# homework 4 - PH 132 SPRING 2005 HONIEWORK # 4 Assigned:...

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Unformatted text preview: PH 132 SPRING 2005 HONIEWORK # 4 Assigned: 01/31/05 CEM'ZCLZ ¥?5f}{371§)1327’%?2)13u’)8_61CZE 7 (MA: LL!) manna; LWL T3§._..__.Wwf c—f'“. 50 SHEETS 22-142 100 SHEETS 21-144 200 SHEETE 22-14] 6%; __., t t given: initial pmmmo’r‘g -' =0 ﬁnal posh‘a‘m of Z, -' 2? )Work From 0 "'52 _ b)8how Hm eIede'e poknﬁal. 01" a charged sheaf is V: Us ” (36'— )Z 0 25-18 and Eq. 24- 13 to show that the electric potential of an; sheet of charge can be written V = VD — ((#230); where V electric potential at the surface of the sheet and z is the pe' ular distance from the sheet. (b) How much work is done electric ﬁeld of the sheet as a small positive test charge go is from an initial position on the sheet to a ﬁnal position 101: distance 2 from the sheet? Work time. £33 (in E/cdn’c Field, {er/hat Pokﬂh'a{ M NW"? N gag (mm sbcdafchmae-‘ﬁ e5. 29x45 P.5?o)(§”;s{q+he q" a . ‘2; 6’2 2 ~ dp'rcdi‘m} - 05 __ - halo/5 " A“ 01:) W(0~»i’3= 7pm -— Wm] 501m +4195 15" We) m .— W I.“ I In D If: 22 I42 100 SHEETS 22-144 200 SHEETS 22-h!" AMPAH e electric ﬁeld inside a nonconducting sphere 1'! charge spread uniformly throughout its volum directed and has magnitude qr 4W80R3‘ 50‘) = Here q (positive or negative} is the total charge withi and r is the distance from the sphere’s center. (a) TaL the center of the sphere, ﬁnd the electric potential V sphere. (b) What is the difference in electric potenti point on the surface and the sphere‘s center? \ C CI ' ‘7 EM: 6:) V (r4 R) mew war-VCR) - c) If” i >013 [(69) > W2), or is VCR)>V(0),7 50 SHEETS 22.142 Ion mam 21-144 200 SHEETS 22441 Q {5L . Fig. 25-32, set V = 0 at and let the panicles have = +q and q; = —3q. aware (in terms of ﬂu: 5819— I distance d] any point on ._ g” is (other than at inﬁnity) I : j __i_ch the net potential due to the q} . 92 ' _’ f2 : “36 PM ~' 2 Where. V(x):o Elecfrfc. Pam! Jae "4v pm'm‘ charges 0,69%: X; : 653M066 {02130965 X 27/36! a We"): ﬁra poi/17‘ diff/ye: sz'smce bdrm}? 7r and?! (e5. 2926: p.903) There are 3 Case; 1‘0 EKAMMe-‘I. x>a’ J 12". ,yaoJ Zﬂ‘.c)<2r(d . r _ f f If W99F0ﬂhe G) marge: _ Case. I. x>d - X: X VJK)‘ ‘16-“? J) mmpmmémdmmr x3" xﬁd X’ ‘X‘ gm (~) poknﬁ’afs 36 6, + 4'; j ' . -.~ : 3 WK) F x?) k(;< * =k (xx-0*; , k -2 —- d ,1 I2 «2 -6! [M] [ ex 2] 4L.) XKX-d) Xéc-d) X-d NOT fem, so Case}? 2'5 nm‘ a pa\$Jbz%'/y. -'—--' xz-wd 1* ' J2 WW" x, i2 d-2x .. vm- mm”) 7} w, -0 Hm; => :29! m5 x-7d'} so (x—00>O. ALSO -,2x 4 -d ,50 (—Zx-WO. 717:3 means VéCMO WK» h(%+§:>= he: —§5)=k[?%] i p f r i m?“ f " In Fi 25-3, what is tﬁﬁ net potential at point P due to the four point chaxgcs, if V = 0 at inﬁnity? +5.0qe\ 22-14] 50 SHEETS 22442 100 SHEETS 22-144 200 SHEETS AMMO «rag / Em: WP) due 1‘?) paw wages (a3. 25-27 F. (90‘?) __._._J____ ......m- _...._m.._ i' ng‘ven=v(oo)=o nSfe ﬁgure, so SHEETS 22-142 mu SHEETS 22-144 200 SHEETS 22-l4'l Mm \. (a 13 A plastic rod has been formed into a cirole of radius R . It has positive charge +Q uniformly distributed along one—quarter of .l its circumferonce and a negative . '3} inﬁnity, {irks—at is tho 6 C C po- charge of —GQ uniformly distrib- hemial (a) at the comer C of the _ ' uted along the rest of the circum- circle and (b) a: pomt P, Wthh 15 . a! ference (Fig. 25-37). With V = Q on the central axis of the .aF ' ' ' ' ‘ . \ distance, 2 from the CCIHCI‘. Given: '90?” 6: O “5W4? Chﬂrjﬁz +6? 49mm 9 WW: Zn charge = '66? v(ov)=o Fnd= aWI-c) b) WP) Eledn'c Pdcnlx'al do”. +0 '0. cmﬁ'nm drlsr‘n'buﬁbn J ohmic I+ is mm 110 do paﬂ- b) 8.3+ lo ' and #16” (15a Ill/FM" .441: speak! ca [0) look m‘ an t’nﬂm'ksfmdl ammf on" aha,- e,’ dz 2521‘. a dx‘sfmyce r 191ml . CP 511‘ an L: 9. 7116?? 'l'n‘l‘e do Mrs mgﬂuo pm; ,5: k6=ﬁz 83:2” _. la WP) — {44\$ + j 7; {99:0 mama eia ' VG?) 3mm! exp/mm ﬁr _ of: ‘0. 5&- a‘ m'hh} Pale/225w. Wagonech ﬁred regx'mr aFCﬁOr‘f. Q-w} 2:593. 59:11: 1%: 441m. ma Ma 0’: 5‘ i166 . Figure 25—40 shows aplastic electric potential at point Pi on; ' rod of length L and uniform pos.-_ the axis, at distance d from (mg: I J itive charge Q lying on an x axis: __ end of Lhe-rod. — With v = 0 at igﬁnity. ﬁnd the _ F4" 0’ = C ) -_- n V P. Ekdrﬁ: Paz'enﬁhl Jae I‘D a dz‘sfrfbuébn dfckagé: changed rod ' _ look 40‘ ﬂ)? Mnmm/mm afckﬂye 4’3 , 0/ 29237196 6/2; '/o(424°/ 927‘ x: _ 73k £5 “mean agar-Hr: rad,.So we (4:? we. Alvaro/aye ', it. 2 W +9 _ 246K 4/50, Pt: L. . a/Z: +§ak 22 14! 50 SHEETS 22-142 ")0 SHEETS 22—144 200 SHEETS O M _ ' U: ,5} ﬁra pam" \w- Now examMe 74"? meaf 5) ‘7’“ 7b _ char 9,, and/f 25 0N: fig: thx 5,024]; magi/1 2’29 2mm dng L(d+x) a poth Marge, J ’6) AMMU 22 It” 50 SHEETS 22442 100 SHEETS 22-144 200 SHEETS ' beﬁve an expresision' for the l; as§umi_n work required to set up the four- '. tlaily mﬁmt charge conﬁguration of Fig. 25- Exercise 56. -q g the charges aft:__ini— - ely far apart. ‘ . Em: Work raga/red {o m up #Ie conﬁguraﬁbn - Hair-(c. Pomahl Md Work 13% pew aka/yes 40th:; fa bnhj each on: :31. _ -124‘Zﬂz w-u- r r. Bnhj (a 35mm we haw V54 : h4345q k W25 7‘ a: (35. Brahj in 22: W]; §ﬂ=£fﬁkuz kg," We pd HM 555m wag-Chad bjchargc, £50605 HM Work ('7‘ 13+ 1%: no work—fa brig ,5»; Z. 2543 , ,9. (015) 7'0er boMf, div/é: i h‘Zr‘iI_ :1 3 z I rig: ._ rm 3 (4X2) Z53 Bring 1'?! cf? , (WW/7373 q! I {a} 33 : } WM: 6% 4L k‘z:€#_ It ' Wz‘l' d'a M. Thc 1%] Work; W: Wu“ Msi*v‘é3*M/*Wz¥ *W—W W: *5? “z a z kak‘ a V3 g?" ﬁfﬁf a? 2- :- 2 —L_...... .J.__ :. z — =3 gig-2+6 IIWZ I) giﬁg 4) £23042- —2) : "éQR‘ ﬂws. d Inn-Ha l—I-l- IIIIIIUI Luna: 1:: “In”! 090 moo I-N I—Nd‘ Q'El‘ﬁl‘ —'-F' I CI UH“ NIH“ @ In the rectangle of Fig. 25— 42. the sides have lengths 5.0 cm and 15 cm, q1 = -5.0 pc‘ and q2 = +2.0 uC. With V = D at inﬁnity, what are the electric-va tentiais (a) at corner A and (b) at corner 3? (c) How much work is required to move a third chug 51x15». - q3 = +3.0 ,u.C from B to A along a diagonal of the rectanglg (d) Does this Work increase or decrease the electric energy , the three-charge system? Is more, less, or the same work required if :3 is moved along paths that are (e) inside the rectangle but not on a diagonal and (f) outside the- reetangle? NOTE: E 1 r and? 7/71; 54545729339 TIC Fawlg A ,6 3 CDJSM “2:69.05141 be \$1 '-‘-—-S.O2</€> C ' THE ELEGKJ ; P07“. A7" A wméészTN/g Page?) 77/5 pom/“<44 teaméf _ I"? £30557‘ 97": TIE ?AW’7’. If] ssz ANS, Aé :24 , 2 I _________________ l l l w a. l _ is 2 ___H____ ‘ 'L[”J+f ‘ E 5 i ( bra-7.- :- Aww ' FMM A 7-»? 4144.265“ a l i l l i i I g i i E l ! E tﬂ‘ﬂlﬂ _Ii-|--r- wlulu WNW 2:: WWW 000 I609 r—N I-N'ﬂ‘ Q‘H‘ their? “NH ’/5) ' _. Consider two widely separated conducting spheres, i and 2, . the second having twice die diameter of the ﬁrst. The smaller sphere initially has a positive charge 5;, and the larger one is initially on- charged. You now connect the spheres with a long thin wire. {a} How are the ﬁnal potentials V1 and V: of the spheres related? 03) What are the ﬁnal charges ql and g; on the spheres, in terms of g? (c) What is the ratio of the ﬁnal surface Charge density of sphere l to that of where 2? think! ere 01‘ Sphere l =% WM chdrje at sphere 2 = O ‘ -‘ 63») Pelaiv’mtshcp bcfween V014, _ b) q! if at; c) 6%; Z. E/ecfn'ﬁPoknﬁ‘aJ dare to cone/mtg ﬁOheres , CW7ng of ' charge, we: Marie 662953 ' ' a) I’iﬂer- Are annealed vzuz ANS. Once Conn-add 1H: ﬁrmasuid/e, 441% ' “A ISO/QM n ﬁre-\$5 (flag: pieced an AW {Ira/diéa/ dcmfwér- will dr‘kfn'bxk risen" an Mum-16;: 01‘ #41” fmdmer Jo aw tympani; grim cmdadbr' 66m: 76 #65001: My“ 10.6% b) We will (assume that ca and f: We efaztraknrpow diary“ at {ﬁe (were me spheres [ma/Z. M can do Ma's Wef4ﬁc\$mn2d53maeﬁ3 _ hf H lac? [3 W “" e“ e #54 3mm Charge is cmmwd) ﬂue; =€ (2‘) J Combmﬁa Ct) and (z): (a siﬂzz E i e: in}: v-—".|> f}? 50’ Z2216?- l _ohd e._ Q c) 6" area _ 4W1 L 4 2. Q, 7. 21.... m 3 f: .-. 2?: 3159.11 eynww 62.3— n. le'312f'ztzZEZ . 4112? R; 3 l l ! ; 50 S H EETS 22-442 IOO SHEETS 27-144 200 SHEETS 12-141 _ . In Fig. 25-33, point P is at the center of the rectangle. W-ith = 0 at inﬁnity, what is the net electric potential at P due to the the ' . Charged particles? 6/63”? Polanth due poin‘l' Wrﬂes _ I d . ‘ _ . _ _|/ 2 g ' ﬂ _: __ . 7 n‘q‘Q'Q' *(z): ) 6"; Z 51) __ 30¢ __ 3.03 5.0 2.0 3, . VP dt’rlg)‘ ; 0' *[zy d * a) a “J - , 5.0'3_0+5.0*30) + «\$201202; 2’12) '0’ = 4L,fé’=lecg'_/Q__ =13319._57] _ = Z - ' x . _ 3] 558334-87)? 0345.? ANS. 42? PH 132 _ Suggested Problems 7 9 The electric potential difference between the gTound and a and in a particular thunderstorm is 1.2 X 109 V. What is the magnitude of the change in the electric potential energy (in mul— tiples of the electron-volt) of an electron that moves between the ground and the cloud? i C‘ N x 6 I .3 <1 . l Eh X E; o x/ 'hen an electron moves from A to B along an electric ﬁeld 6 in Fig. 25-29, the electric ﬁeld does 3.94 X 10—19 J of work on it. What are the electric po- tential differences (a) V3 - 1114, E1 . (1:) VC — VA, and (c) VG — vs? £153” _ - .. t’ Equiporentials Fig. 25-2? Exercise 4. Two large, parallel, conduct- ing plates are 12 cm apart and have charges of equal magnitude and opposite sign on their facing surfaces. An electromatic force of 3.9 X 10‘ '5 N acts on an electron placed anywhere between the two plates. (Neglect fringing} (3) Find the electric ﬁeld at the position of the electron. (b) Whax is the potential difference between the plates? ._._.......s . .._.u....m‘..-mwnm—W__h_._.n.____wn__.__ . x y :la) Use the result of Problem 28 to ﬁnd the electric en: E, at point P1 in Fig. 25-40. (Hint: First substitute" 1 ' able 1 for the distance d in the result.) (b) Use symmet ‘ mine the electric ﬁeld component E_,. at P1. a '-"‘"-"‘ -_" -—-._ "720M 'PR—DB. :3? THE awarmc 70!¢M//AL,A/ A -P02M7‘ um")?! cprmtn. x :59 Quinn 3»). WWW I-I-I- lull!“ IIJIIIIII III Invnn 000 not: -N a-rur ant-ve- 'T'T'T «an «an (“’9 mm»: t f l I l ! i I I I I i __ C3) 9 X'Lﬂ 991' CHAIN PM”: ( "' '- '—_ K Na}; QOD'UEMT Rum? . ﬂ .._ WERE: 5; 4,5354 2J0 FIE-"Q I POI “TS ARE, 5’TUATED 6t,» magi:ch and TH": ' Q‘v-Haz WWMWM NEE" WE" ‘*‘ PO77 WP}? 2‘5 ZERD ' M 14) If Earth had a net surface charge density of 1.0 electron r square meter [a very arLiﬁcia! assumption), what would its po— tential be? (Set V = 0 at inﬁnity.) (b) What would be the electric ﬁeld due to Earth just outside its surface? I CswbvﬂM-‘G v05: WAT 777%: {EA/2377‘ A; A 57/9315 }_ W" THE PDT- LOILL 3‘951— 35 THE.- we; (3‘ 5 0 S HEETS 22-]42 100 SHEETS 22-144 200 SHEETS 22-141 51 nMPﬂIJ 5M ks THAT _ of 1‘: Pi cM‘k—éis 361' A1" r3733; reams z" .119 15: Zea—51; PAIN Ali-‘1’, imwNQ-b . l i i i 3 I Z i l I E E i i I i | l | E E 200 SHEETS 4.1-“!!! q = +2.0 pC are ﬁxed in space a distance , as shown in Fig. 25-49. (a) With V = {J at a) V(C)- @717: work 1‘0 bring ? zrzeuc {a 53¢:ka (1)9“ «13% Zﬂ/C . no oﬁéer 664% piitscrzz‘ )—- w d L- 5.03 8%?qu ...
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## This note was uploaded on 11/04/2009 for the course PHYSICS PH13100 taught by Professor Dr.wick during the Spring '09 term at Clarkson University .

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homework 4 - PH 132 SPRING 2005 HONIEWORK # 4 Assigned:...

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