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Test3.oldtests - a: —aL-[—J:+L —L b‘. -4+’~ -”...

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Unformatted text preview: a: —aL-[—J:+L —L b‘. -4+’~ -” O Cz~i . . . l . . are 1nd1cated. Also shown ar o‘loo s to be used 1n an Ampere's Law calculat1on. Rank 1. (8 points) The figure above s waitphree currents of equal magnitude, whose directions the loops in order of decreasing magnitude of § B ds along each loop. That is, rank them from largest (first) to smallest (last) magnitude. Be sure to note carefully whether the loop passes over or under the currents. 0(7C :CL7b 2. (8 points) Light with a wavelength of 420 nm passes from air into glass that has a refractive index of 1.5. Indicate whether the follow quantities increase, decrease, or remain the same in the glass as compared to the air by circling the correct choice. (a) frequency (b) wavelength (c) speed (d) angular frequency INCREASE INCREASE INCREASE INCREASE w: 1% DECREASE ,f— @ SAME DECREASE ’? dye/WIS 07’: soukce only 50 flemat‘ns SaW'e \/ demeoses In Jr‘he akssl ,c ) 60 X d 9514267585 _C n _/.,_ glass ' ' Vélqss / Wall/15 5W Polarizing direction 3. (8 points) In the figure shown above, initially unpolarized light passes through two polarizing filters. The first (P1) is oriented to only pass vertically polarized light (as shown) and the second (P2) is aligned with a polarizing direction 30 degrees from the vertical (as shown). The initial intensity is 1., . Circle the correct choice for each of the statements below. The intensity after passing through P1 is approximately: (b) 0.2510 (c) L, (d) zero ® The intensity after passing through P2 is approximately: 4. (8 points) For each of the following statements (all are true), circle the ones which are true because of Gauss' Law for magnetism. (b) a time-varying electric field produces a magnetic field (b)0.866Io (0) 0.7510 (d) 0.43310 (a) magnetic field lines form closed loops (c) magnetic monopoles do not exist (d) a magnetic field cannot decrease in one coordinate direction while remaining constan in the other two coordinate directiOns 5. (17 points) A long, conducting hollow cylinder has an ' I‘lbel‘ radius of . cm and an outer radius of m. A current of 100 amperes, uniformly distributed across the cross section of the cylinder, flows along its length in a direction out of the page as shown here. Let r be the distance measured from the center of the cylinder. Annswer the following questions. SHOW YOUR WORK FOR FULL CREDIT (a) What is the magnitude of the magnetic field at r=l.O cm [6,” 90,03 2‘ OW _ ,_‘ __z) «9 ‘ [VI/cm J 5‘7 B “O :flo/[WJ (b) what is the magnitude of the magnetic field at 7:3. 0 cm I . )4 [do (0014) Ban/Q) fflo 4am? ; , J j [00 j . ‘ y 0%. V36»! 4040/ I 377(103’") 17" (c) what is the magnitude of the magnetic field at 716.0 cm /Ua[/pa/l) . ‘ : r _ “7' a)! IYGH.‘ ,(‘Qmop MOI?) B Q77(_)06M)b5i3)(10 (d) make a graph of B versus r from r=O to the end of the axis using the results from (a), (b), and (c). ‘ 6. (17 points) In the figure below, a spherical concave mirror has a focal length of 15 cm. An object is placed a distance 7 cm in front of the mirror, as shown. (a) On the figure above, draw rays to locate the image. Show the image in the proper height, orientation, and distance. (b) Calculate the distance of the image from the mirror 35”- -l/ _L fr/s’cm 40: 7047 .. JO A ‘ «4 ‘3 -— l 3 . / c M (c) calculate the magnification of the image (including sign). 2 -)3»/cvv ._ Why—5:4 -+/.9 76”! (d) is the image Virtual or Real? Circle your choice. $Lux ifi+° Paper Int/leases WrH’i +z'me. f,— ihducle-FIUX Mae‘i' 5C 092‘? i)qu 1.5 60 CHAA-anll/ [DJ PHE/ hat/3+ ie .——-_ 7. (17 points) In the figure above a bar with resistance 0.2 Q is sliding on frictionless perfectly conducting rails 1.5 meters apart, as shown. A constant external force of 2 N is applied in the direction shown. There is a constant magnetic field B=0.1 T into the page. (a) What is the direction of the induced current around the circuit formed by the bar and 9 U1} rails? (circle one) / CLOCKWISE COUNTERCLOCKWISE AW (b) When the bar reaches a constant velocity, what is the magnitude of the current? g/Y/ V;- cohs‘fam‘i’ / arce/‘QQILI'W: OI I 30 géf’ufles : O 50 Femé = 7E :: 1’0 3W0 — “oi 5g 7 5% (c) calculate the terminal velocity of the bar. A ’Fm Q CW xi] am 8% 7A 1.5 Afifiuinecfl / “ILL? 5% clef)st 011514169 Ve/OC'Jy JR - /€/-‘ 514%: fiiKBfil : B 2? :Bfig‘“)“‘)] d _ {8305158) e r velvety 3‘7 v~ E ' (in? X16143 ' mam mom I) 8. (17 points) Your cell phone has a power output of about 0.5 watts. A typical cell phone tower receiver requires a signal of 0.2 iLW/m2 to receive your phone. (a) what is the maximum range of your cell phone? -e Po ,S‘M/ : . 10 ‘77» : 3 If.“ Silva ‘2 x m 77" 7'??- WT 'A’Z (b) at the maximum range, what is the magnitude of the electric field generated by your phone? Snvq : (c) at the maximum range, what is the magnitude of the magnetic field generated by your phone? / F 6 +5 __ ~Mn-X ,H F. _ 3 I 3 137W C 4. 1X10 / // Question 1 [11} points] {i} [5 points] In the figure, the current element idi, the point P, and the three vectors (I, 2? 3} are all in the plane of the page. The direction of (EB, due to this current element, at the point P is: _.~‘ l-N in Jr V WT L, e r' r , r i; Tact/- II ‘5 I e" ’- r A. the magnetic field is zero. .lm Fwd {j E. in the direction marked “2” h "“ "“I _ . : l}; .- n r rare. x v fr?" “egg; 1‘:- _ C. in the direction marked “3” D. out of the page E. into the page {ii} [5 points] If the current in the length element at! is zero, then the direction of the magnetic field will be; ne'er-r ---------- —H__HHH"‘_'—*—"—'-I-u__._ . . “ETI- ' 'fW-lfl'l r -. :I J”) 1-H." I" |'Iili‘l' 1- ' A.thelr1agnet1efteld1s zero. rel“ 6‘" ' ' ' 13. in the direction marked “2” C. in the direction marked “3” D. out of the page E. into the page Problem 1 (a) A selencicl 1.35 m 10:: g and 2.9L“) cm in diameter carries a current of Ill] A. The magnetic field inside the snlennicl is Ill] m'l‘. (i) [T paints] Calculate the number of turns per unit length For this seicneid. E; l fit. 1 ree- In“ T r.- ljfg’dg . HTF'IJCJF'J H/W EXt'nwl (“NI ml: {ii} [T pflints] Calculate the [en tit cf the wire fermin the sawmid‘ g g ml ‘ 'a ' r. F“ -: 'A II {I .I IILII_.I IL PHI-1’1. E 5 If “Till- J HI: IL : H 5 WQ { “VA-Fl ' LIE”:qu ’a— til).er : Ears: « 71-May? w ., .I-Ir"-l'_2‘rm L It} “'f F- thlem 1 [h] [6 points] Twn long straight wires are parallel and carry current in the same direction. The currents are 31} and IZA and the wires are separated by H.413 cm. Find the magnitude of the magnetic field at a paint Inirit'razrr between the wires. i I I 1 1" I r e- '. E13 33mm mist. ' ‘3' - I I —\ 61 £1 Q 5:39 ll't-qf p. t " 'c'fl 'r l' g E. POOH EN U'r L": 2 F -- - -- .91. F .pecn la :71 0W "1 -'.‘r I' 1.I/. ' fair .1- e head-r “h” E-r‘t""‘¥- I .t’. +1“'0 1") .HC' . . .. t 1 N I“ in _ '3? ] 1., ifl’. LL: e #_ ‘1‘ cm lgmr i at l [ts-El k girl all; [J51 J ‘r'ilrlllfir H/w I, last E n Fl h LI mew ,_ "- —-'-'—_--_-__ - __ .a { '..- , Fr t w Int: {Ith fix " M] ' " __.' ._ Quest‘ien 2 [ll] points] The figure shows two circuits in which a conducting hat is slid at the same speed v through the same uniform external magnetic field and along a U—shaped wire. The parallel lengths of the wire are separated by 2L in circuit 1 and by L in circuit 2. The current. induced in circuit 1 is clockwise. [a] (4 [its] Is the direction of the external magnetic field into or out of the page? . , “ 'I 5 :Jr . ("JOHN-Cute “NF “"‘5' Ethel L'5 w h: FAF t. l rim: we. tthfi . . .~ ' E-Ltt‘ Wreath 'l/SIC" m in" END” {1’ LLB HE J f + 1": _ . - wag-qr - , an.“ r, Linn "5 “H ' Q "3 “1 l fltl c- 3'“: ..-——'—"j I {h} (3 pts) Is the direction of the current induced in circuit 2 clockwise or counterclockwise? {1i ti'i (A it? letCH’rfl 13' & HA .' C: MKS "t f :3” t‘U—t-l: lg w a- _,_. Em gt s new s Harrie CC; 2- Eel-— 1 U :- rix-PL") V ‘2 rs Se gt > E52- Problem 2 [20 points} The figure shows a rectangular loop of height h = 2i} cm and width w : 40' cm, which is perpendicular to a uniform magnetic field H directed out of the page. The resistance of the loop is R = it) 5.1. At time t = l], the magnitude of the magnetic field starts to change according to Bit} = illI t1 + [15, where B is measured in tesla, and I is measured in seconds. T [fifitfi I‘fl‘l'! IT."L 31'- {a} {ti pts} Calculate the magnitude of the ernl" induced in the circuit at time t: Ll] s. ;' - I- If '1 Eli—HA Erhre {'5 etcti'lfin m. , III' — -_| r- - —_._”Lfitw , — tee-it “ma tgt a cattle-w '3 ' at ' h J ' '* ~ . t - lamb V IngllflbjIL :- D,;?- {in U..:.L1I D-lma r O (b) {T pts} Find the magnitude (3 pts) and the direction (4 pts) of the mom i induced in the loop at time t = 1.41] s. Indicate the direction en die figure. “3 . l V ' -— .i- ' r: U fl A. t — “I” F in 3" .___________-—--—--—""'_" PE "*1 J- :., _- 41 I 3n, ){acf . . ‘L-. (JV-'1 hi" G 7} "'.-I I i -' Do‘rclwma ' at; H” C MAE L J if' F J? El [ fiflCthJiJ f le. (c) [7' {its} Will the direction of the induced current sta}.r the same for all times aftert = fl"? (Answer yes or no, and explain}. Elli T " ' we now? Sui-'ch i=0 13H} turner; th moi n 1": GIT I .I. ' -- - ’+' t --o . I _ Iii-“3 G r .I' kid? TI '- ;-. :51" IE. .5. i 3. IL- " '5“: ' i' » LI . - i..- .- I, I p; [H 1‘ (all ("i {inc-«Al .( '= (r!) I Jill-{1 --'I F I I I -_.- "r. Ia M It .fi’.l...::_,2-J If: :- Inf-t C .1“ (IL. (:1 Err ( |,_ fit I_.r ‘- r- y I.‘ I ad "If Question 3 [10 points] In an LC circuit the switch is clcscd at r = fl and the current oscillates as shown. We ncw dcahlc [ha inductance L cfthc inductor and alsc dcuhlc the capacitancc C for thc capacitor. Circlc the ccrrcct answcrs to thc statcmcnts bclow. (a) (4 pts] Thc frcqucncy fife" ............ _._ x Dcuhlcs {K Dccrcascs by Half Stays the Same 1 x __ __._, _. s. -——- : -‘_* m L‘Jc ’ fl}:- fimfi-Mflc 1Nisalc '7 “*3 Ii “F " .: 1'. [c] (2.913;)..Ithriud T: Dcublcs Dccrcascs by Half Stays thc Samc k“ ~Hq____.....~a-F" i 'i c r {d} {4 I}sz The amplitude I a Hmsc‘iilatians: Dcuhlas Dccrcascs by Half Stays the Same Egg-us“ rcuscrruaii'dm jhjit': _ ” «J .- if = ‘x 7? ' ILL — '1 r. T '1' E” _@__F ,_ LEI _ [.— “| _L '3- m JET) .-- qEI' Li: 2 C b .. r 1 MINIMI. L. “H3 P L. C. r c “7' ' ': I ' «- ,I' " J-wrh] “L " Problem 3 [20 points] An alternating EMF generator Eff) : 5m Sinfindt} drives the series RLC circuit shew in the figure. Elm The EMF has an amplitude cf 5m = I ltillv'r with a frequencyr of}; = fiflI—lz. The values fer the resi stance, the capacitance, and the inductance are R : 3.0 52, C = 3:0 InF, and L = SJ] rnl-l. {a} [6 paints] Ccmpute the capacitive and inductive reactauce, KC and XL. I I f XL : at : let-"F'C : avast“ Email: : flail-51* xi : apt. e mi L = FTr--~-vv-tm'-—i’--H~ L, -. 2iT-{303"~‘7{~l1'ibh'5i'l ‘- I-gii": IL— (h) [4 points] Compute the impedance Z. ——-—___. .._... ._h L 2_ ,.. _ _- a z '2 + lEE‘I— U-‘Siufi ‘-‘ :,I'{ {4me < a. » .=:__a?~ [e] [S pctntsl Ccmpute the EMF 5(3) at time i = Lt} a. 51(th = rim-stamina” : rlev - 3m ( 2n 'éfla“ - 1.3) : 3 9*» (L Sim CW3” ) F" {3‘ {cl} [5 [mints] Compute the overall circuit phase ccnetant qt. ’5: ‘E”. K: _. ye ' x5 .U é r 133'; dri- _. Iii-ER” .J-i. “1 : 0.39"?" 1 at “we - [an .5 IL ---*— Vac». [3 2 Sr. rurrrrk‘l inn-“- -" "1 t. ._. Question 4 [10 points] The figure shows the inside of three capacitor plates, with electric fields perpendicular through them as shown. The rate of change of the electric field is also indicated. In each case, which way does the induced magnetic field — if an},r — point around the platesr.l Circle one each for clockwise (CW), counterclockwise (CCW), or no magnetic field {NONE}: 4) rm CE 91cm- d-’ Hiram - a c {ii/War r E. J I; {an ,13‘3. SD E") [M oi g 'f mm w w NONE 1"“ r1 "‘= ..._t.. E.) if: ‘ £9 'K ("i i" ". x: “:1. {'3} CW @ NONE G) ti/(‘Ir’n 5 I- -. Saul“- fill-TE!” ." .11.] lI-D fig {film i .4 _ ' i.- Etj ta *3} Question I [10 points] The figure below represents a snapshot of the velocity vectors of four protons near a wire carrying current i. The four velocities have the same magnitude; velocity V2 is directed out of the page. Protons l and 2 ate at the same distance from the wire, as are protons 3 and 4. Rank the protons according to the magnitudes of the magnetic forces on them due to current i, greatest first. ‘_l__ alt is; O G B 0%{' Of» V2 V1 E OLA I lgl " V4 % dQCl‘EO.§’€,.§ wig; all ’3 :3 if} 2: K j, PE 5} ha a U3 K “’3 i “w 7», ® Pg mfi ‘ Hat flog: “.33 it ‘-...r ammo...“s.m.u._...u,...wt.=.t Problem 1 [20 points] The figure below shows a cross section across a diameter of a copper pipe of inner radius a and outer radius b. The pipe carries a uniformly distributed current 1'9 into the page as indicated by the x’s in the figure. a) Using Ampere’s law find the magnetic field for r < a. “t “*1 P s (g anis fi/L‘-o""we£ ‘” Q as 't .s tam/{mam Mal/)5 gifiuoflj :2 Bylaw so , t; b) Find an expressmn for the current density, J, within the copper pipe. \ t: {a CO 0 = ,4 "" TbL'Tn} ‘ flexes?) c) Using Ampere’s law find that the magnetic field, B, for a < r < b. Make sure that #011302 ‘02)] your logic is clearly documented. [Hint the answer is B = 2 2 2m (b — a ) “’1 i p§.§{s 'r Egg-a41th dammedfi v 6136:» 9 8" i E E E l I I Question 2 [10 points] A square conducting loop is moved to the right 31 a constant speed Ivl relative to the shaded region which contains a uniform magnetic field pointed out of the page. The loop and region with magicfic field are shown at four different times in the drawings below where :4 > 13 > I; > n. For each time, indicate whether the induced current flows clockwise, counter clockwise, or is zero in the loop. I} I: D i L i :2 O I ‘ f3 ' r m 5w ‘2' {341C f~§QE§Li§§ \ fisgwbg g 1 LL CiC, a v t3 @ {405 we: ah , é J ME A were 5 r 2 WWW Problem 2 [20 points] A rod oflengthL =10 cm is forced to move at a constant speed M to the right of4 m 5'1 along a pair of conducting rails. The rod has a resistance of 0.3 Q while the rails and connecting strip can be assumed to have no resistance. The apparatus, which forms a loop, lies in a non-uniform magnetic field B that is constant in time and points out of the page everywhere. The magnitude of the magnetic field is given by LB] = 5.0 x 10'3 y2 T when y is measured in meters (a) What is the magnitude of the induced ENIF in the loop? / 8 l = L I”? w: = (Hot d 5 (5’25 iffy/Lt J 3 .‘ L w — L .5‘. ya '1’“ P "_‘ ,F E _/w . _ 4 =7 “a. ' w—I- ., 540’ Jet/ZNHALy : 5‘30 mz'flflZ 5]- 3” m .y C) m C} H "E 7‘ — aifll 3‘ {6 E13“ g MIX E - 3’. J. 3 ’7 " 3 “Mt”"'”“ “'1 .L '/0 L ‘ L V / E f 9 wit" :2? i 0‘4 3 m i , 7 3 3:2 ._ \ i " ‘ V :2 '2‘ /D 5;; 1’0.in ‘ if S *' a (b) What are the magnitude and direction (clockwise, counter clockwise or no current if the magnitude is zero) of the current induced in the loop? re g c. 6? ' {o i/ r i ‘ : _.._-—-v 5; _--—--—---——-.— , 2 2 t ‘ K e 253 “ 2 ' \ 1,“N v 1:3 i @ ti“! C #95? 313/3 fa a i’agflg‘: 3»: E =‘ 5 (06km {2.5 g? L and Question 3 {10 points] + 0000 + 0.00 {1) (2) (3) Examine the three circuits above. The resistors, labeled or not, all have the same resistance. The inductors in all three circuits are the same, as are all three batteries. At the instant the switch is closed; (a) [4 pts.] Rank the circuits in order of the amount of current flowing through the 9. battery, using the language 1<2=3, 2>3>1. CL .2. 0 R z 222 , £2 1 3’3 I f g . . fl _._ [Q + “F If” :2: X f‘ '2:- .:; R [,3 >- L 3 ,Q {1 After a time very long compared to the inductive time constant; (1)) [3 pts.) Rank the circuits in order of the current flowing in the resistor marked R. 24% Ctr/feta" 756%}; fat-C75,“! 5‘1355’3}? ’a t {73 fig .25 m1? raise I) 53% fie (c) [3 pts.] Rank the circuits in terms of the magnetic energy now stored in the inductor. (ta rflrfi’eL 35:7 5 a? I: K13; :' 29,245 a - ’2‘?“ er flu fie .J i5 Question 4 [10 points] The figure below shows the oscillating emf and current in two different simple circuits driven by an AC generator with an emf E = Em sin((cdt). In each of the two circuits there is only one circuit element (other than the generator) — either a resistor, a capacitor, or an inductor. (i) The circuit element in circuit (a) is a (circle the right answer): @ Capacitor Inductor C‘ M f; Lmi—«i (ii) The circuit element in circuit (b) is a (circle the right answer): Resistor / Inductor Probiem 3 [20 points} In an oscillating LC circuit in which C = 4.00 uF, the maximum potential difference across the capacitor during the oscillations is 1.50 V, and the maximum cunent through the inductor is 50.0 111A. (2) (a) Calculate the inductance L. F“ . ( 5’ E r ‘ g : 45w; 41} VLC5) 2 Va CO§(/Ug.£) } L(} C j gain; 3.. Cvflte} 1- {fl/a (33355455) 2 Q {OSK‘VcéJ @mt‘arvmiwdlr {if gage“??? '3 a _/ at LL72 a — (I, W? C’ goal ”' 2— “e Erma); £9” a / £2 / (CV l w ——H _ fl ___ G '9 A 9 C 22 “' “f? z ’77- (b) Calculate the fi'equency f of the oscillations. C. (I; a 2 “r 2 Jr“ P “fa-{n g 2 “c ”" 2?? (ff-{0" F ' Q'Y V) 2 WW {50404 f? j l” I it =2 2:; '» gee 147’ g; F ...
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