PHYS 272H Spring 2011 FINAL FORM B. Duration: 2 hours

Transcription

1 PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish. Imotant: Ent you Nam, PUID, Signatu on th Answ-sht. Show you Pudu ID cad to th Instucto whn tuning in th Answ-sht. You should k this coy of th xam in cas you hav qustions. Maxwll quations q insid E nda, B d B nda d nda, Edl, Bdl Iinsid dt Lontz foc: F qe qv B, Engy dnsity E B E nda dt Elctostatics A 1 q 1 q E, V A VB Edl, V B, U qv E alid, E dilctic K 1 1 Elctic diol qs: E (on axis, s), E (on axis, s) diol diol 1 qz E ( z along axis) ing R z / / 1 Q 1 Q/ L E ( fom cnt) (if L) od L Q/ A z Q/ A z Q/ A E 1 ( z along axis) 1 (if z R) disk 1/ R z R Q/ A Q/ A s E ( Q and Q disks), E caacito fing, C A, QC V, U R s caacito Q C

2 PHYS 7H Sing 11 FINAL Magntism qv Il B, B, F Il B LI I B wi (if L ) L/ I R I R B loo (on axis, z R) / z R z Magntic diol IA I R : B (on axis, s), B (on axis, s) diol diol B U B, diol R NI 1 Lsolnoid N, Bsolnoid, Usolnoid LI d d Cicula motion in magntic fild: qbr, / T q B/ m Elctical cicuits i nav, I qnav, v ue, qnu, R L/( A), J I / A E V IR, PI V, Rquivalnt R1 R R, I R mf mf t t/ RC, () batty L It 1 R R R R R R quivalnt 1 Q t, I sin LC LC E ad Radiation 1 q 1 S 1 cbad, 1/c, Ead a, S Ead Bad, E c c c f 1/ T, v f, f, n dsin, h/, E hc/ ad B ad Aa of cicl Gomty, Sufac aa of sh, Volum of sh 1 9 N m 9 1 C C 1 m lcton 9 1 kg 1 atomic adius 1 1 m G Constants 7 T m 11 C m/s N m /kg 9.8N/kg h 6.61 J s 7 moton mnuton kg 15 oton adius 1 1 m g 8 c 1 m/s 19 1 V J N A 6. 1 molculs/mol.1 6 Elctic fild ncssay to ioniz ai 1 N/C 5 Hoizontal comonnt of Eath s magntic fild 1 T

3 PHYS 7H Sing 11 FINAL Poblm 1 [two ats, total oints] A nutal mtal cub is lacd a distanc d fom a diol consisting of two tiny lastic shs with chags +q and q, saatd by a distanc of s, as shown in th diagam (d >> s). (a) [1 oints] What is th magnitud of th lctic fild at th cnt of th cub du only to th chags in and/o on th cub? (A) 1 q d (B) 1 q d (C) 1 qs d (D) 1 qs d (E) Zo (F) Cannot dtmin bcaus th chag distibution in and/o on th cub is not givn. (b) [1 oints] What is th diction of th lctic fild at th cnt of th cub du only to th chags in and/o on th cub? (A) ointing into th a (B) ointing out of th a (C) ointing lft (D) ointing ight (E) ointing u (F) ointing down (G) Th lctic fild has zo magnitud. (H) Cannot dtmin bcaus th chag distibution in and/o on th cub is not givn.

4 PHYS 7H Sing 11 FINAL Poblm [two ats, total oints] A oton (chag +) is insid on of th Ds of a cycloton. Consid th instant whn th oton is tavling at sd v to th ight, as shown in th diagam (v << c). Th is a unifom magntic fild (diction ointing out th ag) thoughout th cycloton. At this instant th oton is a distanc fom th cnt of th cycloton. A dtcto is locatd a distanc L to th ight of th oton s cunt osition. Consid th tim instant whn th filds du to th oton at this aticula location ach th dtcto. (a) [1 oints] What is th magnitud of th adiativ lctic fild at th location of th dtcto? v (A) cl v (B) cl v (C) cl v (D) cl (E) Th a no lctomagntic filds oagating in th diction of th dtcto fom th oton at this location. (b) [1 oints] What is th diction of th adiativ magntic fild at th location of th dtcto? (A) ointing into th a. (B) ointing out of th a. (C) ointing to th lft. (D) ointing to th ight. (E) ointing u. (F) ointing down. (G) No lctomagntic filds a oagatd to th dtcto.

5 PHYS 7H Sing 11 FINAL Poblm [1 oints] A blu light is shd on a mtal. No hoton-lctons a oducd. Which mthod blow will ossibly oduc hoton-lctons fom th mtal? (A) Incas th intnsity of th blu light. (B) Us d light. (C) Us X-ays. (D) Imossibl to oduc hoton-lctons fom th mtal. Poblm [1 oints] A mtal ba of mass M =.1 kg and lngth L =. m slids with ngligibl fiction but with good lctical contact down btwn two vtical mtal osts. Th ba falls at a constant sd v (zo acclation). Th falling ba and th vtical mtal osts hav ngligibl lctical sistanc, but th bottom od (fixd to th osts) is a sisto with sistanc R = Ω. Thoughout th nti gion th is a unifom magntic fild of magnitud B = 1. T coming staight out of th ag. Th gavity acclation constant is g = 9.8 m/s. Find th valu of v. (A) 9 m/s (B) 9 m/s (C) 9 m/s (D).9 m/s (E).9 m/s (F) 98 m/s (G) 98 m/s (H) 98 m/s (I) 9.8 m/s (J).98 m/s 5

6 PHYS 7H Sing 11 FINAL Poblm 5 [1 oints] In th cicuit shown blow, an idal ammt (no intnal sistanc) is instd in th banch containing R. What will it ad, assuming mf = V, R 1 = Ω, R = 6Ω, R = Ω? (A) A (B) 1/1 A (C) 1/6 A (D) 1/ A (E) 1/ A (F) 1 A (G) A (H) A (I) 6 A (J) 1 A Poblm 6 [1 oints] Just io to t =, th caacito (caacitanc C) in th cicuit blow has a chag of Q. Th inducto has inductanc L. At t =, a switch (not shown) is closd, allowing cunt to flow aound th cicuit. What is th magnitud of th cunt whn th chag on th caacito has falln to Q /? Q (A) LC Q (B) LC (C) Q LC Q (D) LC (E) Q LC Q (F) LC 6

7 PHYS 7H Sing 11 FINAL Poblm 7 [1 oints] Two lag nonconducting shts a unifomly chagd with th sam ositiv chag unit aa, fac ach oth as in th figu. What is th magnitud and diction of th lctic fild to th lft of both shts. (Igno any dg ffcts.) (A) (B) E = to th lft (C) E = to th ight (D) E = to th lft (E) E = to th ight (F) E = to th lft (G) E = to th ight Poblm 8 [1 oints] A cohnt d light illuminats two naow hoizontal slits. Bight d stis a sn on a scn 1 m away fom th slits. S diagam blow. (Th diagam is not dawn to scal: th distanc btwn th two slits is a fw tims visibl light wavlngth, and is much small than 1 m wh th scn is locatd.) If th slits a movd futh aat, what will han to th bight stis on th scn? (A) Th gas btwn bight d stis will gt wid. (B) Th gas btwn bight d stis will gt naow. (C) Th light will chang colo, mostly into blu. (D) Th scn will black out bcaus th light wavlngth movs out of th visibl light ang. (E) Nothing will chang. 7

8 PHYS 7H Sing 11 FINAL Poblm 9 [1 oints] A non-unifom lctic fild E xists ov som gion of sac w will dnot as S. Within S, consid a shical sufac of adius R. Fo this sufac, E nda. Which S statmnt blow is always tu? (A) Th shical sufac ncloss chag oducing a flux that is qual in magnitud and oosit in sign to that causd by th xtnal fild. (B) Th shical sufac ncloss both ositiv and ngativ chags, but th is no nt chag containd within th shical volum. (C) Th shical sufac ncloss zo nt chag. (D) Th shical sufac ncloss no chags. Poblm 1 [1 oints] Two cicuits (labld #1 and #) hav diffnt caacitos but th sam battis and bulbs. Th caacitos in cicuit #1 and cicuit # a idntical xct that th caacito in cicuit #1 has ai btwn th lats and th caacito in cicuit # has a lastic slab btwn th lats. (Th sacing btwn th lats is gatly xaggatd on th diagam, but th sacing is wid nough to vnt any chag fom juming fom on lat to th oth though th ga.) Th caacitos a initially unchagd. In which cicuit (#1 o #) dos th bulb stay lit long? (A) Th bulbs stay lit th sam tim iod. (B) Th bulbs do not light. (C) #1 (D) # (E) Th bulb in #1 dos not light, but th bulb in # stays lit until batty is usd u. (F) Th bulb in # dos not light, but th bulb in #1 stays lit until batty is usd u. (G) Not nough infomation to dtmin. 8

9 PHYS 7H Sing 11 FINAL Poblm 11 [1 oints] A solid sh of adius R has unifomly distibutd chag +Q. Th sh has a small hol staight though its cnt. Th ffct of th hol on th lctic fild can b nglctd. A lightwight ngativ chag q is lasd fom st at on nd of th hol on th sufac of th sh. S diagam. Nglct gavity. What is th kintic ngy of th ngativ chag whn it asss th cnt of th sh? 1 qq (A) R 1 qq (B) R 1 qq (C) R 1 qq (D) R (E) (F) Not nough infomation is givn. Poblm 1 [1 oints] Which of th diagams blow bst shows th aoximat distibution of xcss chag on th sufac of th cicuit? (A) (B) (C) (D) 9

10 PHYS 7H Sing 11 FINAL Poblm 1 [1 oints] In th figu blow, an lctic fild in th +y-diction and a magntic fild in th +zdiction a such that a ositivly chagd aticl tavling along th +x-diction at sd v = E/B xincs no nt foc. (W will nglct gavity.) Oth ositivly chagd aticls follow th cuvd tajctois as indicatd in th figu. Which statmnt blow is tu? Y X (A) Paticls cuving u hav mo chag than thos cuving down. (B) Paticls cuving u hav lss chag than thos cuving down. (C) Paticls tavling with sd gat than E/B cuv u (towad +y). (D) Paticls tavling with sd lss than E/B cuv u (towad +y). (E) Non of th abov statmnts is tu. Z Poblm 1 [1 oints] A hollow sh of adius R is unifomly distibutd with total chag +Q on its sufac. At th cnt of th sh locats a oint chag Q. Th lctic fild insid th sh at adius ( < < R) is: 1 Q (A) 1 Q (B) R 1 Q (C) (D) (E) 1 (F) 1 Q R (G) 1 Q Q 1

11 PHYS 7H Sing 11 FINAL Poblm 15 [1 oints] A bundl of N wis is aangd to fom a long hollow cylind of adius R and lngth L, as shown in th ictu at ight. A cunt I uns though ach wi in th diction indicatd. What is th magntic fild magnitud, at location A, outsid th cylind, a distanc dictly abov th mid-oint of th cylind. (A) NI 1 R L (B) NI 1 R L (C) NI 1 R (D) NI 1 L (E) NI L 1 R (F) NI R 1 L (G) NI 1 (H) zo 11

12 PHYS 7H Sing 11 FINAL 1 Poblm 16 [1 oints] A oton and an lcton a moving at a aticula instant as shown in th figu blow. What is th magntic foc on th oton du to th lcton whn th oton is at th location shown in th diagam blow? (Nglct tadation ffcts.) y x z (G) + vv z (H) vv z (I) vv y (J) vv y (K) vv x (L) vv x (A) + vv z (B) vv z (C) vv y (D) vv y (E) vv x (F) vv x

13 PHYS 7H Sing 11 FINAL Poblm 17 [1 oints] Th diagam dicts two concntic ings, with adius of 5 cm and.5 cm, sctivly. Both ings hav sistanc; th inn ing sistanc is 5. Cunt is un in th out ing. Th cunt is initially A clockwis at t = min, and dcass linaly to A at t = 1 min. Th cunt thn vss th diction to countclockwis, and incass linaly to A at t = min. What can you say about th inducd cunt in th inn ing? (A) Th inducd cunt is clockwis in th fist minut and countclockwis in th scond minut. Its magnitud in th scond minut is twic as lag as in th fist minut. (B) Th inducd cunt is countclockwis in th fist minut and clockwis in th scond minut. Its magnitud in th scond minut is twic as lag as in th fist minut. (C) Th inducd cunt is clockwis in th fist minut and countclockwis in th scond minut, but its magnitud is th sam thoughout th minut tim iod. (D) Th inducd cunt is countclockwis in th fist minut and clockwis in th scond minut, but its magnitud is th sam thoughout th minut tim iod. (E) Th inducd cunt is always clockwis, and its magnitud is th sam thoughout th minut tim iod. (F) Th inducd cunt is always countclockwis, and its magnitud is th sam thoughout th minut tim iod. (G) Th inducd cunt is always clockwis, but its magnitud in th scond minut is twic as lag as in th fist minut. (H) Th inducd cunt is always countclockwis, but its magnitud in th scond minut is twic as lag as in th fist minut. (I) Th is no inducd cunt. 1

14 PHYS 7H Sing 11 FINAL Poblm 18 [1 oints] An lcton is initially at st at oigin. At tim t =, th lcton stats to acclat at a constant acclation a in th diction shown in th diagam. Th idntical dtctos snsitiv to lctomagntic adiation a locatd along a staight lin fom th oigin, at ositions A (1 mt fom th oigin), B ( mts fom th oigin), and C ( mts fom th oigin), sctivly. At tim t = 7 ns, you mak masumnts of adiation at ths th locations simultanously. Th masud lctic fild amlitud of th adiation at location A is E A. What a th masud amlituds E B and E C at locations B and C, sctivly? C (A) E B =, E C = (B) E B = E A, E C = E A + B (C) E B =, E C = E A /9 (D) E B = E A /, E C = + A (E) E B =, E C = E A / (F) E B = E A /, E C = (G) E B = E A /, E C = E A / (H) E B = E A /, E C = E A /9 1

15 PHYS 7H Sing 11 FINAL PHYS 7H Sing 9 FINAL Answ-Sht Nam PUID Signatu Multil-choic Poblm Answs: (1a) C (1b) F (a) A (b) B () C () D (5) D (6) F (7) B (8) B (9) C (1) D (11) D (1) B (1) D (1) A (15) G (16) C (17) G (18) F 15