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finalexamsolutions - Physics 2102, Final Exam, Spring 2011...

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Unformatted text preview: Physics 2102, Final Exam, Spring 2011 May 11, 2011 Name: Section: Instructor: - Please be sure to write (print) your name and section above. 0 Please turn OFF your cell phone and MP3 player! 0 Feel free to detach, use, and keep the formula sheet. No other reference material is allowed during the exam. 0 You may use either scientific or graphing calculator, but not the calculator in your phone. a GOOD LUCK! Notice that the points in the exam add up to 150 points - since the final exam is worth 150 points of the 375 points available SHOW WORK on all problems that are NOT multiple choice. Question 1 (14 pts) The figure shows two electric charges of equal magnitude q and opposite Sign, on the x—aXis at coordinates tea. The point P is on the y—axis, at a distance d from the origin. (a) (5 pts) What is the magnitude of the electric field at the point P? (k = 1/47r60) e 2kq/(a2 + a?) 2kqd/(a2 + d2)3/2 fl/(ag + CW/2 Ex: _ 2ku View : r2 £2 a. r “23% (b) (3 pts) What is the direction of the electric field at point P? m.-.‘ w‘ws—nwflw 0 #4 j T i W (C) (3 pts) What is the electric potential at point P? [/02 qu/x/ a2 + d2 2kqd/(a2 -{- d2) 2kqa/(a2 + 052) f I; ,. j" "‘31: g 3» w g:- (:3 if f (d) (3 pts) What is the Sign of the work done by the electric field if a third, positive, charge Q is moved from point P to the origin? /‘\ 0 Positive Negative It depends on the numerical values. ‘- i viii-iii; w (it) «a m 52 t _ 52 [V i W) I C) I; H Question 2 (12 pts) Initially, a single resistor R1 is wired to an ideal battery with emf E. Then resistor R2 is added in parallel. Circle the correct answers below. fl" (a) (3 pts} Is the potential diflerence across R1 now more than, less than, or he same as previously? More Less {2 1 f2 . a; z 5 2 mm Maw law—4 _: p owfil F21 I; <3 More Less ; KNEW M// y ; 3: lift“ “.3: 91m I if” 8d 1 R} Q} to... (d) (3 pts) 15 the total current through the battery more than, less than1 or equal to the current through the battery before R2 was added? Less Equal “ '6’ i , (J {1 i} } gifts/“.1 A A! m} 5)} “r i»: r f_ g i .3 ,, T, *w gawk/3W at}; My» ’ “I? E «Jiwire «RA I I; ! "HM-'2' \J Question 3 (14 pts) Two long straight wires pierce the plane of the paper at vertices of an equilateral triangle as shown below. They each carry 2A, out of the paper. (a) (3 pte) What’s the direction of the magnetic field at point P? l,” , B I O +— —> Out of the page Into the page kw (b) {5 pts) What’s the magnitude of the magnetic field at point P? B : 0 2 x 10-52“ 1.7 x 107517 Q 0.87 x 10-5T wflwwx'flfl 1 \ :3 Mia,“ :1 m5 ’8: 2;: ref Law to ix tan/10’ eff/4M (4,7331 1,17an (e) [3 pts) What is the direction of the force of the ieft wire on the right wire? F:O 4> i T w; {.2 g fiClLlL fig—Lil 0.0—1. l1 .' (d) (3 pts) What is the magnitude of the force per unit length of the left wire on the right wire? F = 0 10"5 N/m x 10%;th 4 x 10’5 N/m K J _¥ m Ia I’rzimfflz’a x F: Gait : W 1 N Y) . (A Tl 21> n M {3 7?. §‘\~. Question 4 (9 pts) The figure shows two circuits in which a conducting bar is slid at the same speed 1: through the same uniform magnetic field and along a U—shaped wire. The parallei lengths of the Wire are separated by 2L in circuit 1 and by L in circuit 2. The current induced in circuit 1 is counterclockwise. gig) I B 22." ’U" 30 inmflijL'Lé—Q’ Wt“ &J_ P l P :5) V‘ L‘ MC D (I’llfijg—(‘prm Illa mil/l Frog'wa 52 'HZ; ‘ “Mr.” Ufggfiwg Mi” 2” y I {it arm 9‘ r; g] z A: a at) fifljffiaufm 73.1, {airbag} i2. #1 Ou‘i' 9:0; Hog So Ubu‘jcorm 1/ (b) (3 pts) What’s the direction of the current induced in circuit 2? //r, llll “flflm‘NN Clockwise Counterclockwise If; Rightward Leftward LthMkLmfi Mm w A I“ “W!” C \ 5- 5W 3,] Q ELM; a“ t our/«Art 4.5m air/Ii; m wig, v r v a; (c) (3 pts) Is the emf induced in circuit 1 larger than, smaller than7 or the same as that in circuit 2? (2;?) Smaller The same W9 Z, £l>§2 Question 5 (9 pts) The figure shows a paraHCI—platc capacitor and the current in the connecting wires that is discharging the capacitor. : 3““ 67 - w, i e = wJFQkJ¢Q Emmi, £12 he it“: fine 3* i“ j. a (a) (3 pts) What is the direction of the electric field 11:," between the plates? M. E 2 0 1/ —> ) 4— into the page Out of the page (b) (3 pts) Is the magnitude of the electric field E‘ increasing, decreasing, or constant? B = 0 Increasing (/Decreasm Constant ; \w I‘M/“y” ‘ “ Mme < ‘ <1 Om fig/bgtsiLQF IS 0 and?) d5) Jiéié’itflf, 4:590, (c) (3 pts) What is the direction of the magnetic field E? at point P? B : 0 —> <— into the page Out of the page flat/V/ (a P Di'sftaaapmfii’ Wrrx‘ft é—‘I‘M £4 Question 6 (6 pts) In the figure, a beam of unpola’m'zed light with intensity IQ is sent into a system of two polarizing sheets whose polarizing directions make angles of 61 2 62 2 30° with the éirection of the y axis, as shown in the figure. (a) (3 pts) What is the intensity transmitted through the first sheet? ./ } IO 10/2 / 100052800) Igcos2(60°) ‘ .\ // -x__._r— Mtge mm is eatsgwr‘fieef’ (b) (3 pts) What is the intensity transmitted through the first two sheets? 0 Io C034 30“ 100034 60° 106082 300 2 100032 600 2 ] :\ f] kfl/ 9 s g 9 z” r’ i / , i /// E {I " l ,i, f _ 14? fi¢9;§.;;mj ,_/,./"I’- i [x (I; mt?!“ if“ 1-; " r - (é //'/ r 51/ E w}? fl f? I , r Hwy; Essw'flfe; w Problem 1 (22 pts) As shown in the figure, a solid insulating sphere of radius a is concentric with a spherical conducting shell of inner radius 5 = 2a and outer radius c = 2.50.1. The sphere has a net charge (1 uniformly dis— tributed in its volume; the shell has a net charge —q. Answer the following questions in terms of q,a,b,r and constants such as 1T, 69 or k : 1/47reo. (a) (4 pts) Sketch in the axes shown the magni— tude of the electric field E(r) as a function of radial distance r. (Hint: answer this part after you have done the other parts of this problem) (b) (6 pts) What is the magnitude of the electric field within the insulating sphere7 at a distance r < a? f—v‘p “b 5mg? Zea.) 3 3D éE-éjii E we?" origin? A9940} U342”)? (gaging? ', / a: : "m‘v firm ’2 L.» .J gangs f Sea} ! gm 3,. 6/5 ____ 8 36 E”. sis—£1? / m in c, itfirrfla w p (d) (6 pts) What is the charge on the inner surface of the shell, at r = b? eeaesndaneflihfiflfi (gar; 6/51; s 23 :2 T mi 7g 0 5 “Wm—w! if E’ng is}: (c) (6 pts) What is the magnitude of the electric field at a point at a distance r, with a < r < b from the “ii/5Q w . __ F ram-{\- k-, m m C? «.- é-ric é? W/ £2 \ {WWI gm"; -_‘_“ a m" m fi‘ inn-ax gm W. {2* 7L, .1‘ 2 I {to flag a ctargg’ Problem 2 (21 pts) The figure shows an inductor connected to a battery and two resistors through a switch that is initiaily open. The battery has an emf of 5V, and the resistors have a resistance R = 29 each. The inductor has L 2 3.0 mH, and is an ideal solenoid with 100 turns/cm. Initially, there is no current through the inductor. 2 32,. (a) (7 pts) At t I 0, the switch is closed. What is the current through the battery immediately after the switch is closed? \ > 56 hi 5: so, r-r cut through , fist 75:0} [member does a W ‘5 1?" i 4: Wm" 39 l :33?» is?) i 2: “13:5” 2-" ‘5: ” a» Mrs“ E rm immi (b) (9 pts) After a iong time has elapsed, the current through the inductor is constant. What is the magnetic field in the inductor at this time? ,. , . r . Ash; if 3.: so) Loxff‘téufif 5:352: 5:21 i” Q0131 ate / y m ‘ f it ear-ass if; daisies a Iii: si‘s‘im % ‘5’; b "7 Egg” 3”” e; ' “9 ’1" i: {i “in, «mm 6W; 3W F MD h‘z “PM, a 3 i9 R 5} r:- iih) } 9 WE >45. 455: 2 ~13- """'i :3, F [D ,3 j if a i —.2 (c) (5 pts) After a long time has elapsed, the switch is opened again. How much total energy is dissipated by each resistor from the time the switch is opened again, until the current through the inductor is again equal to zero? (Hint: do not attempt to solve this problem using a power calculation - we ask for total energy). ‘ I g If 4‘ ‘ a as? g €142,ng stored to tnflvlatdi'fl 1‘“ ma saw fiery-WW6?! éi 2 G’- s “3 i: ( > i _ ,1 i P“ a $5; 2 2 gm??? dissipajifli $7,? resistor“ 1‘5; 4.; 3‘.” Problem 3 (22 pts) In the figure, R : 14.09, C’ = 6.00pF, and L = 54.0mH, and the ideal battery has an emf of 35V. The switch is kept at a for a long time and then thrown to position b. (a) (6 pts) What is the charge on the capacitor immediately before the switch is flipped to b? 4 W’s ~,é: F is . a Q . I f0 C (b) (4 pts) What is the angular frequency of the electromagnetic oscillations? l i "WM—MW WWW,“me :1 (l: g {3293 (9541’; E: U z u l i j Z _" girl ‘5‘) LMQK :: : an" 3 E “5 2M9 “9 2i): 'iugfi K53 = 9,35 A (d) (6 pts) If the switch is thrown to b at t = 0, what is the earliest time when all the energy is stored as magnetic energy in the inductor? 10 Problem 4 (21 pts) A green beam of coherent light with wavelength of 54011111 is incident on a plane with two slits a distance 0.2mm apart1 producing an interference pattern on a screen at a distance of 900m, with its center aligned with the middle point between the slits. Hint: you can use the “small angle approximation“: sin (9 a tan :9 a: B. (a) (9 pts) At what vertical distance from the center will the pattern have the second dark fringe? Draw a diagram explaining your answer. nun“ I E ' “-5 NHL-:fi‘h : / \ 9&9»: '4', has, if. A > 2:”! M W d S Q flit} if \ I) T ’<" “if”: i in t“ .37; r: \ 4‘ f2} elm 0:2; is it} ~ east? is w. e r L ‘ »’ ,Lj’ d’élrlé U4 =0 {gry'qiii Eu. —; __ 3/? dim-Tidy WA "E El w 535'}; .| _ 57, fl {La—Aww—hmnfiuu _ _/ z a tax 05 amid L 2 [3‘ ~22 I) :13 f] M “(i—PW“ 7 p _ i , Q i “ i” F3 -‘ : 3 5.0, f Wtsem M" 3W 4H“ (b) [5 pts) What is the path length dilference of the waves traveling from each Slit to the point you found in (a)? A1, 2 @43ng = 3/2 h 0 A/2 /\ \w/ (c) (7 pts) If the incident beam is an infrared beam with wavelength of 1064 nm, wiil the distance you calculated in (a) b arger, mallet or the same? Explain your answer. .7". x J} m i _ ‘ bl : i“ i“ $0 9’?! 3x lI/i ems flail", "50 5W ” “f w <l 2 a; J ’ <7" 11 ...
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finalexamsolutions - Physics 2102, Final Exam, Spring 2011...

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