a? magmwée E em‘sh baa-human 4mm corded-{n Flag 1.- —+ Steamed-2.1 by a dl‘fiqnge d. An cud-non Cs releasecl $mw- r554- 03 a l: I_ Mu, negaA'ive, Pla’re Md {5 03-4-mc4-ecl +0 4kg PosH-iue PloA-e. 04 'L “ (a) NRA \‘5 Una kCneL‘c energy 04” Mae a‘edron wLen {-1- collde; E= \5 N/C W‘H,‘ MM; PosH-ive \o‘oflre ? = "0 5'“ U0} Wk“; {5 Mag“ quocih/ a: impad; ? Lu W = AK FAA =6K 3 Kg-KC: V; E e A = K; , 40$ Kg: Lt6)(t.bxlo"°)(\010)= 1.6xl0 V1,: L”) id = K; -— twp.) vf= 29.9; a, M (em = M 9.“ xto‘31 : l|9KIDS m/5 (4- 15'2 EKerJI-ic View Co.\c.u\a.+\'ons |- You can cdcu‘od’e H‘s «Jack-fa Crelcl a.“ {mix} P I? You know A", M“ ".4ch a“ 905mm 0? and. charge, Una} con¥r§bu¥e> +0 HM, 99):! ad 90M PA Acooreling +0 Coulomb's law, {4‘9 Caro; Per \MH- charge on +29} charge 1" due *1) charge is is 1 = E = —-~ E q,’ 41720 a}? I? 'tl' f: a on“ wad-or alrqu Cram (6 +0 16,, +L‘en a = 4 a; : 411-60 r1 when :3 \‘9 posflive, +\ne. Cw; ad (8' cm; «WA SA, . wk .- m u. 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For eqdn szl o. ch x are “we SWMEA 5° F 5 I_ “X JQ - = .L X 4 0x m5“ («kW/1 mo («new ‘5 ’ 41:6 (mx‘r‘h "‘ rm: ° 4. Example An e‘tchic dams; Q .‘s Jishébui-ul umformly D.an a line. wk»: Influx 20., Nan aloha HM, Y “:5 as skuwm Ch“! w; g\u<\'f;c :Ceh‘l a." a. 90:6 P on “(W- X duds, aA a . disktmce X gwm We ofialn, For amok 90:13 P0300”. “42 x axis, +Ltefe (5 a pain; Pl bdow Hue x axis 5w.“ de- 4kg thdru'c Geld compontn+ of P Wad 1‘s perpend-‘cular 40 “no. it mu‘s bum“); Una duh-fr, Yaw compound 09 PI Unad- 1'5 pupméicuhr *1: “as x was. The eled'm‘c Weld 0A” (.290) Cs Para-Mel ‘\-o MM; x axis. agfld Q 20. 20‘ AE : 4.. a - 1 A n 6059 - —' 11 = i— x '1 4'1TC. I" 4W6. 73 P 4775‘) 03.17:)”; 3 = I x Q +1re. (x‘+y‘)3" 2a 4" G g = S _Q_ 1 5 .1 . o 1 “at a J 3..“ 1“ 411's. aux)” y 222' 4115. X a (*5 .)y, ‘ $ To Sm; my; , HA 7: x Tame y Y d1: X Sake 49 X AL. - x 5.139 JG 2 3/1. — 5 : X 33‘. 9 Dawn) (Xusz-Mzef/y. Jm = Jig; 9 x c l = II {co5959aé SMG = —'—- —L - _._y x* «I? ' 71* a Y x K 1 $°E=Qx jgwso (L a)_ Q a. a +1 five. new) cameo Jx‘4'Y‘ o ’ 4W6. \ \ ax! a1+xi 4W€oxgaz+x2 Non, {Y Hw. “M. 0? charge .‘5 VUY long #19» “Eng- ~ 2 ~ ‘ J ~ (1 =a. Decuw. 1 = claw-8e. yer unr‘ lena+L = 30: r lkzn Q: 3 2a E = A 20. = a 44ng Q. 2W€.X The ma nHviLe. 0C Hm eluJ-r-‘c gala 0L4“ ‘* 3554mczx fr ‘ - ' lme, oi dam-3e mm akarae 406141 2 ‘l‘W‘WL'S/Mchar :M +13; mg‘m‘hl’ I“; E = 1 ” Z'I'L'eax (6 5. Exam-pk An duh-‘9 (Large, is Aishikflea Unierly aver Hm ark”. xi plane, The. Surface chart dumfia‘ 1'5 4L: ckurae Per UM" area . wkaA is Hue eledfu‘c. 99ml ad a. (:0;th V, a MB,“E'5 alcove 4L1; Plane To, vim DMJ: Hue, P‘ane in’to ships 0: CJAur a. For «wk 5%}: 4-0 we fish¥ 0‘; q, 4H,". .‘s a ship +o +ke la“ 9‘; a Soda %a-\ “at korizon-kfl componawk o? E due. +0 +ke 5+9? on MA: (E I“ . cancels Mae horizon-had componen—l- ‘ g‘ 0;; E Aug, 49 9, ship on We leg}: The glad-rm CI'eU .' 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Tkvb, i‘; am :rrR‘ulqr surfincg surrogan at), -\—\«e sum 2 EJ_ AA: ZECMQAA 35 .um, Same Gar a mag-Elm Surface as i+ woolé b9. $or- wrresPoml.‘nj stermJ are“ elemwk' No” 2 st‘rm‘Ll area. demands clan? make up a single SPLere' ‘00" 0X8 a.“ el-‘gg‘uen-lr J\'S‘\'qn¢es from L9 The groévd ELAA Aces mfi Awe/“1 an ranvs gar a wlnaie sphere. ‘fine Same I"; hut. Cor 9N4 OS a. sphere. as welL 9’ Lu: AA in “no, area 99 “‘2 small schrn‘cal Q‘emgrd. r The Aimensions 0‘; l¢n3+k and wicH-k 09 Unalarger elemevfl [1‘ ER are eta-ck fir 44M“ larger 44mm Cur “we smaHer elemen+. Thus ,Hae omen 0‘; +1“ [cu-89 dame-«4 {5 AA(%:) 30* ER =—EL. = 5—1 El’ Wr)‘ 2* l EKBAM“ = Er)<AA,"~4) ET: z Er AASMRLL EAA $985K+ Jepeml on ra4§05~ La 44w inverse S‘bvqf‘a \am so / AAJCna EAA Qor an 44m spkericol frrfl'cc-l-cons 0? Ha: Irregular surgace you“ 3;” +1“ Same FESOH' as 044113 EAA $0? a SPLU-e “Mae ke A;S*ance a: eacl‘ spLefl‘ml e\emen¥ g:rom :3 Ann noJc afifed EAA Cor 4L: dew-3.4+. wt cam .‘mn ine ro'edin each 59L”ch demevd 4-0 some. meon :1;st 4-D proAuQ, g g P d ‘3 Sphere, } we w.‘.5|n. TEAAA Sor trreafimr surguce = Z EAA {or PmJ-eCLM,‘ ___ ZEJ‘AA go'- a >M°D+k ~ 1 0‘; fire Olav AA5 0'3“ Spherical surVQLE, SpkeriLoJ A A 's “95, Z EC059AA cor any (40ng suffix“; — _%_ , +4“ same vane m one 60 would O‘D’rmin for sum, sphere 4L9} enrJosGs 6- ZEAA 0°59 = EacaseaA = 3:. 60 l: %=0 we" ggcme $A = O’c "- geld lme Mud mid-er; a. closecl surface; +kod- covfiains no charge mus+ leave 'Hnrogln Some o-k—L‘er 90;“. on 4|ne surface. Frelé Una, can log in Male a ('83,:on of space, only {‘4- J—ker‘e is CLnr g In 'Hae real‘on' § means Enharad'e E0159 AA over Mae em‘ire arm a? Mac SurS—‘oce. 1. 1: E is AU‘QLLQA ‘wwoaré Unen ECose 6A 40- Thus, is (6‘0, Lke, in‘egrql {S neaahve, \aJ’r so {5 1, amé §£C0L54A: i. .‘5 com-can éo 8‘ §ECO>94A = %; Lu:le Var euok Poink' chad}; §EL£AA ‘ $5: &(E"‘+E+Z+EL3) ¢LA= ‘4' 1+ 3 §E+2 6" = $1; ‘9 6° ea é EMA- JA = fl. § E44 AA = $1 6° 60 Th” I §E¢JA= 7:30 and Gauss's him ‘nolslb even [S More “nah clauae 55 loc‘fleg 20 m Una ream“ enclose; b3 ‘ufle “’4‘”- §EJA= :74, : §ECMBAA= g5.“ 2 ch 3 Q , Had adagbrcu‘g sow. 09 a.“ ohara es EHCIOSEA ‘Hne Surcace. E. AAs cloJc froioc’r DC E «ml 4‘ = [EHJAI Case 9_ §E‘JA : g E. AA .‘s “as; q,\u.+r|‘<. $19; ‘4) ‘H’Vooak “NZ surgaco. KP= §EMAA - §ECo;SJA- §E.4A , CE}: ‘0. “m “'0‘.” 0;; Saw “a” crosLin3 PgrfgnA;C\)\qf lo cm arm is PrOPorL.‘onal +0 E. 00 The MA mm." a: has crossing a. Sue-Que (DU">WQ.f‘d Haas mum; InwDJ‘J h‘nes) f5 44mm eroeor‘\'§onon\ +9 EH“; . The ma" number a? [has arossin a surgace .‘s ProporL‘anl 3m flux mu! ~l—L‘u5 HA2. IMJ damage, uw‘osaé L3 Mm surg‘oce. n. Examph. Wkw‘ Cs -\—L\e val“, as: charge X ? 1mg int a SPLer¢ aman 0' Tha sflnere ;5 00+ '1 cu vow-3 “mas. The S:ka a-«J Mame n24» charge 0 Is Pmpor‘hona‘ 4-0 7. A sphcr: arm,va X .‘5 cu\- 14' inward lmes. The A2; C14“? ¢ ‘In 4kg srLgrg IS mega-hue, QHA *Wl’ce Mae Mugni‘fllée 0? Q_ TL“; x=__2Q 25-5 Applimkons o‘i Gaoss'a Lava " whln you use Gnvsa's ‘n—u. «cu mub§ “fled a. sat-$ch (cult; a Genusm'an ‘orcq‘g) +0 use. NAM Gwss‘s LD-N' The Gooosium surfing. Jo“ nd- kuuz h: be. a read sun-9;“, 9‘; Ha; phjgd’. H' can In. .mamara. The, wrcuu Maw Lg, parka“, embcddd in U»: oLjecA- aml PaA-‘n‘ly .3 mm 59"” 1. The s Mme‘hu‘ a? Hm vassicm surfing, allow; ’00 b evaluod'e §E¢Jk The ¢3M-¢("at 0: “M- gausiu surge-<4 vsualLY «flakes “wk 9‘; 4kg Problem, 0‘ . “I. a 3‘ IS‘ E :5 Perpen-‘mulou- *0 We ansm‘om surfing «M44 ,S.‘ acndnnj' MA “Awh 4419M Cut-Rae so §E AA = EA 3 “M” 5 ‘3 J_ . cousin"; our 4‘ 1‘; E I. yourde +0 Hag Gawain-a surg-‘ace +L\1n 5 54. 4“ a o. a-(v- ltu’l’ Par-l . OF HM. Sarina: s_ l‘; g so o.-\- gnu-1 Pond on a guy-Qua. 44W,“ §&L.¢A= o . anJ Karo ovu.r we ‘ rub (,. The E m §E,JA :g Hm. +o4aJ e\¢¢¥n‘c 9:21,] ad each poinL TL; 2 may LI. lua 4’0 ants“ bow fnsiJe. and «whale. 44m SUF¢¢A¢¢o 7. The chm-82 on a. oonévc’cor Mu5+ Le \ocadecl enL‘rely on [#5 surface. “1.) 11“, fight; “an; E .‘s zero as." all Poid's u‘n Hue Kathy-For o? a. aondvolgr who. u,“ chug“ M .HM; maiurA-or a.“ a.<\- res'h l? E were nu+ {cl-o Hm.“ Mn. clams.va would Move” “a E:o “5&2 'H'If- QMAUGL)"; 5° §E"JA " O ‘0 3-:0 , 5° “W”? "5 “w shuffle inaido. HA: 59"?W46- You can 9.0le53. 6° Ha: surfing 5° +"‘““' H is very SMAH. Slant. HIKE Sur$ace waver cowl-om; any charge) V00 oomJuJe “‘04 'HMB “WWW‘J‘ o: “L‘NS‘ 0"" (OM... P is it"). The same a» uMaM Ln:le 97°" 4“ 9""‘4‘ Ms“; H“ “mud-ml 50 “max: :5 no ckmfae [mule “he couJucl-or. A” u“: cknrg‘ was on Hue Sutcmu a? We waive-hr, .. Covlunb“ \au now he Au-‘vcd Tram Causs's Law- E :s Perfcncl-‘cu‘taf *6 W2 Gaussian surface as} a“ {mafia L, C‘m’sec““ samwmkra (We. (3'41 Palm‘s ruJI'odLy ou‘wdard). Since. a.“ POUJ" 5‘”me . on Hm sufgnca are «Mae Son-Me, Aid-anga Sir-om g, H“. MQGV'H‘HJJE 07 Hat Qua is Him same. a} a.“ pond-.5 on 4&2 SurCM-e- N" POCNF 0“ 444% surrnc: is J;§:e_r¢n4 .‘n any way E‘DM 4N] OHM; eox‘nh $0 -Hn¢re. {5 mo reason Br E 4‘0 413:?“ prom One void k emoJr‘aer, 53EJA= EAIEt4n'r‘)=§°--7 Iii—$5— 4K!“ fa F: E43] = Air-6‘0 13-1— (Cwbmb's luv) 9. “dd 0? a; c‘uusd “dock-‘8 sphere L” I? a. ckm-ae. is p‘ucu‘ on a conc‘lvc‘ina sqkue Mun a.“ “u. Juana; No.5 on Hue surfing of “ne sekgre. From gamma—max Hue charge ‘I5 Jfihnw'l'eé un'Ierly over Hm “Jan 0? {4‘5 sphere_ To oPpH Gaves‘s law, You use sammeh'y ‘ro candule “no.4 Hue crew I“ rah“! (J Feb”; 9. line. Ara-w“ from Hm ctnx—er or Hug svk‘rg +0 44"; fiwa“ POM,‘ ) . TL“ Mn “Rh-’42 0; We. :{dé is onlvotm evujwlvmre on 44kg Surface CS 0‘ fikefical oonA uc’ror. o.\ on seiner: acumen-hr; NHL Man ‘0.) For r>Q , nuke-'2 R (.5 «HM. raJ'xus of HA9; waded” - JA = 411' r" = Govsskm Suvme 5) E E ( ) 2; E = —‘~ % 411'50 rz “W duh“ $9M ou-LsCJc. Mn. sphere ;s us “away “ll Hm charge was conceerrM-acl 9.; {Me GUNHJ' o? Jrke sflmre. ufl Fof r<R, +Me, fleck-CL CNN E=O. Tiu‘s is 4N: var any oonéuchar. x0- nL‘A a? 0. “he 0? charge anJ era. cylx'nirl'ml GOV‘JW‘JDF- Fov a. erY \053 “no, 9: ckufae’ Una Qt“ lints “re, raJIQHY ou¥wqr3 From HM; line. a“; \Ce. in flames ‘Hficfl are ferpthCcuhar *0 We \ine. Thu majni‘wla or 'H‘E. “@146 cons'mn" a} 0-“ 904n*s HwA are. We. same radial A‘sbmce from Una Una. Choose. a. G¢ues€an Survnce Wed: «‘5 a. calim‘ler, wfiW e.an PerpenJ-‘Lulu Jn3 44M. line a? dun-8e. yam” gig-4A + E-JA = .‘L Lfiinhx M45 5. mm 1'5 Plrpbvulicoku‘ +0 MM. cavrder, so éE-JA= EA = 2T1‘V‘LE is PornHel *9 we "‘45,; were, is no componewi- 09 E W04» {.5 Perpeml.‘culo.r -\-o Mae. cowl” enls‘ Thus, §7E~AA ‘0. tn}, §>E'JA= 21rrLE= L1") a) E= 1 e“ ZTrgr Nah. Ham! on” Hm} god-ion a? Hat uni-re M554: HA3 Gaussian avri‘qu, :5 madam] wk“ w; cakuth-e §E-JA omJ This 409.5 n01; Mean Had HM. 9.11.1 49¢ 41; a. 5k°r+ wire wauIJ hp. We smug ob ku¥ 93‘ ‘Wt \ovxa wirfi- T‘ne Vad anA- “a: wire is long allowul us h 951 sammd’ry +9 concluJe Mud “All. 2w is rndcql . For a skorl W‘ng +ke manfloée 0: “‘9— :iP—u 0‘4 “‘6 cenhr a? Mac calI'nJer would n04 be 44w. Same as Home. 9d; DJ: «Hm. uni 0&3 HM; cal-RAM. E wool; n04 be evtrflwkzra eerpenJ-‘cular *0 Mae oahmhr Cor a. 5kor¥ \mrzr T‘ne finhre dam-39 of We. wire {5 ’mke" "V‘J'U 0.90mi“)? wken Gauss's low.) is USGA, [904 fnéirec‘l-‘y. (Gavs5‘s law couli my} Lg cash? «was *0 Mae. Sher-l wirt.) IO. Fde a? an (“Y-unfit. Home ska-{- a? dam-82. sud Gwfliw smug! 3‘6 $3MME‘r3, 4L“. shah-{c Geld {s erPQn-ligulmr *0 “w. 5|»qu 05‘ A mind" wflrk cLarae anrallal 1m {Jae wall a? “A: calmller) we.“ etrpenJfiwlm are sum. 5’94": “A + E‘JA ' 5“ LSHMU en‘s 5: 56-— —E) Since EL =0 S70! wall 0? c. “ruler, 5.113 =0. LU \fl I dwarf]: Anni“, {SJA = E‘A Cor teak EIAJ. O“ coulomba/M1 > ZER = $- = GUA =7 E = ‘2: 60 ea 250 The Rehl hues 03' Ha dad are shgiehh Parana, uwcot'mly spALaJ anJ are Pu‘oemdicular 4o Hw Skzek‘ Th; ¢a\cu\¢kon assumes a... :ded, large skid, W4 “A: resuHs are a 3005 aquxlmkon *0 Ha quouwior a? E for a ‘arae 53mg; 1 a4 poinh nnar 44“; “A,” 0‘; Mn 5M2»): and dose. *0 “n2 shed ralaA-‘ue. h 44“ s‘n¢&-.-‘5 J;Mensions. In such mus, 4M; Cid; is nearly uniform and peremeJL-Ar 4o 44"; sLeeL u. Pam 0? an :nVCnHw‘ plane duran {flu-"e, when an. «minding 91.31. (r. 3N9»; a (“J/Huge) 4kg ckarae J§s¥ribu¥u {Belg uni-Yorle our HM; emX-{re Sargon“, a: “no. phfie. The chm-35 Par unH’ area. is uniiorm on Ind-la gala: a? 44.9, Plug. 83 sammel-ra’ H“, ehdvru. Cidd i: altruhA awe-1 Yrom Una plqh, is fUPMJchlqr {0 HM: 9b}; cud is unifirm. “,1 You on.“ wnsiJer Una glulric Eda JUL *0 “no. p‘aA'E- (15 Mac resul‘md a? Hae {:1le AM; -\-0 4mm shad: o: gland-5.3, 0': ohms; 9V und- area ‘A/ M unma¢ F“ Wu": arta. {5 also 0-1 + A ’ B + c, In regions A and C (wgae “M 4?+_E_-, ~ Nah). E=E.+E1= g 1 + E q. 69 «- 1 fiEl L+ke clack-[L “this N44) + + In reafon B, H”, gleam-G Ellis K K 5‘; 9-1. oppose, each 0%" E.=E 2&0 E = _ _ 260 L E2. ‘ 0 1 as mus+ be +|ne case, insiJa a conJvc-l-or wLase. charges are a} resin 0-) You um SMJ We. deck”. ELM ou-‘sIJe UM; plqhz using Gauss}, 1m» JN‘edly " * Ckousg o cal-filer as a Gaussian svrrace. « + * " S’E'JA ‘ §E-JA + §E-JA 1- §E.JA : .‘é. ‘ * MN eqlx‘vxdcr n'aH 50 * + and walk .M “' a + " gag E‘dA = EA 5"“.6 E Cs PerPencl-‘cular +0 Una ‘2“ em] Rm! vm'rorm ené EH” = 0 Sim-"— 'Hnere {5 no $‘ul Marooak Hm ma“ (E is 3nd. Slant faraHel {'0 Has, waH) §E-\1A =0 Since. E=O insiJe 47kt 9‘42.“ E-JA=E-A:$_= 0’: E=2f § en A: 7 so 12. F114 Lawn.“ npgosihhl ckarggd 910.415 Ln wk“ Pardld Phdeg, are, alum e‘bua‘ and. opposfle charges, +1“; $11.3 .‘5 neon-l1 uniform i... 4L4 59mg Lflwzen We \alal’es. There is some c‘nqrae on 44,“: maker sv(Ca¢.¢5 a? 44‘: 9‘03“, \wlc mos¥ a: We Unarae conun-‘vra‘les an Hat inner svrgqces- Tkzre “5 some Sfreme‘; (Sh-Mama) 0? Jr‘nt “eh; near HA9. e435 0? Hm 9‘03”. For large 9141s, “Mama :5 09h.» ncsh‘aibhz, and Hm fade! lad-ween 44W- phl-es can be, assumei 40 be unigorm. Q3 Lb) You can comihr “a dachk— Crud *0 Le, H" ruuHavA a: +ke “this due *0 +wa skuks o? ckorae In region A ‘ +kv. ‘3le; E. and E; are abunl in MQJVH‘LUJE bvfi opposih M Aka-Hon. This is also 4mg {n reimn C. Thus, ou-\s\'Ae Um p‘aA'es, E:o. :n r¢3§on E, Luann CF:le Pmm‘ 4O “ne rfak-I " B C E = 19.1 + ml: 2’ +51: cJ (+0 u“ mam 25° 25» Ea 7 K at.” e W‘Ze Aug; 0" Aenbifi —0’ (who flak) (lash '5 PM” “A V0“ 90“ use, Gauss; La»: 4» {‘an Jr‘ne 9,12:th “a” Region A 1" : §E-M= §NA+ MA + §Eu lfii- had r ‘ k4 L‘ J B W :5ch :9; A flag-Silk : EA (‘Hnt field, {f Ana, is perpgnJKcular 41 “a: Flak) 2M 2‘ \ gen-3: :0 (+1“ flew, x “a, (5 Parallel In; How. 954mg" wall) M D; Em“ dwfl" EQJA : 0 (E =0 Made Hm conduulor) fl anal §EHJA= EA+0+O= i :fl:0 en en EA = 0 =7 e = o. Rggfovx 8 §>E-dA - §E-JA + éE-JA + #E-M 15W (:3 l . aler fisifi Md wan em; ; O + 0 + EA = ge_ ___ 04A 60 0 so EA = LA =7 E = 0—.) -5 Eu \3. Elwin-(c. Cu,” tor 0. char 9. unworle Jig4r§bglga in a gpkar-‘cxfl volume, Here, “\e clams: migH he, Ju‘s-I-ri‘oflul In a non~ conJch-or'. Suppose 44w. ¥o+ad almrae I3 Q omA ‘Hne rmlias o§ +‘ng sPLgricad Vo\vwxe .‘s R. Govbsiun “43cc. 8% SaMMd‘j. Hm crud Cc wan, auhmrd and ez‘ua‘ in «Ayn-1rva oi a.“ {min}: on “‘5 Gaussian swraQ- E-dA = EA: 41tr‘E = 2;. ca é a» _ Q | = Li $~QV= m3)%rrj 02; 3 So, 4nrze= or“ @369 E: _Q_ r (r<2) 41r236o L The glad—n}, $116 ma3n(+q;lg .3 4&tu Proper .oml +0 r) +1“— JCs+ance from “Hag canhr. . For me) HM». Gaussfqn spLere endose; cLaraeQ omfl‘ §E-4Aa EA > %— .7 g: 9... (charge “Law We a 6’- .+ (An Qlocafialad’we 6° W Dr EakrcoFrdj-ke sphere} h m, *L; duh-{c Sula as a. finnch cg Jis'kmoe. has Hue ruuewinz ampL. U4. wt. E xmy‘; A MM CWAVd‘MQ Sykere has :1 “CHOWCOFM (‘ofi raéiqlkj sammg‘h—ic) OLarae Juxsfily given 53’ [c {0 LR , when: r Is 4L2 AJAan gram fine aenl—er oi 44‘; 991w“ and R is Hug raéfos 0? {Arm spherdrgQ). CMJ A“: dwhm fit“ as a $onc¥i°n cg A§$¥ovxce :- ¥fom “no; cenkr a? 4L9. Seker‘e. usc'na Gauss's lauJ- [9:0 ¥0r r>R. Nol'c “~03! um": are hue cute: -. cast I z N- R (£2 and ("2. Assume 51 0an. 1 Guam surfing § 2.“ = 2. [/ng t fDZQo%)(4TCf1)‘-lr 5.4'fir” = e e: 55‘"%““"“'= L2" (HE). ,+ 5-4113": QUIZ r4 :3) E: Q—orz 5" 46.2 Case. I '~ r>R Again use a concenl’fib :fku‘e (NH—In r>R) as q Gauéfidan Surrqge . §E-AA = $— 60 41v2 E = Lem-HHE'LHF = 49°" SQ r’Jr HR \_ ED 6' - +211 4‘ ~T°($".)= QORRS \ 2 5° e. 41“ E: (“1:23 a) E: 2R3 ‘ 6” 77‘ NM: “‘04 In“. e‘flefibna $0? E a QR “he” r: a. 42° 15-5 Charges ow. ConAod-ors |. chn all charge-s are 0A- res’t, “he didn‘t: C-‘dd o~+ eVlv‘y P01“ in a mdvc+or {5 zero. 1. Wk“ dwx3e is NW On a. soL'J con-lud’Ofl'4‘L‘e charge :5 [Dani-GA enhle an +9": 50"?” o? +ke “misc-hr, 3. Gaussian Surfing de Charge. OS: “N‘s whduc$or is gourd baht-le on Hag 00R! sot-gnu. o? “a: Cvac-toh N0 chug; f5 92an on com! ’«or H» H Y 4- ; wwficnu duty % v. we 0 'nc cm: {a . Nd“ ‘u‘w‘ g E 'JA -‘- O $nr We Gaussham surface Since. *4". Sat-Vase .‘s .‘nsidg Mu. conich-or’ «have E f0 - newton.) Hue dam-3‘; enc‘oseJ L; 44": sat-face *5 EU“- 02 (B hasqu HA: anuL-‘oq' + I?) and” um.” + % {n.Su-JE uni-‘4)! 30+ .0 .‘nsIle Una unlock: CS fare and ‘HAEI‘C a no gknrga, ins-'4! “no, hollow (Luv-'4): (“"5 I} a aha“) . Thu-Jere, :6 on 4k: “~37 wan is tero_ 4' Md rJAargLi-a SOHO“ a no.1: dnarga 0? +0 is plucul on q V5 (gaucssur mnAQLl-or and Man a. posfln'ue charge + is or ac .‘nscrhé Eula We cmn’ly +LH'O“3L\ a. Small hole .‘n We wnduglor- ch charaz in +lu. axng rash on on fnsulal-M slaml. La) charge. on Inner wall 0: candy fie.“ = o: 3; (s; .3 We “mug H12 maul”) The Llflal’at Msiie Ha: Gaussian surfing .3 eve O = (b Mild: wmlud'or + :3 on cuvfily mu + (B ,‘n mm“, 0 = O .5 1) an uni-l). wall +1 1 on mull-b mall = "1 Lb) Clam-3e on ouler surrace as Mel-“l Ba aoneuvwl'lav‘ of alumnae, +lnz ‘l'olul clung). on We, conJvcl-or clots nofl' dnnnae wlnen 4M2. (Auras, +3, is Placul in Hap. hollow: muwa. Q + = 233:; 3-3:“ Owen-u : 00R“:an - meos = Q — (‘2) = Q"? summa— U" Suepose Mme. charge. «b in We. lnollow cowl), lie:- on a mum conical-u" Lull- I? llne loo“ Cw 09$ We schJ «ml low.th Una inner wall 99 HM, lnollow conCva‘l’Of' “men Were u:le no law er Lt “3 Jun 9; on ‘Hfie inner wall 0? 4kg conduclor. The bu.“ woulJ .‘n 05%.; became, Pant o 44% wnclvdor (sinne dun-a: covlul Qua.) belcqu We, luuo (motive-low)- Tl“ chairml “may wall anal 44w SUFSDLL: o? Una loo.“ M50013 i‘orm a new inner cmml-Y 5w age_ Tkere would be no Cliniée (“mafia cram We \nollov.) unévolor) :n use cowl-l . In pur+ 3, we Sow ml we charge on HA; pawl-3 wall (5 zero when +lnere. {a no anare "" ‘l'laa l’iollw’ (Andra. We dflarae on +L\g hm“ we.“ I)? +ln£ conducl-or woul lag {-ero apler we wx sl—dkm +m inner waH- 8;) Conuwalion o? clmgm “‘1 5"“ Ll“?! Q+ remoms onclnom e‘l. SM» Jrlvxare .3 no char 2, insuale -l-lne conclUUl'D“) °" MM). MM” anvil-1 wall or homing in ll“. ecu/(l? ) “ll “"9 Charge 0+1 may} h’: on UN. oulrer Sorgace 0% +lne °°"‘4"°‘l’°r- 5. "in a. l:onmous experimeml, q ball was glnoxaul omJ lowereJ in‘l’b an unchargecl Mt‘l'al coal—nine“ é H¢r¢, “a charge on “x: [nnfl Quill-a wall {.5 —~ (+Ake q Gaussfim 65 50(9)“ insiJe. Jim Conclvc-lor -lvo SLouo Hm lo ql clnarae inst): 4M2 sorCoce is zero T1» 4. o ' 2" firm“: wall = ' I mule a ' ‘ibal (69 avshfnn %Innef mm = - (sham = —% ) swig.“ 11"" d‘a'ge 0n “llne mall-er we“ is (I; ($.w;‘t+% an.“ “a : 6""5l“‘l = 0) SO fiovhlée = - g," =cB ) mu w.“ No.“ Wk“ “he laall l-oudnu. We malal conlainer, l'l' Income; purl 0: ll“: lealner (and-flux“ The inner Surcnce 0? 44M conJuol-fing \\ con-laine: IncJoA¢5 MAE Lam's surgace- Tlngre {5 no Clnaf‘ae lnomain :n We comluclwr's (maul-ya As we have seen) -|-lne Blur e on 'qu (made wall Musl mow 5"- i'ero, CD"‘¢,VQL,'M 09 ulnarae =9 993mm, on + $flfil'flhn‘r =% ‘ $0“ m’hu‘ner I Since nOhL OS -\-lne clam; {a W 4.1,“ MM“. wan of We con'l'ainer (Wlfllf—l‘ Mdudes HM. loan), +ke gal-{re chm-as; (E is on “M col-er wall lb 0‘ Nut com‘ah‘er. Au «Hag duraz Mud» was on Hm: La“ 30" K's-ans?”ch #0 Ha k ov‘er you“ a? {7kg Mfl+ugnnh If “W LA“ I'; 4Akln MH- a: ‘Hat. M€+A| f—On‘kau'ngf‘, H wH‘ ‘02 seam; +0 \n. undxaraewl, 9- Expefimznks Such as Hue. one in pofi 5 his-\- +L\¢ vans-14y a? Gangs's Inn), W‘J kgnce Cou\omb‘s \mu. 'Dirtd- measorw¢n+ a? We —:_-1 Jepemlcnce ac elcc’rroshhc $0“: wmn 0» "of‘im ‘odame are, A.‘§C-‘cuH. InJ-‘red Led; uscnj Qauss's (cm, are muck more Free-‘31. The Power 509‘“; dang“ 44m col-2r SUtS‘QLI. 09 Hue lor : SPLgrg. An ehéromder E Measures shun a? c‘nqrac Bdween 44m unchargeé hm" 59kg" cmcl (any “00" oi *Lw. lure sPL‘ere- Gauss; “and, 4km: S‘noo‘ never Le any chvae on Mae innar mom 0‘; Mn! large 5 Rare. Tim‘s means no cer a Show” ever glow Harong .H‘e, ehnhomglrgg {-0 Lke Swan Spkeft- . . . In cad. no char 3 {5 okserveJ 4'0 new. The. dec’cmmehr ‘5 v9.01 Stfl‘brhuel 5° Hm"; l-s “HI: 3400“ “m4 GOMSIS km) (.5 vadié‘ This Means Cedar/Mo‘s \ouu is ValLJ. We Know.) 44‘; exponen+ in Coulomb's low com me“: vara ‘G‘om 2 [,3 more Hm“ 10"5. "L Hu’rros’m’n‘c 5 kid 4 Eng // W a sgnsfliue Chs#filmzn¥ {5 Place} in a waded con¥ainer 4M¢n Hat shy!ng Yuld .‘nsKJe Una be»: mi” (flu-"~15 be zero ad Mae Ins¥rumen+ w-'l\ be sku‘eldeJ $rom We exkernad duh‘ic grew. The Q‘eld raJx‘driLuks UM, aled'ronb in Hag (Lenka-Mar So “up! are on 'Hae (an. The charges on HM out.“ survoce of HM cmfl'aincr “adomdicoiwn cred-e cm elechu‘c (:(ela 'Hna“ 9,“;ch cancab “we edema! Ciekd 50 “~04 E everywherc insic‘a “a: Conhziner'b oul'ar suryace {.3 taro. 3. Charge Acnslfi on U»: Sur$ac¢ 0: q concludor {a rah-Ltd «k, Mae E $3.114 Jug oohmh HA2 umJodror. Fés §§.JA:%; ( m §E.4A: §E_JA +§§.4A + §E.JA hum q lad" 1” end won ".4 E-éfi = 0 since E :0 “‘34. a conéudor 5‘45 = 0 sfnc: HA6 'E {mu M054 Le pgrpenJ.‘wlur 40 {-kg wan condvd'or's sofgaca and heme Par-aha! +0 "ule cal-n40: um“. Kl? E L‘QJ any LDMPOflBn+ farollel 40 Mac acndudori SurCAC—c “new charge—5 On ‘H‘e ‘Vrr‘u'e Wm)” “0+ Le ad rest”) a g’E‘JA = EA , shoe E {s perplvaI'w‘af la Hue +op «M §E~JR=EA‘ 3: 2’4 =7 E:£._’_ 59 60 £0 Tk-‘b Nqu is consuls‘hn" wH-k pas-\- rest. FM Example, E Jud col-sue a SPanrical cwéodo: 0? rain); R uml ckarae O {s E.._L_ 9, b“ 01: chung : _Q__ (y (2/4112z 0 47m R: , we“ “"2! I 50 E: a: T ‘ m; c We 0‘50 saw {that} E=%J; gr 0 Karat. conJod>Mj Plod'e. 9. E unfit @ A coal-«Aha QM.“ 9‘ 5"er “In” R “"1 “"3 "Aids 2“ E“ M} °“"3° 20" A Md duq" O? m3m491¢ Q is sospuéd 3631: “‘9' 5"“H- A55““"‘ 51 ‘”"l'$' my wMoA “fie ckarae M U“ {uner we.“ 0‘; H“. ska.“ 1. L“ wkoA is MM. okm-ge, on “HM- ov‘ef SUTSuLE o: We sluu ? Lq wkoA (5 «We. OM31}; Ausfl-Y 0' on «HA: ooh: surge: a; Una Skull 7 h“ Skdck Una dukfic Emu as a. Quack“ a? 4kg 4.3%.“; r :rom «Uh: (Lenin 0? 4L: ngu m. Exnnf‘fl; Ln.) Choose a Gaussian Sat-came 3";qu ‘HM 5kg“- éE.JA = 0: %_ a) m): chm-Be. insiac {-Le Surge: i: o 1): char : "made + du‘rat on scalar/inf an}, m.“ o = 0 + rim-83 on 4 Q mm}, wan Thus, 4%: dun-3., on +1“, cmn'kl man is -Q charge on AM.“ 3 dung: on oukr Surfamd- dum- {tr-o. 4, Charge i” Candy (b) r. on c, {4 ll 2Q : char}; oh baht swam: 4- 3(-Q) ‘u , um That, Hm charsq. on «Hog oukr {wt-{ace is 30 m 0': charge = 3Q = 3H0 mm 4-1: cm? 15118“ ‘J) For 0" ‘ R Us: a sfhncnl Gaussian Sofia“ of rmltu; r42- E~JA=4nrlE3$~nQ a 2.4. Q Go Go 41mg rl FD“ R<r< 2R The fig; Ins-1L: Hue coniudor For r : ZR Us; is zero, ‘1 spher'mal Guessian sorrow. oL‘ rashes r> 2R 5:.“ = «HrrLE: 2,. . ZQ+Q o 60 E: 30 . . E m: , Nah +Lm+ EMR) .3 ’AQ Hamel 41750“ _a_cz_ ’4' Inma‘ The kohow conductor“ Has a (bid cl‘arag of 20 suspgnéd in {4-5 {rd-Erich. cu How onch (Jung; lius'on Hue u'nnu Na“ 99 44M condodor? m How much charge lies on ‘Hne afier wall a? “me Mntluchfz “) wk“; is Hm: M): dun-3.: on W condvdor? V“ 0"“5‘ a Guess-am sot-Que insue Hue eondador. _ §E'JA = é. ’ O —) m4- dnrae Ins-'4: Jake Gaussian Sdfgnce vs 22m. 0 w nu. 1mm. +o+ 10:0 -><6 no u {n ran-[~45 lag-39' “an” 00+" u') an“ a? Etefiznfizizfi NWL" 0‘ mu" “‘5 W55“ 4mg“ .unc Gaugan Surface :5 rmporhonat +0 -\-L\e *‘flad (Jun-82, ‘msKJe 4k: Govssiam sorgzce. Since 2 HM “ms cuss +1": 9521;“ 9“” (a) and HM $Rf31 was 20, _8_ = +05! C1“- ‘ 'h'mlue Causs' n sorcace 2 20 Thus, H“ ‘65“ dung" Made 41". Gaussian son-face is 80. m ‘ ‘63:: * 3m “gm = Mal Mac 9‘2: core: : nun» u.) ‘buer : 1- 3:3: 3 861+ (32(3): 6Q Gaussr‘an Surcoce ('3 ...
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Ch 25C Notes pdf - Che*u 25 Tlnr Had-Ho Fieh‘l We{Mink as...

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