PH2200 Practice Final Exam Spring 2004

Transcription

1 PH2200 Practic Final Exam Spring 2004 Instructions 1. Writ your nam and studnt idntification numbr on th answr sht. 2. This a two-hour xam. 3. Plas covr your answr sht at all tims. 4. This is a closd book xam. You may us th PH2200 formula sht that is includd with th xam.* 5. Equations may not b stord in calculators, nor may calculators b xchangd. 6. Rcord your answrs in th form A, B, C, tc, on th answr sht. 7. This xam consists of 20 concpt qustions worth six points ach and nin problms having a total of 30 parts. Th problm parts ar qually wightd: ach is worth six points. Th total numbr of points on th xam is If you hav any qustions during th xam, plas rais your hand and wait for assistanc. * Th formula sht is omittd from this practic xam.

2 PH2200 Practic Final Exam Spring 2004 Concpt Qustions: Each qustion has a singl corrct answr and is worth six points. 1. Th figur blow shows fiv pairs of plats: plats A, B and D ar chargd insulating plats and C is an lctrically nutral conducting plat. Th lctrostatic forcs btwn th plats ar shown for thr of th pairs. For th rmaining two pairs, do th plats rpl or attract ach othr? A A A B C B C D D D B and D rpl; C and D rpl B and D rpl; C and D attract B and D attract: C and D rpl B and D attract: C and D attract 2. Th figur blow shows four situations in which chargd particls ar fixd in plac on an x-axis. In which situation is thr a point on th x-axis to th lft of th particls whr an lctron will b in quilibrium? Exclud th point at infinity. q -q q -2q 2q -q 2q 2q Th following two qustions rfr to th figur to th right. A sphrical shll with a uniform positiv surfac charg dnsity is nar a positiv point charg. 3. What typ of matrial is th sphrical shll? Mtal Insulator Nd mor information! E =? insid 4. Is th lctric fild insid th sphr zro? Ys No Nd mor information 2

3 PH2200 Practic Final Exam Spring On proton is acclratd from rst by a uniform lctric fild whil a scond proton is acclratd from rst by a non-uniform lctric fild. Th two protons mov through th sam lctric potntial diffrnc. Is th final spd of th proton in th uniform lctric fild gratr than, qual to, or lss than th final spd of th proton in th non-uniform lctric fild? Gratr than Equal to Lss than Not nough information is givn Th figur to th right applis to th nxt two qustions. A capacitor C is mad of two paralll plats sparatd by a distanc d. Th dimnsions of th plats ar vry larg whn compard with d. This capacitor is connctd to a battry with mf E and a switch as shown. Th switch is initially closd. E - A B C 6. With th switch closd, th lctric potntial of plat A is highr than th lctric potntial of plat B. Tru Fals 7. Lt E b th magnitud of th lctric fild btwn th plats whn th switch is closd. At t = 0, th switch is 1 opnd, and thn th plats of th capacitor ar pushd closr to a distanc d' = 2 d. Th magnitud of th lctric fild, E ', btwn th plats aftr making ths changs is 1 E' = E 2 E' = E E' = 2E 8. Two typs of rsistors ar mad of th sam matrial. A typ 1 rsistor has twic th diamtr of a typ 2 rsistor but is half as long as th typ 2 rsistor. Which of th configurations shown has th highr nt rsistanc? A B A and B hav th sam rsistanc. A Typ 1 B Typ 2 3

4 PH2200 Practic Final Exam Spring An ordinary rsistiv light bulb and a rsistor R ar in sris with a battry that provids an mf E. Th circuit is first at room tmpratur, and thn th rsistor R is immrsd in liquid nitrogn so that its tmpratur is significantly dcrasd. As a rsult of this chang, th bulb glows mor brightly bcaus R incrass. th bulb glows mor brightly bcaus R dcrass. th bulb glows lss brightly bcaus R incrass. th bulb glows lss brightly bcaus R dcrass. thr is no chang in th brightnss of th bulb. E R Th figur to th right applis to th nxt two qustions. Thr particls having th sam charg and th sam spd, but diffring in mass, ntr a rgion of uniform magntic fild dirctd into th plan of th pag. 10. Which particl has th largst mass? A B C particl A particl B particl C Not nough information is givn A, B, C 11. A uniform lctric fild is now applid in th rgion of th magntic fild so that particls continu to mov up toward th top of th pag without bing dflctd. What should b th dirction of this lctric fild? right lft up down into th pag 12. A point charg Q is placd at th nd of th scond-hand of a watch, as shown in th figur. What is th dirction of th magntic fild at th cntr of th watch du to this moving charg? into th pag out of th pag dpnds on th position of th charg Q 4

5 PH2200 Practic Final Exam Spring Rcall that th magntic fild of a long, straight wir consists of circular fild lins. Dos Ampr's Law hold for a squar loop surrounding this wir? Ys No Not nough information is givn loop 14. Thr is a wir carrying currnt out of th papr as shown by a thick circl with a dot in th middl. Concntric circls with arrows outsid th wir rprsnt th magntic fild lins. Which on of ths diagrams bst rprsnts th magntic fild lins? 15. A uniform magntic fild is prpndicular to th papr within th nclosd rgion indicatd by th dots. Th four rctangular loops of conducting wir ar lying flat on th papr and ar moving to th right with th sam, constant vlocity. Th rsistanc is th sam for ach loop. At th instant shown in th figur, in which loop is th inducd currnt th largst? A B C D Th inducd currnt is th sam in all loops B D C A 16. Th nrgy stord in an inductor dpnds on th dirction of th currnt passing through it. Tru Fals Not nough information is givn 5

6 PH2200 Practic Final Exam Spring Two ac gnrators produc sinusoidal voltags with th sam amplitud but diffrnt frquncis. How do thir rms voltags compar? Th rms voltag of th highr frquncy sourc is gratr. Th rms voltag of th highr frquncy sourc is lss. Th rms voltags ar qual. Not nough information is givn 18. A plan lctromagntic wav (for xampl, a radio wav) propagats in a vacuum. Th lctric fild of this wav is ntirly in th plus and minus z dirctions in spac as dscribd in an xyz coordinat systm. Slct th incorrct statmnt about this wav. Th magntic fild of this wav must b ntirly in th x-y plan. If th magntic fild of this wav is ntirly in th plus and minus x dirctions, th lctromagntic wav is propagating in ithr th plus or minus y dirction. Assuming that th maximum lctric fild is unchangd, th nrgy dnsity associatd with th wav incrass whn th frquncy of th wav is incrasd. Th magnitud of th magntic fild of th wav is a maximum whn th magnitud of th lctric fild is a maximum. Th ratio of th maximum valu of th lctric fild of this wav to th maximum valu of th magntic fild of th wav is a constant, and this constant has th sam valu for all plan lctromagntic wavs in a vacuum. 19. A bam consisting of rd and blu light is incidnt from air onto a slab of glass. Th indx of rfraction of blu light is gratr than that for rd. Whn th light mrgs at th bottom, th rd and th blu light mrg at th sam point. th rd light mrgs at a largr valu of x along th axis than dos th blu light. th blu light mrgs at a largr valu of x along th axis than dos th rd light. glass x 20. Th prson in th figur to th right is 2 m tall. A mirror is locatd 20 m away and is 0.5 m tall. Th top of th mirror is at th sam hight as th top of th prson s had. Assum for simplicity that th prson s ys ar at th hight of th top of his had. What part of his body dos th prson s in th mirror? 20 m.5 m top 0.25 m top 0.5 m top 1 m top 1.5 m ntir 2 m 2 m 6

7 PH2200 Practic Final Exam Spring 2004 Problms: Each part of ach problm is worth six points. 1. Positronium consists of an lctron with charg - bound by th attractiv Coulomb forc to its antiparticl, th positron with charg. As shown in th figur blow, assum th distanc btwn th lctron and positron is d. Rport all answrs in trms of, d, a, and any ncssary physical constants. - A d a (a) What is th magnitud of th lctric forc xrtd on th lctron by th positron? k / d 2 k / d 2 2 k / d k /4πε od k /4πε d 2 2 o Point A in th figur abov is a distanc a from th lctron on th lin conncting th lctron and positron. (b) What is th magnitud of th lctric fild at point A? kd( d 2 a)/ a ( d a) 2 2 kd ( 2ad 2 a )/ a ( d a) kaa ( 2 d)/ a ( d a) 2 2 ka ( 2ad 2 d )/ a ( d a) kd ( a )/ ad (c) If th lctric potntial at infinity is takn to b zro, what is th lctric potntial at point A? kd / ad ( a) kd / ad ( a) kd ( 2 a)/ ad ( a) kd ( 2 a)/ ad ( a) ka ( 2 d)/ ad ( a) (d) What is th potntial nrgy of positronium? k / d k / d k 2 / d k 2 / d 2 2 k / d (F) k / d 2 2 7

8 PH2200 Practic Final Exam Spring In addition to a magntic fild, th Earth also has an lctric fild. During days of fair wathr (no thundrclouds), th atmosphric lctric fild has a magnitud of 135 V/m at th Earth's surfac, and it points toward th cntr of th 6 Earth. Trat th Earth as an isolatd, uniformly chargd conducting sphr of radius m, and tak th zro of lctric potntial to b at infinity. E = 135 V/m (a) What is th nt charg (sign and magnitud) on th Earth? C C C C C 25 (F) C (b) What is th magnitud of th flux of th lctric fild through a sphr concntric with th Earth but having only half its radius? V m V m V m V m (c) What is th lctric nrgy dnsity nar th surfac of th Earth? J/m J/m J/m J/m J/m 10 3 (d) What is th magnitud of th lctric potntial of th surfac of th Earth? V V V V V 8

9 PH2200 Practic Final Exam Spring Th cabl conncting th positiv trminal of an automobil battry to th startr motor is m long and cm in radius. Th rsistanc of th cabl is Ω. (a) What is th rsistivity of this cabl? Ω m Ω m Ω m Ω m Ω m. (b) Whn th motor is stalld, th currnt in th cabl may b as much as 600 A. What is th potntial diffrnc btwn th nds of th cabl undr this condition? V V 4.57 V 11.7 V 12.0 V (c) At what rat is hat dissipatd in th cabl undr th condition of part (b), that is, what is th powr? W 4.82 W 23.6 W 112 W 189 W 9

10 PH2200 Practic Final Exam Spring To protct srvic prsonnl against shock, larg capacitors in th powr supplis of lctronic quipmnt ar usually connctd in paralll with "bldr rsistors" whos job is to discharg ("bld") th capacitors aftr th 4 quipmnt is turnd off. Suppos a F capacitor with an initial charg of C is in paralll with 4 a Ω bldr rsistor F Ω (a) What is th initial lctric potntial diffrnc across th capacitor? V V 4.56 V 123 V 355 V (b) How much charg is on th capacitor aftr a tim corrsponding to on tim constant? C C C C C (c) How much tim will it tak for th capacitor voltag to rach th saf valu of 30.0 V? 8.85 s 11.2 s 19.2 s 27.7 s 35.0 s 10

11 PH2200 Practic Final Exam Spring At th surfac of a pulsar or nutron star th magntic fild may b as strong as 10 8 T. A proton with a spd of m/s is on th surfac of such a pulsar. Consult th figur blow for th dirction of th magntic fild and th proton s initial vlocity. Assum that in th rgion of intrst th magntic fild is uniform with a magnitud of 1.00 x 10 8 T. z B! v! y x (out of pag) (a) What is th dirction of th magntic forc on th proton? x -x y -y z (F) -z (b) What is th magnitud of th magntic forc on th proton? N N N N N 5 (c) What is th shap of th path or trajctory of th proton? straight lin llips circl parabola hyprbola (d) What is th cyclotron frquncy of th proton in th givn fild? rad/s rad/s rad/s rad/s rad/s 11

12 PH2200 Practic Final Exam Spring A long cylindrical conductor having a radius of m carris a currnt of 10.0 A uniformly distributd ovr its cross-sction. A long thin wir lis paralll to th cylindr, a distanc of m from its cntr, and carris a currnt of 2.00 A in th sam dirction as that in th cylindr. In th figur blow, both currnts ar out of th pag A (out) 2.00 A (out) m (a) What is th magnitud of th magntic fild producd by th cylindrical conductor a distanc of m from its cntr? (b) What is th magnitud of th magntic forc pr unit lngth xprincd by th long thin wir? N/m N/m N/m N/m N/m (c) Suppos th long thin wir is now rmovd. What is th magnitud of th magntic fild at a point insid th cylindrical conductor, a distanc of m from its cntr?

13 PH2200 Practic Final Exam Spring A car altrnator consists of a 250-turn coil 5.00 cm in radius in a magntic fild of T. Th altrnator is turning with a constant angular spd of 105 rad/s. This implis that angl θ shown in th figur blow is givn by θ = 105t whr t is tim xprssd in sconds. " " θ B! (a) Find th inducd mf in th coil as a function of tim. ( ) ( 1 ) V sin105t V sin105t ( 20.6 V) sin105t ( 120 V) sin105t ( 170 V) sin105t (b) If th angular spd of th coil wr doubld, by what factor would th maximum inducd mf incras? Thr would b no chang. (c) What is th orintation of th coil with rspct to th magntic fild whn th maximum inducd mf occurs, that is, for what angl θ is th inducd mf maximum?

14 PH2200 Practic Final Exam Spring A lasr bam of wavlngth 632 nm and cross-sctional diamtr d = 2.00 mm is incidnt at an angl of θ = 40.0 on a glass plat having a thicknss of t = 2.00 cm. Th indx of rfraction of th glass is d θ t glass (a) At what angl is th lasr bam rfractd as it passs from air into th glass? (b) What is th wavlngth of th lasr bam insid th glass? 408 nm 556 nm 632 nm 825 nm 980 nm (c) What is th cross-sctional diamtr of th lasr bam aftr it has passd through th glass plat? 1.02 mm 1.24 mm 1.69 mm 1.80 mm 2.00 mm 14

15 PH2200 Practic Final Exam Spring Whn a woman's hand mirror is hld 20.0 cm from hr fac, a virtual imag is formd 30.0 cm from th mirror. Th mirror is sphrical. (a) What is th radius of curvatur of th mirror? cm 12.0 cm 24.0 cm 60.0 cm 120 cm (b) What is th magnification providd by th mirror for th givn objct and imag distancs? (c) If th mirror wr flat, how far from th woman's fac would th imag b formd if th mirror wr hld 20.0 cm from hr fac? 20.0 cm 40.0 cm 80.0 cm 120 cm Th imag would b formd at th sam position as th woman's fac. 15

16 PH2200 Practic Final Exam Spring 2004 Nam: ID# Rcitation Sction: 8:00 Zhou 9:00 Zhou 10:00 Tboh 11:00 Tboh 12:00 Yap 1:00 Roy 2:00 Roy Concpt Qustions Problms D A C B D E (a) 3. (a) 6. (a) 9.(a) B A A A A D (b) (b) (b) (b) B A B E B B (c) (c) (c) (c) B B D E C (d) 4. (a) 7. (a) B C C B A (a) (b) (b) A B A D E (b) (c) (c) B C B A C (c) 5. (a) 8. (a) B C D B A (d) (b) (b) B B C E (c) (c) C C A (d) Column Subtotals = Exam Scor 16