CHATE 22 ELECTIC FIELDS viw & Summr Elctric Fil To lin th lctrosttic forc btwn two chrgs, w ssum tht ch chrg sts u n lctric fil in th sc roun it. Th forc cting on ch chrg is thn u to th lctric fil st u t its loction b th othr chrg. Dfinition of Elctric Fil Th lctric fil E : t n oint is fin in trms of th lctrosttic forc F : tht woul b rt on ositiv tst chrg q 0 lc thr: E : F: q 0. (22-1) Elctric Fil Lins Elctric fil lins rovi mns for visuliing th irction n mgnitu of lctric fils. Th lctric fil vctor t n oint is tngnt to fil lin through tht oint. Th nsit of fil lins in n rgion is roortionl to th mgnitu of th lctric fil in tht rgion. Fil lins origint on ositiv chrgs n trmint on ngtiv chrgs. Fil Du to oint Chrg Th mgnitu of th lctric fil E : st u b oint chrg q t istnc r from th chrg is E 1 4 0 q r 2. (22-3) Th irction of is w from th oint chrg if th chrg is ositiv n towr it if th chrg is ngtiv. E : Fil Du to n Elctric Diol An lctric iol consists of two rticls with chrgs of qul mgnitu q but oosit sign, srt b smll istnc. Thir lctric iol momnt : hs mgnitu q n oints from th ngtiv chrg to th ositiv chrg. Th mgnitu of th lctric fil st u b th iol t istnt oint on th iol is (which runs through both chrgs) is E 1 (22-9) 2 0, 3 whr is th istnc btwn th oint n th cntr of th iol. Fil Du to Continuous Chrg Distribution Th lctric fil u to continuous chrg istribution is foun b trting chrg lmnts s oint chrgs n thn summing, vi intgrtion, th lctric fil vctors rouc b ll th chrg lmnts to fin th nt vctor.
QUESTIONS 651 Fil Du to Chrg Disk Th lctric fil mgnitu t oint on th cntrl is through uniforml chrg isk is givn b E s 1 2 0 2 2, 2 (22-26) whr is th istnc long th is from th cntr of th isk, is th rius of th isk, n s is th surfc chrg nsit. Forc on oint Chrg in n Elctric Fil Whn oint chrg q is lc in n trnl lctric fil E :, th lctrosttic forc F : tht cts on th oint chrg is F : qe :. (22-28) F : Forc hs th sm irction s if q is ositiv n th oosit irction if q is ngtiv. Diol in n Elctric Fil Whn n lctric iol of iol momnt : is lc in n lctric fil E :, th fil rts torqu t : on th iol: t : : E :. (22-34) Th iol hs otntil nrg U ssocit with its orinttion in th fil: U : E :. (22-38) This otntil nrg is fin to b ro whn : is rniculr to E : ; it is lst ( U E) whn : is lign with E : n grtst ( U E) whn : is irct oosit E :. E : Qustions 1 Figur 22-22 shows thr rrngmnts of lctric fil lins. In ch rrngmnt, roton is rls from rst t oint A n is thn cclrt through oint B b th lctric fil. oints A n B hv qul srtions in th thr rrngmnts. nk th rrngmnts ccoring to th linr momntum of th roton t oint B, grtst first. A B A B A B (c) Figur 22-22 Qustion 1. 2 Figur 22-23 shows two +6q 2q +3q squr rrs of chrg rticls. Th squrs, which r cntr on oint, r mislign. 3q +2q Th rticls r s- rt b ithr or /2 2q q long th rimtrs of th squrs. Wht r th mgnitu q q n irction of th nt lctric fil t? +2q 3q 3 In Fig. 22-24, two rticls of chrg q r rrng smmtricll bout th is; ch roucs n lctric +3q 2q Figur 22-23 Qustion 2. +6q fil t oint on tht is. Ar th mgnitus of th fils t qul? Is ch lctric fil irct towr or w from th chrg roucing it? (c) Is th mgnitu of th nt lctric fil t qul to th sum of th mgnitus E of th two fil vctors (is it qul to 2E)? () Do th comonnts of thos two fil vctors or cncl? () Do thir comonnts or cncl? (f) Is q q th irction of th nt fil t tht of th cncling comonnts or th ing comonnts? (g) Wht is th irction of th nt fil? Figur 22-24 Qustion 3. 4 Figur 22-25 shows four situtions in which four chrg rticls r vnl sc to th lft n right of cntrl oint. Th chrg vlus r inict. nk th situtions ccor - ing to th mgnitu of th nt lctric fil t th cntrl oint, grtst first. (1) (2) (3) (4) + + + + + + + + : 5 Figur 22-26 shows two chrg rticls fi in lc on n is. Whr Figur 22-25 Qustion 4. on th is (othr thn t n infinit istnc) is thr oint t which thir nt lctric fil is ro: btwn +q 3q th chrgs, to thir lft, or to thir right? Is thr oint of Figur 22-26 Qustion 5. ro nt lctric fil nwhr off th is (othr thn t n infinit istnc)? 6 In Fig. 22-27, two inticl circulr nonconucting rings r cntr on th sm lin with thir lns rniculr to th lin. Ech ring 1 ing A 2 3 ing B hs chrg tht is uniforml istribut Figur 22-27 Qustion 6. long its circumfrnc. Th rings ch rouc lctric fils t oints long th lin. For thr situtions, th chrgs on rings A n B r, rsctivl, (1) q 0 n q 0, (2) q 0 n q 0, n (3) q 0 n q 0. nk th situtions ccoring to th mgnitu of th nt lctric fil t oint 1 miw btwn th rings, oint 2 t th cntr of ring B, n (c) oint 3 to th right of ring B, grtst first. 7 Th otntil nrgis ssocit with four orinttions of n lctric iol in n lctric fil r (1) 5U 0, (2) 7U 0, (3) 3U 0, n (4) 5U 0, whr U 0 is ositiv. nk th orinttions ccoring to th ngl btwn th lctric iol momnt n th lctric fil E : n th mgnitu of th torqu on th lctric iol, grtst first. 8 In Chckoint 4, if th iol rotts from orinttion 1 to orinttion 2, is th work on on th iol b th fil ositiv, ngtiv, or ro? If, inst, th iol rotts from orinttion 1 to orinttion 4, is th work on b th fil mor thn, lss thn, or th sm s in?
652 CHATE 22 ELECTIC FIELDS 9 Figur 22-28 shows two isks n flt ring, ch with th sm uniform chrg Q. nk th objcts ccoring to th mgnitu of th lctric fil th crt t oints (which r t th sm vrticl hights), grtst first. 10 In Fig. 22-29, n lctron trvls through smll hol in lt A n thn towr lt B. A uniform lctric fil in th rgion btwn th lts thn slows th lctron +q 2 without flcting it. Wht is th +q 1 q irction of th fil? Four othr 3 n rticls similrl trvl through A B smll hols in ithr lt A or lt B n thn into th rgion btwn Figur 22-29 Qustion 10. th lts. Thr hv chrgs q 1, q 2, n q 3. Th fourth (lbl n) is nutron, which is lctricll nutrl. Dos th s of ch of thos four othr rticls incrs, crs, or rmin th sm in th rgion btwn th lts? 11 In Fig. 22-30, circulr lstic ro with uniform chrg Q roucs n lctric fil of mgnitu E t th cntr of 2 (c) Figur 22-28 Qustion 9. 2 curvtur (t th origin). In Figs. 22-30b, c, n, mor circulr ros, ch with inticl uniform chrgs Q, r until th circl is comlt. A fifth rrngmnt (which woul b lbl ) is lik tht in ct th ro in th fourth qurnt hs chrg Q. nk th fiv rrngmnts ccoring to th mgnitu of th lctric fil t th cntr of curvtur, grtst first. 12 Whn thr lctric iols r nr ch othr, th ch rinc th lctric fil of th othr two, n th thr-iol sstm hs crtin otntil nrg. Figur 22-31 shows two rrngmnts in which thr lctric iols r si b si. Ech iol hs th sm mgnitu of lctric iol momnt, n th scings btwn jcnt iols r inticl. In which rrngmnt is th otntil nrg of th thr-iol sstm grtr? Figur 22-31 Qustion 12. 13 Figur 22-32 shows thr ros, ch with th sm chrg Q sr uniforml long its lngth. os (of lngth L) n b (of lngth L/2) r stright, n oints r lign with thir mioints. o c (of lngth L/2) forms comlt circl bout oint. nk th ros ccoring to th mgnitu of th lctric fil th crt t oints, grtst first. L L/2 L/2 (c) Figur 22-32 Qustion 13. 14 Figur 22-33 shows fiv rotons tht r lunch in uniform lctric fil E : ; th mgnitu n irction of th lunch vlocitis r inict. nk th rotons ccoring to th mgnitu of thir cclrtions u to th fil, grtst first. E (c) () 3 m/s b c 10 m/s 16 m/s 5 m/s 7 m/s Figur 22-30 Qustion 11. Figur 22-33 Qustion 14. roblms SSM Tutoring roblm vilbl (t instructor s iscrtion) in WilLUS n WbAssign Work-out solution vilbl in Stunt Solutions Mnul WWW Work-out solution is t Numbr of ots inicts lvl of roblm ifficult ILW Intrctiv solution is t Aitionl informtion vilbl in Th Fling Circus of hsics n t flingcircusofhsics.com htt://www.wil.com/collg/hlli Moul 22-1 Th Elctric Fil 1 Sktch qulittivl th lctric fil lins both btwn n outsi two concntric conucting shricl shlls whn uniform ositiv chrg q 1 is on th innr shll n uniform ngtiv chrg q 2 is on th outr. Consir th css q 1 q 2, q 1 q 2, n q 1 q 2.
OBLEMS 653 2 In Fig. 22-34 th lctric fil lins on th lft hv twic th srtion of thos on th right. If th mgnitu of th fil t A is 40 N/C, wht is th mgnitu of th forc on roton t A? Wht is th mgnitu of th fil t B? B A Figur 22-34 roblm 2. 10 Figur 22-38 shows two chrg rticls fi in lc on n is with srtion L. Th rtio q 1 /q 2 of thir chrg mgnitus is 4.00. Figur 22-38b shows th comonnt E nt, of thir nt lctric fil long th is just to th right of rticl 2.Th is scl is st b s 30.0 cm. At wht vlu of 0 is E nt, mimum? If rticl 2 hs chrg q 2 3, wht is th vlu of tht mimum? Moul 22-2 Th Elctric Fil Du to Chrg rticl 3 SSM Th nuclus of lutonium-239 tom contins 94 rotons. Assum tht th nuclus is shr with rius 6.64 fm n with th chrg of th rotons uniforml sr through th shr. At th surfc of th nuclus, wht r th mgnitu n irction (rill inwr or outwr) of th lctric fil rouc b th rotons? 4 Two chrg rticls r ttch to n is: rticl 1 of chrg 2.00 10 7 C is t osition 6.00 cm n rticl 2 of chrg 2.00 10 7 C is t osition 21.0 cm. Miw btwn th rticls, wht is thir nt lctric fil in unit-vctor nottion? 5 SSM A chrg rticl roucs n lctric fil with mgnitu of 2.0 N/C t oint tht is 50 cm w from th rticl. Wht is th mgnitu of th rticl s chrg? 6 Wht is th mgnitu of oint chrg tht woul crt n lctric fil of 1.00 N/C t oints 1.00 m w? 7 SSM ILW WWW In Fig. 22-35, th q 1 q 2 four rticls form squr of g lngth 5.00 cm n hv chrgs q 1 10.0 nc, q 2 20.0 nc, q 3 20.0 nc, n q 4 10.0 nc. In unitvctor nottion, wht nt lctric fil q 4 q 3 o th rticls rouc t th squr s cntr? 8 In Fig. 22-36, th four rticls Figur 22-35 roblm 7. r fi in lc n hv chrgs q 1 q 2 5, q 3 3, n q 4 12. Distnc 5.0 mm. Wht is th q 4 mgnitu of th nt lctric fil t q 1 oint u to th rticls? q 3 9 Figur 22-37 shows two chrg rticls on n is: q 3.20 10 19 q C t 3.00 m n 2 q 3.20 10 19 C t 3.00 m. Wht r th mgnitu n Figur 22-36 roblm 8. irction (rltiv to th ositiv irction of th is) of th nt lctric fil rouc t oint t 4.00 m? q q Figur 22-37 roblm 9. +q 1 q 2 L 11 SSM Two chrg rticls r fi to n is: rticl 1 of chrg q 1 2.1 10 8 C is t osition 20 cm n rticl 2 of chrg q 2 4.00q 1 is t osition 70 cm.at wht coorint on th is (othr thn t infinit) is th nt lctric fil rouc b th two rticls qul to ro? E nt, (10 8 N/C) 2 0 2 4 Figur 22-38 roblm 10. 12 Figur 22-39 shows n unvn rrngmnt of lctrons () n rotons () on circulr rc of rius r 2.00 cm, with ngls u 1 30.0, u 2 50.0, u 3 30.0, n u 4 20.0. Wht r th mgnitu n irction (rltiv to th ositiv irction of th is) of th nt lctric fil rouc t th cntr of th rc? 13 Figur 22-40 shows roton () on th cntrl is through isk with uniform chrg nsit u to css lctrons. Th isk is sn from n g-on viw. Thr of thos lctrons r shown: lctron c t th isk cntr n lctrons s t oosit sis of th isk, t rius from th cntr. Th roton is initill t s 0 3 4 (cm) 2 1 s Figur 22-39 roblm 12. c Figur 22-40 roblm 13. istnc 2.00 cm from th isk. At tht loction, wht r th mgnitus of th lctric fil E : u to lctron c n th nt lctric fil E : c s,nt u to lctrons s? Th roton is thn mov to /10.0. Wht thn r th mgnitus of : : (c) E c n () E s,nt t th roton s loction? () From n (c) w s tht s th roton gts nrr to th isk, th mgnitu of E : c incrss, s ct. Wh os th mgnitu of E : s,nt from th two si lctrons crs, s w s from n ()? s q 1 q 2 L 14 In Fig. 22-41, rticl 1 of chrg q 1 5.00q n rticl 2 of chrg q 2 2.00q r fi to n is. As Figur 22-41 roblm 14. multil of istnc L, t wht coorint on th is is th nt lctric fil of th rticls ro? Sktch th nt lctric fil lins btwn n roun th rticls.
654 CHATE 22 ELECTIC FIELDS 15 In Fig. 22-42, th thr rticls r fi in lc n hv chrgs q 1 q 2 n q 3 2. Distnc 6.00 mm. Wht r th mgnitu n irction of th nt lctric fil t oint u to th rticls? 16 Figur 22-43 shows lstic ring of rius 50.0 cm. Two smll chrg bs r on th ring: B 1 of chrg 2.00 mc is fi in lc t th lft si; b 2 of chrg 6.00 mc cn b mov long th ring. Th two bs rouc nt lctric fil of ing mgnitu E t th cntr of th ring. At wht ositiv n ngtiv vlu of ngl u shoul B 1 b 2 b osition such tht E 2.00 10 5 N/C? 17 Two chrg bs r on th lstic ring in Fig. 22-44. B Figur 22-43 roblm 16. 2, which is not shown, is fi in lc on th ring, which hs rius 60.0 cm. B 1, which is not fi in lc, is initill on th is t ngl u 0. It is thn mov to th oosit si, t ngl u 180, through th first n scon qurnts of th coorint sstm. Figur 22-44b givs th comonnt of th nt lctric fil rouc t th origin b th two bs s function of u, n Fig. 22-44c givs th comonnt of tht nt lctric fil. Th vrticl is scls r st b E s 5.0 10 4 N/C n E s 9.0 10 4 N/C. At wht ngl u is b 2 loct? Wht r th chrgs of b 1 n (c) b 2? E (10 4 N/C) E s E s 0 90 180 ing B 1 (c) E (10 4 N/C) Figur 22-44 roblm 17. E s 3 1 90 180 0 Figur 22-42 roblm 15. B 2 2 Moul 22-3 Th Elctric Fil Du to Diol 18 Th lctric fil of n lctric iol long th iol is is roimt b Eqs. 22-8 n 22-9. If binomil nsion is m of Eq. 22-7, wht is th nt trm in th rssion for th iol s lctric fil long th iol is? Tht is, wht is E nt in th rssion E 1 q E 2 0 3 nt? 19 Figur 22-45 shows n lctric iol. Wht r th mgnitu n irction (rltiv to th ositiv irction of th is) of th iol s lctric fil t oint, loct t istnc r? +q /2 /2 q + Figur 22-45 roblm 19. r 20 Equtions 22-8 n 22-9 r roimtions of th mgnitu of th lctric fil of n lctric iol, t oints long th iol is. Consir oint on tht is t istnc 5.00 from th iol cntr ( is th srtion istnc btwn th rticls of th iol). Lt E r b th mgnitu of th fil t oint s roimt b Eqs. 22-8 n 22-9. Lt E ct b th ctul mgnitu.wht is th rtio E r /E ct? 21 SSM Elctric quruol. Figur 22-46 shows gnric lctric quruol. It consists of two iols with iol momnts tht r qul in + + +q q q +q mgnitu but oosit in irction. Show tht th vlu of E on th is of th quruol for oint istnc from its cntr (ssum + Figur 22-46 roblm 21. ) is givn b E 3Q 4 0 4, in which Q ( 2q 2 ) is known s th quruol momnt of th chrg istribution. Moul 22-4 Th Elctric Fil Du to Lin of Chrg 22 Dnsit, nsit, nsit. A chrg 300 is uniforml istribut long circulr rc of rius 4.00 cm, which subtns n ngl of 40. Wht is th linr chrg nsit long th rc? A chrg 300 is uniforml istribut ovr on fc of circulr isk of rius 2.00 cm. Wht is th surfc chrg nsit ovr tht fc? (c) A chrg 300 is uniforml istribut ovr th surfc of shr of rius 2.00 cm. Wht is th surfc chrg nsit ovr tht surfc? () A chrg 300 is uniforml sr through th volum of shr of rius 2.00 cm. Wht is th volum chrg nsit in tht shr? 23 Figur 22-47 shows two rlll nonconucting rings with thir 1 q 2 q ing 1 ing 2 cntrl s long common lin. ing 1 hs uniform chrg q 1 n rius ; ring 2 hs uniform chrg q 2 n th sm rius. Th rings r srt b istnc 3.00.Th nt lctric fil t oint on th Figur 22-47 roblm 23. common lin, t istnc from ring 1, is ro.wht is th rtio q 1 /q 2? 24 A thin nonconucting ro with uniform istribution of ositiv chrg Q is bnt into comlt circl of rius
OBLEMS 655 (Fig. 22-48). Th cntrl rniculr is through th ring is is, with th origin t th cntr of th ring. Wht is th mgnitu of th lctric fil u to th ro t 0 n? (c) In trms of,t wht ositiv vlu of is tht mgnitu mimum? () If 2.00 cm n Q 4.00 mc, wht is th mimum mgnitu? Figur 22-48 roblm 24. 25 Figur 22-49 shows thr circulr rcs cntr on th origin of co- 4Q +9Q 3 2 orint sstm. On ch rc, th uniforml istribut chrg is givn in +Q trms of Q 2.00 mc. Th rii r givn in trms of 10.0 cm. Wht r th mgnitu n irction (rltiv to th ositiv irction) of th nt lctric fil t th ori- Figur 22-49 roblm 25. gin u to th rcs? 26 ILW In Fig. 22-50, thin glss ro +q forms smicircl of rius r 5.00 cm. Chrg is uniforml istribut long th ro, with q 4.50 C in th ur hlf n q 4.50 C in th lowr hlf.wht r th q mgnitu n irction (rltiv to th ositiv irction of th is) of th lctric Figur 22-50 fil E : t, th cntr of th smicircl? roblm 26. 27 In Fig. 22-51, two curv lstic ros, on of chrg q n th othr of chrg q, form circl of rius +q 8.50 cm in n ln. Th is sss through both of th conncting oints, n th chrg is istribut uniforml on both ros. If q 15.0 C, wht r th q mgnitu n irction (rltiv to th ositiv irction of th is) of th lctric fil E : rouc t, th Figur 22-51 cntr of th circl? roblm 27. 28 Chrg is uniforml istribut roun ring of rius 2.40 cm, n th rsulting lctric fil mgnitu E is msur long th ring s cntrl is (rniculr to th ln of th ring). At wht istnc from th ring s cntr is E mimum? 29 Figur 22-52 shows nonconucting ro with uniforml istribut chrg Q. Th ro forms hlf-circl with rius n roucs n lctric fil of mgnitu E rc t its cntr of curvtur. If th rc is colls to oint t istnc from (Fig. 22-52b), b wht fctor is th mgnitu of th lctric fil t multili? +Q Figur 22-52 roblm 29. +Q r 30 Figur 22-53 shows two concntric rings, of rii n 3.00, tht li on th sm ln. oint lis on th cntrl D is, t istnc D 2.00 from th cntr of th rings. Th smllr ring hs uniforml istribut chrg Q. In trms of Q, wht is th uniforml ' istribut chrg on th lrgr ring if th nt lctric fil t is ro? 31 SSM ILW WWW In Fig. 22-54, Figur 22-53 roblm 30. nonconucting ro of lngth L 8.15 cm hs chrg q 4.23 fc q uniforml istribut long its lngth. Wht is th linr chrg nsit of th ro? Wht r th mgnitu L n (c) irction (rltiv to th ositiv irction of th is) Figur 22-54 roblm 31. of th lctric fil rouc t oint, t istnc 12.0 cm from th ro? Wht is th lctric fil mgnitu rouc t istnc 50 m b () th ro n () rticl of chrg q 4.23 fc tht w us to rlc th ro? (At tht istnc, th ro looks lik rticl.) 32 In Fig. 22-55, ositiv chrg q 7.81 C is sr uniforml long thin nonconucting ro of lngth L 14.5 cm. Wht r th mgnitu n irction (rltiv to th ositiv irction of th is) of th lctric fil rouc t oint, t istnc 6.00 cm from th ro long its rniculr bisctor? 33 In Fig. 22-56, smiinfinit nonconucting ro (tht is, + + + + infinit in on irction onl) hs uniform linr chrg nsit l. Show tht th lctric fil E : t oint mks n ngl of 45 with th ro n tht this rsult is innnt of th istnc. (Hint: Srtl fin Figur 22-56 roblm 33. th comonnt of E : rlll to th ro n th comonnt rniculr to th ro.) Moul 22-5 Th Elctric Fil Du to Chrg Disk 34 A isk of rius 2.5 cm hs surfc chrg nsit of 5.3 mc/m 2 on its ur fc. Wht is th mgnitu of th lctric fil rouc b th isk t oint on its cntrl is t istnc 12 cm from th isk? 35 SSM WWW At wht istnc long th cntrl rniculr is of uniforml chrg lstic isk of rius 0.600 m is th mgnitu of th lctric fil qul to on-hlf th mgnitu of th fil t th cntr of th surfc of th isk? 36 A circulr lstic isk with rius 2.00 cm hs uniforml istribut chrg Q (2.00 10 6 ) on on fc. A circulr ring of with 30 mm is cntr on tht fc, with th cntr of tht with t rius r 0.50 cm. In coulombs, wht chrg is contin within th with of th ring? + + + + + + + + + L Figur 22-55 roblm 32.
656 CHATE 22 ELECTIC FIELDS 37 Suos ou sign n rtus in which uniforml chrg isk of rius is to rouc n lctric fil. Th fil mgnitu is most imortnt long th cntrl rniculr is of th isk, t oint t istnc 2.00 from th isk (Fig. 22-57). Cost nlsis suggsts tht ou switch to ring of th sm outr rius but with innr rius /2.00 (Fig. 22-57b). Assum Figur 22-57 roblm 37. tht th ring will hv th sm surfc chrg nsit s th originl isk. If ou switch to th ring, b wht rcntg will ou crs th lctric fil mgnitu t? 38 Figur 22-58 shows circulr isk tht is uniforml chrg. Th cntrl is is rniculr to th isk fc, with th origin t th isk. Figur 22-58b givs th mgnitu of th lctric fil long tht is in trms of th mimum mgnitu E m t th isk surfc. Th is scl is st b s 8.0 cm.wht is th rius of th isk? E m 0.5E m 0 Figur 22-58 roblm 38. (cm) Moul 22-6 A oint Chrg in n Elctric Fil 39 In Millikn s rimnt, n oil ro of rius 1.64 mm n nsit 0.851 g/cm 3 is susn in chmbr C (Fig. 22-16) whn ownwr lctric fil of 1.92 10 5 N/C is li. Fin th chrg on th ro, in trms of. 40 An lctron with s of 5.00 10 8 cm/s ntrs n lctric fil of mgnitu 1.00 10 3 N/C, trvling long fil lin in th irction tht rtrs its motion. How fr will th lctron trvl in th fil bfor stoing momntril, n how much tim will hv ls? (c) If th rgion contining th lctric fil is 8.00 mm long (too short for th lctron to sto within it), wht frction of th lctron s initil kintic nrg will b lost in tht rgion? 41 SSM A chrg clou sstm roucs n lctric fil in th ir nr Erth s surfc. A rticl of chrg 2.0 10 9 C is ct on b ownwr lctrosttic forc of 3.0 10 6 N whn lc in this fil. Wht is th mgnitu of th lctric fil? Wht r th mgnitu n (c) irction of th lctrosttic forc F : l on th roton lc in this fil? () Wht is th mgnitu of th grvittionl forc F : g on th roton? () Wht is th rtio F l /F g in this cs? 42 Humi ir brks own (its molculs bcom ioni) in n lctric fil of 3.0 10 6 N/C. In tht fil, wht is th mgnitu of th lctrosttic forc on n lctron n n ion with singl lctron missing? 43 SSM An lctron is rls from rst in uniform lctric fil of mgnitu 2.00 10 4 N/C. Clcult th cclrtion of th lctron. (Ignor grvittion.) s 44 An lh rticl (th nuclus of hlium tom) hs mss of 6.64 10 27 kg n chrg of 2.Wht r th mgnitu n irction of th lctric fil tht will blnc th grvittionl forc on th rticl? 45 ILW An lctron on th is of n lctric iol is 25 nm from th cntr of th iol. Wht is th mgnitu of th lctrosttic forc on th lctron if th iol momnt is 3.6 10 29 C m? Assum tht 25 nm is much lrgr thn th srtion of th chrg rticls tht form th iol. 46 An lctron is cclrt stwr t 1.80 10 9 m/s 2 b n lctric fil. Dtrmin th fil mgnitu n irction. 47 SSM Bms of high-s rotons cn b rouc in guns using lctric fils to cclrt th rotons. Wht cclrtion woul roton rinc if th gun s lctric fil wr 2.00 10 4 N/C? Wht s woul th roton ttin if th fil cclrt th roton through istnc of 1.00 cm? 48 In Fig. 22-59, n lctron () is to b rls from rst on th cntrl is of uniforml chrg isk of rius. Th surfc chrg nsit on th isk is 4.00 mc/m 2. Wht is th mgnitu of th lctron s initil cclrtion if it is rls t istnc, /100, Figur 22-59 roblm 48. n (c) /1000 from th cntr of th isk? () Wh os th cclrtion mgnitu incrs onl slightl s th rls oint is mov closr to th isk? 49 A 10.0 g block with chrg of 8.00 10 5 C is lc in n lctric fil E : (3000î 600ĵ) N/C. Wht r th mgnitu n irction (rltiv to th ositiv irction of th is) of th lctrosttic forc on th block? If th block is rls from rst t th origin t tim t 0, wht r its (c) n () coorints t t 3.00 s? 50 At som instnt th vlocit comonnts of n lctron moving btwn two chrg rlll lts r v 1.5 10 5 m/s n v 3.0 10 3 m/s. Suos th lctric fil btwn th lts is uniform n givn b E : (120 N/C)ĵ. In unit-vctor nottion, wht r th lctron s cclrtion in tht fil n th lctron s vlocit whn its coorint hs chng b 2.0 cm? 51 Assum tht honb is shr of imtr 1.000 cm with chrg of 45.0 C uniforml sr ovr its surfc. Assum lso tht shricl olln grin of imtr 40.0 mm is lctricll hl on th surfc of th b bcus th b s chrg inucs chrg of 1.00 C on th nr si of th grin n chrg of 1.00 C on th fr si. Wht is th mgnitu of th nt lctrosttic forc on th grin u to th b? Nt, ssum tht th b brings th grin to istnc of 1.000 mm from th ti of flowr s stigm n tht th ti is rticl of chrg 45.0 C. Wht is th mgnitu of th nt lctrosttic forc on th grin u to th stigm? (c) Dos th grin rmin on th b or os it mov to th stigm? 52 An lctron ntrs rgion of uniform lctric fil with n initil vlocit of 40 km/s in th sm irction s th lctric fil, which hs mgnitu E 50 N/C. Wht is th s of th lctron 1.5 ns ftr ntring this rgion? How fr os th lctron trvl uring th 1.5 ns intrvl?
OBLEMS 657 53 Two lrg rlll cor lts r 5.0 cm rt n hv uniform lctric fil btwn thm s ict in Fig. 22-60. An lctron is rls from th ngtiv lt t th sm tim tht roton is rls from th ositiv lt. Nglct th forc of th rticls on ch othr n fin thir istnc from th ositiv lt whn th ositiv lt Ngtiv lt Figur 22-60 roblm 53. ss ch othr. (Dos it surris ou tht ou n not know th lctric fil to solv this roblm?) 54 In Fig. 22-61, n lctron is E Dtcting shot t n initil s of v 0 scrn v 0 2.00 10 6 m/s, t ngl u 0 0 40.0 from n is. It movs through uniform lctric fil E : (5.00 N/C)ĵ. A scrn for tcting lctrons is osition r- Figur 22-61 roblm 54. lll to th is, t istnc 3.00 m. In unit-vctor nottion, wht is th vlocit of th lctron whn it hits th scrn? 55 ILW A uniform lctric fil ists in rgion btwn two oositl chrg lts. An lctron is rls from rst t th surfc of th ngtivl chrg lt n striks th surfc of th oosit lt, 2.0 cm w, in tim 1.5 10 8 s. Wht is th s of th lctron s it striks th scon lt? Wht is th mgnitu of th lctric fil? Moul 22-7 A Diol in n Elctric Fil 56 An lctric iol consists of chrgs 2 n 2 srt b 0.78 nm. It is in n lctric fil of strngth 3.4 10 6 N/C. Clcult th mgnitu of th torqu on th iol whn th iol momnt is rlll to, rniculr to, n (c) ntirlll to th lctric fil. 57 SSM An lctric iol consisting of chrgs of mgnitu 1.50 nc srt b 6.20 mm is in n lctric fil of strngth 1100 N/C. Wht r th mgnitu of th lctric iol momnt n th iffrnc btwn th otntil nrgis for iol orinttions rlll n ntirlll to E :? 58 A crtin lctric iol is U s lc in uniform lctric fil E : of mgnitu 20 N/C. Figur 22-62 givs th otntil nrg U of th iol 0 vrsus th ngl u btwn E : n th iol momnt :. Th vrticl is scl is st b U s 100 10 28 J.Wht U s is th mgnitu of :? Figur 22-62 roblm 58. 59 How much work is rquir to turn n lctric iol 180 in uniform lctric fil of mgnitu E 46.0 N/C if th iol momnt hs mgnitu of 3.02 10 25 C m n th initil ngl is 64? 60 A crtin lctric iol is lc in uniform lctric fil E : of mgnitu 40 N/C. Figur 22-63 givs th mgnitu t of th torqu on th iol vrsus th ngl u btwn fil E : n th iol momnt :.Th vrticl is scl is st b t s 100 10 28 N m. Wht is th mgnitu of :? E : U (10 28 J) (10 28 N m) s E 0 Figur 22-63 roblm 60. 61 Fin n rssion for th oscilltion frqunc of n lctric iol of iol momnt : n rottionl inrti I for smll mlitus of oscilltion bout its quilibrium osition in uniform lctric fil of mgnitu E. Aitionl roblms 62 Wht is th mgnitu of n lctron s cclrtion in uniform lctric fil of mgnitu 1.40 10 6 N/C? How long woul th lctron tk, strting from rst, to ttin on-tnth th s of light? (c) How fr woul it trvl in tht tim? 63 A shricl wtr ro 1.20 mm in imtr is susn in clm ir u to ownwr-irct tmoshric lctric fil of mgnitu E 462 N/C. Wht is th mgnitu of th grvittionl forc on th ro? How mn css lctrons os it hv? 64 Thr rticls, ch with ositiv chrg Q, form n quiltrl tringl, with ch si of lngth.wht is th mgnitu of th lctric fil rouc b th rticls t th mioint of n si? 65 In Fig. 22-64, rticl of chrg Q roucs n lctric fil of mgnitu E rt t oint, t istnc from th rticl. In Fig. 22-64b, tht sm mount of chrg is sr uniforml long circulr rc tht hs rius n subtns n ngl u. Th chrg on th rc roucs n lctric fil of mgnitu E rc t its cntr of curvtur. For wht vlu of u os E rc 0.500E rt? (Hint: You will robbl rsort to grhicl solution.) +Q +Q 66 A roton n n lctron form two cornrs of n quiltrl tringl of si lngth 2.0 10 6 m. Wht is th mgnitu of th nt lctric fil ths two rticls rouc t th thir cornr? 67 A chrg (uniform linr nsit 9.0 nc/m) lis on string tht is strtch long n is from 0 to 3.0 m. Dtrmin th mgnitu of th lctric fil t 4.0 m on th is. 68 In Fig. 22-65, ight rticls form squr in which istnc 2.0 cm. Th chrgs r q 1 3, q 1 q 2 q 3 q 2, q 3 5, q 4 2, q 5 3, q 6, q 7 5,n q 8. In unitvctor nottion, wht is th nt lctric fil t th squr s cntr? q 8 q 4 69 Two rticls, ch with chrg of mgnitu 12 nc, r t two of th vrtics of n quiltrl tringl with g lngth 2.0 m. Wht is th mgnitu of th lctric fil t th thir 7 q 6 q q 5 vrt if both chrgs r ositiv Figur 22-65 n on chrg is ositiv n th roblm 68. othr is ngtiv? 70 Th following tbl givs th chrg sn b Millikn t iffrnt tims on singl ro in his rimnt. From th t, clcult th lmntr chrg. 6.563 10 19 C 13.13 10 19 C 19.71 10 19 C 8.204 10 19 C 16.48 10 19 C 22.89 10 19 C 11.50 10 19 C 18.08 10 19 C 26.13 10 19 C /2 /2 Figur 22-64 roblm 65.
658 CHATE 22 ELECTIC FIELDS 71 A chrg of 20 nc is uniforml istribut long stright ro of lngth 4.0 m tht is bnt into circulr rc with rius of 2.0 m. Wht is th mgnitu of th lctric fil t th cntr of curvtur of th rc? 72 An lctron is constrin to th cntrl is of th ring of chrg of rius in Fig. 22-11, with. Show tht th lctrosttic forc on th lctron cn cus it to oscillt through th ring cntr with n ngulr frqunc v A q 4 0 m 3 whr q is th ring s chrg n m is th lctron s mss. 73 SSM Th lctric fil in n ln rouc b ositivl chrg rticl is 7.2(4.0î 3.0ĵ) N/C t th oint (3.0, 3.0) cm n 100î N/C t th oint (2.0, 0) cm.wht r th n coorints of th rticl? (c) Wht is th chrg of th rticl? 74 Wht totl (css) chrg q must th isk in Fig. 22-15 hv for th lctric fil on th surfc of th isk t its cntr to hv mgnitu 3.0 10 6 N/C, th E vlu t which ir brks own lctricll, roucing srks? Tk th isk rius s 2.5 cm. Suos ch surfc tom hs n ffctiv cross-sctionl r of 0.015 nm 2. How mn toms r n to mk u th isk surfc? (c) Th chrg clcult in rsults from som of th surfc toms hving on css lctron. Wht frction of ths toms must b so chrg? 75 In Fig. 22-66, rticl 1 (of 3 chrg 1.00 mc), rticl 2 (of chrg 1.00 mc), n rticl 3 (of chrg Q) form n quiltrl tringl of g lngth. For wht 1 2 vlu of Q (both sign n mgnitu) os th nt lctric fil ro- Figur 22-66 roblms 75 uc b th rticls t th cntr n 86. of th tringl vnish? 76 In Fig. 22-67, n lctric iol swings from n initil orinttion i (u i 20.0 ) to E finl orinttion f (u f 20.0 ) in uniform trnl lctric fil E :. Th lctric iol f momnt is 1.60 10 27 C m; th fil mgnitu f is 3.00 10 6 N/C. Wht is th chng in i th iol s otntil nrg? 77 A rticl of chrg q 1 is t th origin of n is. At wht loction on th is shoul rticl of chrg 4q 1 b lc so tht th nt lctric fil is ro t 2.0 mm on th is? If, inst, rticl of chrg 4q 1 is lc t tht loction, wht is th irction (rltiv to th ositiv irction of th is) of th nt lctric fil t 2.0 mm? 78 Two rticls, ch of ositiv chrg q, r fi in lc on is, on t n th othr t. Writ n rssion tht givs th mgnitu E of th nt lctric fil t oints on th is givn b. Grh E vrsus for th rng 0 4. From th grh, trmin th vlus of tht giv (c) th mimum vlu of E n () hlf th mimum vlu of E. 79 A clock fc hs ngtiv oint chrgs q, 2q, 3q,..., 12q fi t th ositions of th corrsoning numrls. Th clock hns o not rturb th nt fil u to th oint chrgs.at, i Figur 22-67 roblm 76. wht tim os th hour hn oint in th sm irction s th lctric fil vctor t th cntr of th il? (Hint: Us smmtr.) 80 Clcult th lctric iol momnt of n lctron n roton 4.30 nm rt. 81 An lctric fil E : with n vrg mgnitu of bout 150 N/C oints ownwr in th tmoshr nr Erth s surfc. W wish to flot sulfur shr wighing 4.4 N in this fil b chrging th shr. Wht chrg (both sign n mgnitu) must b us? Wh is th rimnt imrcticl? 82 A circulr ro hs rius of curvtur 9.00 cm n uniforml istribut ositiv chrg Q 6.25 C n subtns n ngl u 2.40 r. Wht is th mgnitu of th lctric fil tht Q roucs t th cntr of curvtur? 83 SSM An lctric iol with iol momnt : (3.00î 4.00ĵ)(1.24 10 30 C m) is in n lctric fil E : (4000 N/C)î. Wht is th otntil nrg of th lctric iol? Wht is th torqu cting on it? (c) If n trnl gnt turns th iol until its lctric iol momnt is : ( 4.00î 3.00ĵ)(1.24 10 30 C m), how much work is on b th gnt? 84 In Fig. 22-68, uniform, uwr lctric fil E : of mgnitu 2.00 E 10 3 v N/C hs bn st u btwn two 0 horiontl lts b chrging th lowr lt ositivl n th ur L lt ngtivl. Th lts hv Figur 22-68 roblm 84. lngth L 10.0 cm n srtion 2.00 cm. An lctron is thn shot btwn th lts from th lft g of th lowr lt. Th initil : vlocit v 0 of th lctron mks n ngl u 45.0 with th lowr lt n hs mgnitu of 6.00 10 6 m/s. Will th lctron strik on of th lts? If so, which lt n how fr horiontll from th lft g will th lctron strik? 85 For th t of roblm 70, ssum tht th chrg q on th ro is givn b q n, whr n is n intgr n is th lmntr chrg. Fin n for ch givn vlu of q. Do linr rgrssion fit of th vlus of q vrsus th vlus of n n thn us tht fit to fin. 86 In Fig. 22-66, rticl 1 (of chrg 2.00 C), rticl 2 (of chrg 2.00 C), n rticl 3 (of chrg 5.00 C) form n quiltrl tringl of g lngth 9.50 cm. ltiv to th ositiv irction of th is, trmin th irction of th forc F : 3 on rticl 3 u to th othr rticls b sktching lctric fil lins of th othr rticls. Clcult th mgnitu of F : 3. 87 In Fig. 22-69, rticl 1 of chrg q 1 1.00 C n rticl 2 of chrg q 2 2.00 C r fi t istnc 5.00 cm rt. In unit-vctor nottion, wht is th nt lctric fil t oints A, B, n (c) C? () Sktch th lctric fil lins. + 2 2 A 1 B 2 C Figur 22-69 roblm 87.