A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m.

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1 1. Young s doubl-slit xprint undrlis th instrunt landing syst at ost airports and is usd to guid aircraft to saf landings whn th visibility is poor. Suppos that a pilot is trying to align hr plan with a runway as suggstd by figur (a) blow. Two radio antnnas A 1 and A 2 sparatd by 40.0 ar positiond at th nd of th runway. Th antnnas broadcast cohrnt radio wavs at 30 MHz. A 1 A 2 a) Find th wavlngth of th radio wavs. Sinc c = f, thn = c/f = (3x10 8 /s) / (30x10 6 Hz) = 10. b) Th pilot locks onto th strong signal radiatd along an intrfrnc axiu and strs th plan to kp th signal strong. Suppos that th pilot is flying along th first sid axiu (figur (b)). Calculat th angl btwn th plan s trajctory and th cntrlin of th runway. 10 o d sin sin d 40 c) How far to th sid of th runway is th plan if it is 2 k fro th nd of th runway and is flying along th first sid axiu? x sin x (2k)(0.25) 0.5k 500 2k 2. Considr th ass spctrotr shown blow whr a proton of charg + and ass travling with vlocity v ntrs a rgion of lctric and agntic filds whos agnituds ar 720 N/C and 0.2 T rspctivly v E

2 a) If th agntic fild, B is dirctd into th pag vrywhr, what is th dirction of th agntic forc F B on th proton? (Explain your rasoning.) up sinc th dirction is givn by th rh rul and th charg is + b) Draw th lctric fild lins on th diagra abov and thn find th agnitud and dirction of th lctric forc on th proton. Elctric forc = E = 1.15 x N c) Basd on your answrs to parts a and b abov, what is th vlocity of th proton such that it travls in a straight lin? vb = E so v = E/B = 3600 /s d) If th proton lavs th lctric fild and is only undr th influnc of th agntic fild, what is th charg to ass ratio of th proton if it travls in a circl of radius 0.188? (In ordr to rciv crdit, do not siply tak th proton s charg dividd by th proton s ass!) F = vb = v 2 /r so / = v/(rb) = 9.57 x 10 7 C/kg as it should 3. Considr th following circuit whr th rsistors ar 150 and th battry is 45V. 6 B 5 4 A a) What is th quivalnt rsistanc of th circuit? Labling th rsistors as shown: R 6 in paralll with R 5 so R 56 = 75 R 4 in sris with R 56 so R 456 = 225 R 3 in paralll with R 456 so R 3456 = 90 R 1 and R 2 in sris with R 3456 so R = 390. Thus R q = 390. b) What is th currnt producd by th battry?

3 Sinc V = IR q, I = V/R q = 45V/390 = 0.115A = 115A. c) What is th voltag diffrnc btwn th points A and B? V battry = 45V and V 1 = V 2 = IR 1 = 17.3V, so V 3456 = 45V 34.6V = 10.4V. Sinc R 3 in paralll with R 456, V 3 = V 456 = 10.4V. By Oh s law, I 3 = 0.069A and I 456 = 0.046A (which su to 0.115A) This givs V 4 = 6.9V and V 65 = 3.5V (which su to 10.4V sinc V 4 and V 65 ar in sris.) Th potntial diffrnc across points A and B is givn by V 65 = 3.5V. (For copltnss, I 5 = I 6 = 0.023A = 23A) 4. A proton sits at th origin with an lctron to ithr sid of it along an axis, ach at a distanc of 0.53 x fro th proton. a. Draw a sktch and find th lctric fild (agnitud and dirction) at on of th lctrons du to th proton and othr lctron k k 3 k r (2 r) 4 r 11 E 3.84x10 N / c b. Find th xtrnal work rquird to hav brought th scond lctron fro a larg distanc away to its distanc fro th proton and first lctron in part (a). Is it positiv or ngativ work? Explain why. k k k V but W xt = V = - 2.2x10-18 J; ngativ sinc you nd to apply a forc r 2r 2r away fro th chargs as th lctron is hld back whil oving in towards its final position. 5. a. In th circuit shown blow, find th currnt through ach rsistor, using th labls shown. 1 K 4 K I 2 I K I 1 10 V 1 K Can find quivalnt rsistanc dirctly top branch has 5K which is in paralll with iddl branch so ths togthr giv 1.67 K which is thn in sris with 1K so th total Rq = 2.67K. Thn I 1 = 10/2.67K = 3.75 A; this currnt thn divids in th ratio

4 1:2 with th top branch gtting 1 part and th iddl branch gtting 2 parts thrfor th top gts I 2 = (1/3)I 1 = 1.25 A and th iddl gts I 3 = (2/3)I 1 = 2.50 A. b. Suppos that in th circuit of part (a) th battry and cntral branch ar rovd so that thr is a continuous singl outr loop with only 3 rsistors. If th squar loop has dinsions of 10 c x 10 c and is in a rgion of spac whr thr is a unifor B fild dirctd into th papr and incrasing at a rat of 0.1 T/s, find th currnt (agnitud and dirction) that flows through th 4 K rsistor. 1 ( BA) 1 B I (0.1x0.1 ) x10 A R R t 6K t i. a. A vrtically polarizd ba of light of 350 n wavlngth passs through a polarizr with its transission axis rotatd at 30 o to th vrtical in th clockwis dirction, and thn through a scond polarizr with its transission axis also orintd at 30 o to th vrtical but in th countr-clockwis dirction. If th transittd intnsity of light is 1.0 W, find th intnsity incidnt on th first polarizr. With Io = incidnt intnsity, aftr th first polarizr th transittd intnsity is I 1 = Io[cos30] 2 and aftr th scond polarizr, aking a 60 o angl with th first polarizr, th transittd intnsity is I 2 = Io[cos30] 2 [cos60] 2 = 1 W (as givn, so w can solv for Io to find Io = 1/{[cos30] 2 [cos60] 2 } = 5.3 W ii. In a doubl slit xprint with a ba of lctrons, th slit widths ar 1 and th slit spacing is 10. Th lctrons ar acclratd through a potntial diffrnc of 10 4 V starting fro rst bfor arriving at th slits. a. What is th wavlngth of th lctrons? h h p 2V = 1.22 x b. What is th sparation btwn th intrfrnc frings ford on a scrn 10 away fro th slits? y d sin d D or y givs spacing = 1.22x10-5 D d iii. An lctron travling north in a horizontal plan at a spd of 10 7 /s ntrs a rgion whr thr is a unifor 0.05 T agntic fild pointing vrtically down. a. Find th diatr of th orbit that th lctron travls in and indicat its dirction of travl as viwd fro abov (spcify ithr clockwis or countrclockwis). Th forc on th lctron is givn by vb and is dirctd to th East (rbr q<0) So F = a = v 2 /r givs us that r = v/b = or diatr = and th lctron gos in a CW circl

5 b. What is th axiu accuracy with which th position of th lctron can b dtrind? Sinc x p h, w hav that x h/ p = h/ v. Th ax accuracy occurs whn th quality sign is usd (iniu x) and whn th axiu v is usd. If w tak th ax v as v itslf, thn w find x iniu = 7.3 x = 0.73 x = 0.73 Angstros or just about th siz of an ato Part II Multipl-Choic Circl th bst answr to th following qustions. Each qustion is worth 2 points (20 points total). 1 Suppos that a chargd particl of charg q and ass ovs in a agntic fild of strngth B with a vlocity v that is prpndicular to th agntic fild. If particls with twic th ass (with th sa charg q travling in th sa agntic fild with th sa vlocity) ar usd, what will happn to th trajctory of th or assiv particls? a) Th two trajctoris will b th sa. b) Th or assiv particls will follow an orbit with a radius twic as larg as th sallr ass particls. c) Th or assiv particls will follow an orbit with a radius half as larg as th sallr ass particls. d) Thr will b no way to dtrin th orbital radii of th particls. 2 Suppos that two wirs ar carrying currnts I in opposit dirctions. Th agnitud of th agntic fild cratd at th cntr of th two wirs sparatd by a distanc d is I a) 2 0. d 0I b). 2 d 0I c). 4 d d) zro. 3 If it taks 1 scond for blu light ( = 450 n) to travl straight through a block of glass (n glass = 1.5) and it taks 0.87 sconds for th sa blu light to travl through a block of ic of th sa thicknss as th glass, what is th indx of rfraction of th ic? a) 1.64 b) 1.53 c) 1.42 d) Suppos that polarizd light with intnsity I 0, has its axis of polarization orintd at 45 o with rspct to th vrtical. If this light is incidnt on a polarizr whos transission

6 axis is orintd at 65 o with rspct to th vrtical (and to th sa sid of th vrtical as th axis of polarization), what prcnt of th incidnt light is transittd? a) 0% b) 12% c) 18% d) 88% 5. If a particl with charg 3 and ass is acclratd fro rst through a rgion of spac whr thr is a diffrnc in potntial of 100V, what will th particl s approxiat spd b whn it lavs th acclrating rgion? a) 25. b) 25. c) d) Th total nubr of diffrnt quantu chanical stats availabl in th n = 3 shll of an ato is a. 18 b. 16 c. 10 d. 24. non of ths 7. Th nubr of photons in a ba of light is proportional to a. E, th lctric fild b., th wavlngth c. I, th intnsity d. f, th frquncy. p, th ontu 8. Th Rayligh critrion rfrs to a. scattring of light b. polarization of light c. diffraction of light d. rfraction of light. abrration of light 9. Contrast in a icroscop rfrs to a. foring a clar iag of two narby points b. foring a vry larg iag c. distinguishing objcts of diffrnt colors

7 d. sing brightnss variations at dgs. foring a vry bright iag 10. An lctron in an xcitd stat of an ato has a lifti of 1 ns. Th uncrtainty in th nrgy of th ittd photon whn it aks a transition out of this stat (in V) is f. 6.6 x 10-7 g. 4.1 x 10-6 h. 1.1 x i. 6.6 x j. non of ths 11. Which of th following is a fals statnt about conductors: (a) just outsid, th lctric fild is prpndicular to th surfac, (b) at quilibriu, th nt charg insid is zro, (c) a charg locatd within a hol insid th conductor fls no forc fro chargs outsid th conductor, (d) th lctric fild insid is always zro.

Unit 7 Charge-to-mass ratio of the electron

Unit 7 Charge-to-mass ratio of the electron Unit 7 Charg-to-ass ratio of th lctron Kywords: J. J. Thoson, Lorntz Forc, Magntic Filds Objctiv: Obsrv th rsults of lctron ba influncd by th agntic fild and calculat th charg-to-ass ratio of th lctron.