ph132s04_hw3 - PH 132 SPRING 2003 HOMEWORK 3 Assigned 22...

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Unformatted text preview: PH 132 SPRING 2003 HOMEWORK # 3 Assigned: 01/27/03 22 141 50 SHEETS 22442 100 SHEETS 22-14% 200 SHEETS 6 AMMD --~—-—--....._——___...._..._ .~_ .— QLVEQ“ L =/. ‘lom is": a) 6.006 “a b) £00”ch A c) 6.00% f 1* 450%b EM: @ +firoujh fie n'jhf Pace, 6:- a), 15 and c.) A d) fir each 5 m. ‘5 Nahg (PJ‘s-51d? 5‘35 (whirli— in “this pram,» ms 5mm Q; E‘- at? . flair, “a 5E The cube in fig. 24-26 has Houlomb. as given by (a) 6.9m. edgclmgdmoflAOmandisori- 3(1)) —-2.00j. and (c) #100: +. . enwdasshwninarcgionofmfi- 4.00E. (d) What is mental flux ' form electric field. Fmdtheelec- through the cube for each of " n'icfluxlhmughmerightfaceif thcscfields? the electric field, in new per Nah: @553 aim by A 501“ PRMT,se all E/Cdfl'f- F/‘V cums me be we. fl) Q“: E"? 35 c/efih:%3n)ao area Vedvr a/ways poMb owiward 100/ a (2/de Jarfiwoe; and ’3 4/ J“ r :taérr'fbwlfi sumac . 50) Kb-fir ‘Hle fljfifie‘ =Aj e qegfi": (6.00%)? o (Ac/0...)? 3W5 3-1113?!» = (6.00%)4 40mm. 2E] Am. .:.5, W _.-. a, , a); f-jémm b) «lire-A = (-2.oo~e>3- (2.40m) c 3mm. J = (Wemww’: Alas. 6) é=gfis (‘3-00”c€ f 1100‘“; a). (Ayomyjt e o v A o .—. [(300%)(Homflfl/I/Jr) + [(#aowe)(z4ou)fl%") E m5. (15:3:— 'A 5g no! So when 1%”? (Is. no charge {fie/0M4 '3 ' (£5 fr: 147:3 problem-Me JefzzflF/ax Md Spaw/ am'fixm 14% #erl! a dwarf Surfing is zero; @Emm “For 0,5), 4176(6). N5. ! I g | 50 SHEETS 22442 100 SHEETS 22 144 200 sugars 22-141 0 flMMfl 11?. A point charge q is placed at one corner of a cube .- What is the flux mmugll each ofthe cube faces? (Him: " ';;-'- law and symmeujr arguments.) '=- ’— ffléfi’ 457' ’5 LABEL 7"»; Frags : “BAcK. NOTE : 7,95: Fz—ux 7' 22201292} 7295 g may); Eon-ow; + BAUL i 9:332:79 WILL BE.— 2510 5 space: 7745 RAN/XL- ' 7—754.) Lungs ammmfdé ‘— wH/L. BE.— TO THESE i l I 1 i i Pflmuw (EACH FACE OF I 22 141 50 SHEETS 22-142 100 SHEETS 12-144 200 SHEETS 6 Am 13F. A uniformly éonduaing spine of 1.2 m - ' a surface charge density of 8.1 ,uChn’. (an-71nd 1h: nct I thespian-c. (UWhatisll'Ietotalclecu-icfiuxleavingthe -- fliesphem? 6- 64% Law 6" 6C) 3 gig? I So 6‘(4an):qfi'(%n)z(g'lflo~‘qmz> Ms b) 053/ 9093' Law: PM A Muslim Sal/153m drama, He. spkmz. \ f : ifi=nzfl r ‘ q; 6 01A ’ \ . 1 @ = (2.9143 1: 3.0éX/O'5C. \ / E 6: 5 .' Emma: d=2r:/.ZM(M surfade dew 6 gym) ' {swatwymigiwxgw/Mf/ m:a)2 QQ’ 50 SHSETS 22-142 100 SHEETS 22-144 200 SHEETS 22-14] 6 «mm Ix. intemept a significant number of electrons. The resulting-Z buildup can damage eiectlmic components and disruptope ; Suppose a spherical metallic satellite 1.3 m in diameter :--= lales 2.4 pC of charge in one orbital revolution. (3) Fmd u suiting surface charge density. (b) Calculate the magnitude I electric field just outside the surface of the satellite, due ' .:--__.-_- - surface charge. 50177. AREA OF A 9:45;; 2 i ‘95 A : 9”th §E SKEW? b 2 :5/77’ : ’t‘r‘bL 7-”; 601K CHA-iég MNéIW 53$: 90 THE E-FIEI-«b AT i “T—LIE— I.-o 1: «1: al— CDXJbUCWQ I 50 SHEETS 2244! IOO SHEETS 22-144 100 SHEETS 22-141 ESP. ‘Charge is disu-ihmed unifm'mly lhmghout the volume of an [ mfimtely long cylinder of radius R. (a) Show that. an a distance r from the cylinder axis (for r < R), when: p is the volume dm'gc density. (b) Write an expression for Ewhenr>R. luv-“mm!” LONG-r co 99.1.5572. mVs-opm an” N155; KHZ-TH ¢ I Fifi-b 4.4%; n 0401' Show”) ' A733 RADML “OK 1wmb5'N$>AMnx 6N35L* hun-CII—w—lll- 2.. a .— p 'WFDJZfK £QG$UDE§ H 80 I To? +3c771bM : OF 6.5. t ' Ma EOZSF>El LDC/ATE A ggusstAMC‘eL. / 001—9le MT.) AWL? ENE-s i i t .l g i J I LU __ 29'. In Flg‘ 24-33, a small, nonconducfing ball of am m = 1.0 mg and charge q = 2.0 x 10-8 C (distributed uniformly through its volume) hangs from _ an insulating thread that make; an angle 6 = 30” with a vertical. unifon‘nly charged nonconduct— _ ing sheet (shown in cross sec— :3 lion). Considering the gravim lions] force on the ball and assuming that the sheet extends far vertically and into and out of the page. calculate the sur- face charge density at of the sheet .ssm- 22 141 50 SHEETS 22-142 100 SHEETS 22 144 200 SHEETS E/ec'h’fc. field due 40 a chemical sheef' 4rd Ueurba‘s 2"“Law Draw a 14166 body I ‘1’? - 1g fsfieérce dmipflx (Jacobi. 99.151015 Sheet E-‘gé- E6: {‘5 ‘ha fire n3)» 5:12“ fie aka“ 35 f’epukt'rfj 1%: ball. The sflsm is M (ya/fifinum. @ “Sl'nj NW3 2""Law: ZFrmAe-O ' 'X d’tirzcfi'm: €5- “T775:'n99 "-' O rjdr'recfim: TCDSZMS = O E: .321". m x (2) a; m 5i"? " mmrré Plugging (2) Mo 0): 5“ case i ‘ a _ m E: 22 21/43 P. 5%) :2” f2 '_ {fine I Q r "‘ £32119 15m 9. 2 43.55%“ ¢7~-m1)(1.0xzo*’g)(<zmz) v‘zméo‘ ‘ «Z _ 2.0x_/o"c. I Am 22 141 50 SHEETS 22-142 IOO SHEETS 21 I44 200 SHEETS 6 ammo 15.0 cm. The charge on the inner sphere is 4.00 x] that on the outer sphere is 2.00 X 10“ C. Find lb: 6 {a} at r =12.0 cm and (b) at r = 20.0 cm. '@1: 405m fir r=/2.0om b)E(r) fir r=20-06M we will pwr'a 663669201 Sphen: Hm. figfidfia : Quad A is five arm 0+" #16; ' 5° Mussm Sphere. EH __, e! F'Mdfi‘am 1h MC .54” CW”(I$M,?1°S 60 CW and q” at e l ' E: Z: ._. 13:! =. (3.1%10’41} java/6%): Z Qx/omfi (0"20m)‘ ANS Now we are (Wake! :‘n r‘=20-0a,~. (r >5). \ 77715 6041813!) Spitfire surraumic 601% Spfura (n2). 1 I} ég'drx ("Z—g! ‘Zend=€r'qz EA= ‘2? 680%): ‘32" -.- ‘7: {Egg = kcfri‘h) Wfix/o’m'ycs‘ (Wanna V 4c {0. 200m.)2 =ms. I I m~_—m- »-- WE are {WK/81166! I'll 7“!" “gm” r=/Z.0an(fiér<f;)80 I 50 SHESTS 22-142 300 SHEETS 22-144 200 SHEETS 22-141 @ a) Place a Gauss-«2m 3pm ' I g. 24—34asphere, of radius "m dirongfiou: its vol- 1 I ing 511d! qf inner ra— Land outer radius :3. This i5 am'firmlj défn‘bu/t'd #IfDuJ/I if; we. :01?! MW. 1'2: look 41‘ Me 5,01% ’0 I3 urn/firm fir- {fit sphzrc: QM= share: Ha, 1‘W .5106“ r r: b for Infersurfi - r=CForoukrsun§¢g “a (Wfldhj) 6050‘“) - b)€(d<r¢lo) -’ c)E(b<r<c) ‘05 (r >6) | ! §)ch42c an inner and cider ! Sur (a 01‘ She“ I . l volume. 73 657d 3:“! 3s Marga [0. (f): m HM ream r<a,.7'h‘e charge MWSP’BI'E ! l ! 65:43; Vdum 6r #WIS f9§fi[email protected]%&mm$Mz' .i- _ (fend 11 Abw we arc ram? 13 we (Sims Lam: 353M” 5%? “’0‘” 9% 39‘ EKWTr‘Vé -jL: i::’ r E’Wéo (‘1 r‘ J— 613 ANS. fir a more dzM/ed JezAPmn 04' if; we of 54”“? bWJsee 1% 50mm 1'» CAM-we: b) a<r<b Plate 0. 6mm spin/a in H1 realism 63<V<lo‘ §€dzr= 4%“ E[</nr")= 3 => 41) -50,‘E=O laws. bur-<6 The ski/(Sawmflwfaqso are xhsdev’flS/zed 22 141 50 SHE"! I: 2244! I00 SHIETS 22 I44 200 SNIITS 41’. An electric field given by E = 4i — 30:1 + 21i piercesthe Gaussian cube of Fig. 24-5- (5 is in newton: peremllomb andxis in meters.) What is the electric flux through (a) the lap face, (b) the. bonom face, (c) thc left face, and (d) [be back face? (1:) What . is Ihc net electric flux through mambo? .x, =A0m an! Xz=5.0n¢,50 #10 {any}! Mead) $1716 #19:: Cube)J)/s 1,0,“, flflds' @E +hma In: 0.)»): hp cc (0% bohbm 1ch 044m leg-Face 60th baddbcc. 8') @flm‘ : §E=SB¢JF WMEaMdF-FarhbrW‘ 37f: dflj 7 3:20;“ M44): ‘I‘DP‘EICC-Sofiz): #33 Nate=2335mfi Q=j?-dfi"=f(4z‘-xzj). an; =j[4(*)°- zzgpfjflda = “rm am = as“: A = -Ie “é, (2.0.91: ‘ N5. 5) MM {aw am owe-j), 341:0) = 42"— ej‘ Nae- amend. «gem @g'j?-JFJ”=J(4E-6j)- (-wn {My .53) -%Z.§)]d,q z (0% M = WM = we (2.0mY'-'Fw$. ONeFHézcu 6F= MG?) 14%— égjf-df'flq ‘30:! 2+2) 6.3).“ :J[4V_-E) -3011”) ‘ “W = "4% CZ-°-3‘= . m d) back «(ice J3; dM-E) 1 g van'tg over #7: {caceJ ©E=F£J£4f~3gm>31wim =JfWE)-3{5az¥§5¢3]dfl [email protected] §E+hMJh #1: $5M Fate 2': also 0. b\“...-1' n'r- .Jfl /.. .. .. \ O o ~12“ flan Fade ‘S Affine. u'n ' 1' r.'l J'Mcfi'fl!‘ Eve } I n...- ._ ._...__ _.._____.._ __.._.____.,.. .u..._......_..._.. __———.—_ ..__._._ ._.. —..___.....__.. 131’. What unchargciscnclosed byzheGanssiancubeomeb- 1cm 4 and Fig. 24-5? PH 132 Suggested Problems 'RW Co 8?. When a shower is turned on in a closed bathroom, the splashj of the water on the bare tub can fill the room’s air with negative] charged ions and produce an electric field in the air as great 1000 NIC. Consider a bathroom with dimensions of 2.5 m x; 3.0 m X 2.0 m. Along the ceiling. floor. and four walls. 3131:113qu mate the electric field in the air as being directed perpendicularto i the surface and as having a uniform magnitude of 600 NC. Also, treat those surfaces as forming a closed Gaussian surface around the room’s air. What are {a} the volume charge density p and (b) the number of excess elementary charges 5 per cubic meter in the room's air? flit/wk. at 3.0% x 2,0“ @m dwelt? mtg f \5 waamg (- olyumi Q, Mimi-3 all em came “Bari-We WQ‘I‘MOLL {‘0 i 2 fi‘w‘ SWJEQU’ '5 ZC’ZKX 3.0 t' 3.0x 2.0 + 2.0 x25) M *5 37M?" ,2 1 ‘5’ 5 mz)( 1: 22.2500“ ! i i i t It i i t. 50 SHEETS 22-142 100 sums 22 I44 200 SHEETS 2244! 6 am I 3m charge with a lin- ’-a-—-- gun-cc..- u: dulsityofmagnimdelfincmmwireismbcen- byathimnomouducfingcylinderofwmidcradiuslficm. Withlhe wire. The cylinder is to have positive chargeon nr smfaoewidlasmfaocchargedmsityasuchmatflnml _ electric fieldiszcro.Calculalcfl1cra]uhed a". Hfiwe Gwen '. J! >\ = 5.éx/D 12. = OIOISM El“ IR Ab‘rHouQ-r «E wELE‘moT Agze , *7 CALC. THE E-F/ELA :02, r422 BUT ixrimhLy-DTAE M, g N075 THAT THE £4501: . Fzm HMES (no? 13Mng H525) Porn‘r TowAzb E THE N56. Luce 03“— 04:11:45 NbthLfi" % i i i ! i i i . 50 SHEETS 22 142 100 SHEETS 22-144 200 SHEETS 22-141 6 _ «mm 5' Twohl'gc.fllinmetall GIVE-fl '- 3“! parallel and close topaz: O“ 2.1 C other asmFig. 24-16;- Ondneiffl'merfm mpmfihaveexcess O- J:- 7- O X K :2- M7- 324w A 7": c7121; co): m: PA4E$ ma- -U/£Ia'- F\—>x ~01; '- avg»: THMH --C' 141‘ 75:55.; ALE cpqu - 5/9503 SINCE 75¢. A25 "gm; EACH oma 77M: OPyfifil'TE CM 4—— .‘__ FROM?G' 5172.557" ONE 5! IE : __.__p. I O —--I- _. 4——_.. Afib 773w; we" 0‘“ mfim E FHA MEG. mm- THE—"K AS F ZM’M HON G i 4: :0 £20 9,9557; my CNA - AND meme-r Abb'. 4 2- (—0” $499135 £0 + - 250 W _ W?» WW": We 50 SHEETS 22.142 ‘IOO snssrs 22.144 zoo swans 22-141 6 AMMb ; I | ' i 50 WE M555 A» EXP/2.5990»; For; E“ ! W | 6 HERICAL GAU§§IM SPHCKE O7: M32115 {‘1 i ll :7.— -.A GMf‘b w ’02.: _r‘<.a\ a __H §£.m ___. 2; C4 ‘2 /° Ea AWLV’ING GAUGE’ LAW 52:54:55: PPLYI m awe! Mm WELBS: 1/ 3 3 ...-- £3 .— 77" r A: X __ 2 Cfl“ | f E I 1237—15.} Fa?- ‘THE 31:52:? a; r”"TW”3 :35”; N01) l; 1 E : ffl [_3_ a“; f) = 2m. 3 a r.2. ’ g'WCIj—ai i F52. P 4.7mm, QAUéQ’I—Aw YIELDSJI a) P—ngbg—géi l NOTE: FUZ- THE M 5PHE—7—E #0 TE CW A7" r27}, % EON” :- Eb F = ——————Z‘E”“'M WE": fl (73-13 3 2 5 “‘3‘?er ~63) . M 320 r" I I | gm 9011515 3 I I”: b: OD'Z-O N I 56.6 ‘2' n g?" - ’ f‘ I 3 9E. lnfig.24-30,apoint¢arge+qisadistamed12direcdy 1134:} *he wa/C’a-S abowdlfceutuofasqmofsidedmismcmagrduxdeof modem-reflux throughthcsquarcHHiam'nfinkoflhcsquarea OncfaoeofacubeuimedgedJ I : ég'fhroujh ‘HK Sfddfdl $3? . i éAlbs’s Law } (Rig-W 310M 5‘73 M WWW We” W SW“: 3% l I I 22-14] 50 SHII'H 22-142 I00 SHEETS 22 164 200 SHEETS @ This Mayra! is afifiwif 1h: 1' ‘ calm/41%. Oar W 13’ mm, £045??er usihj (aw:fi=§gfidfi. I t I 1 n Gaussl's Law (5 firdosec/ Eur-625$) 5o : Ur .,: ._ wccomwefirecmwfihvzfifls_ _.' -_' .t (8”le _ 777a ebdn'c flux :3 am'fima Hang/l each flute/fire Cube,.so 37‘ 1'5 _ A??? 4 6am Sulfide. .. -~ ._ _ . E‘Z ‘ . @E:%-dflx $5425.— .. é-é; "film :5 D ‘ . _ I l I t ' 'Hlnmjh 14! Gabe. 75 find i Jfimujh Me Sffldrc,w€ W flux Mmujh one. face 0M“. cm :12, 01"+fi¢ w. 9 Qfirflresguarcfir , CH2. -2 v w 25?. Fugun: 24-33 shows a section through mo long thin cow centric cylinders oftadii a and b with a c. b. The cylindus have equal and opposite charges per unit length A. Using Gauss' law, provc(a) :hatE = Oforr < aand(b) than between theeylinders. when: a < r < b. CURE 24-33 Pmblun 25. -Solu41‘on Gangs -- E ' “5e 4 6466.921” cymb- of i i 22 Mn] 50 SH"?! .2244? 100 SHEETS 22-]44 200 SHEEYS 5 m I”; (34.515513?! Mdfus r J (Mfm‘h‘k 501.5% 50% «J 5mm c (makes,ch rca. ms Mu "‘ a an: as in (ht/mam Me Wafer: (‘40.. i i | i i I V hm” r 33-44 31‘s Cmsbrd W151 fie mafia/56mm :4 594%?“ 4%"? A Mk‘mfl‘WW i Eli"? = “if We. MY! ‘5 CMSIW 'Hte 06"de pita; of bar Gaussian body, some 46m mm ream pow , in affirm»! afiflofimfi: __‘ w A EW”"€§#€93‘+€ASM o'= ’53:“ A1 M ' inc. :- = I. . E/zm-L)= 45 Zm-L ,L knfimd 53 hala- % f . ' . E(r')= —— “7' 5mm {he CM on #1: Inner Mm ' 6' (2" L found af NJ?“ =0 fir- :24. u‘. E(l"')=o ,f‘<6?. 22441 50 SHEETS ' 224 42 100 SHEETS 22-144 200 SHEETS .m Hie. a<r<b,$o we pa! our édw’an 631M” 4421:. We dim/y worked ad I ekdn'c. Reid 16" 035?!an in par-f a) : £0.) =‘ JUL-L) The Chair endcsed Me Gaussian Cgltmér {.5 HZ Charflcof ' rjzjhhda. We are no! given f , bd- wc an: lefn 7}. rQ I 22 I 4| 50 SHEETS 22442 100 SHI‘TS 22-144 200 SHEETS Q mm. “mm ‘mfimfl$flfmm-‘flfi Cjwmr r; =0 , q“ -b ‘ rl; - 7 {A Find: a) Ear-<4.) b) 501‘ rcb) c)€<r>b) (Damage on (MrWaw’crsurfm: If sh! f 6b) «a Place a Gaussian swim WM fie ream “a. . % 4e“! :0 ’50 ' l, b)a4r4b Plaa a 54mm sphc/c {)1 fire ream a< rdo. _‘_ Ndv for a m alth prfmef w lad: 6w; can,“ we mm 1'» caz4~4oet .6" s 6(4nr*)= 2 => 9422:3546 mg a) r>[, Plate at Gawain Sphere 50 1'71 sumunds be”! sheik». 5%” a .1— e‘ 2 H 5(4nr-)= fig}: => 9- %. -——-"- = M 9N6- .d) Use Gauss‘stawr egg-«Ram Iancc E=0 ‘Br rm. #:e charge. on 4}: imsaréxe on Mafia/H5 aim? zero. _ ‘ _ 11'. The charge, an die oukr .Sm’fice. J #1: warm/I may! be ed. Esme. E=O M +1.2 warm” (#3 min/Km mam/Ah m : chaff “WW I}? 4 Gama” Jurém #w' is Med W 462 zhner and oak/Mikes of #6 om‘cr she” 1'; zero. a; @J-chdgs on fire fhfltf’ Surfiuc a! m oat-fer shll.'l'heam #Ie diary; on Me. funer- s‘lrfivm of file gammy mm be ~g‘. In orddr 1E» 44M WM 'fo [we a. nffdmyc a? {6, Hz Oukrsurfice ...
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ph132s04_hw3 - PH 132 SPRING 2003 HOMEWORK 3 Assigned 22...

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