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1e3apr2003solutions - Physics 1E03 Version 1 Day Class Name...

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Unformatted text preview: Physics 1E03 Version 1 Day Class Name: 40 l -. ‘ Mg; Duration of Exam: 3 hours Student Number: Instructors: Dr. Venus (section 01) Dr. McKay (sections 02 85 03) Dr. Kudian (section 04) Dr. Harris [section [15) Instructor: Lecture Section: lVicMaster University Final Examination April 2003 This examination paper includes 17 pages and 26 questions. You are responsible for ensuring that your copy of the paper is complete. Bring any discrepancy to the attention of your invigilator. Special Instructions: a Only the McMaster standard calculator may be used. a A sheet. of formulae is attached to the end of this exam paper. Do not write solutions on this formula sheet. a. Answer all questions directly on this examination paper in the spaces provided. In part A [multiple choice) only the answer is marked. In part B (problems) you must provide a solution showing clearly how the correct answer was obtained to receive full marks. Your solutions may be continued on the blank page at the end if you indicate clearly where the continuation may be found. 0 Each question in part A is worth 2 marks, and each question in part B is worth 3 marks. 0 This Paper must be returned with your answers. PLEASE DO NOT WRITE BELOW THIS LINE 1-18 19 20 21 22 23 24 25 26 Total I (36) A {3) (3‘f (3) {3) (3) (3) (3) (3) (60) r l physics 1E(1.‘5_ Page 2 of 1? pages Part A (multiple choice): Print the letter corresponding to the most nearly correct answer in the box. Each correct answer is worth 2 marks. I. An uncharged ctmducting sphere is brought close to a small insulating sphere with charge +Q. ’l‘lie corrducting sphere (A) experiences no net force from the insulating sphere. (B) experiences an attractive force due to the insulating sphere, which gets stronger as the spheres gel. closer. (C) is repelled by the insulating sphere until they touch, after which there is no force between then}. (D) has the same electric potential as the insulating sphere. answer 2. A tetrahedron is made of four equivalent equilateral triangles, as illustrated. A charge Q is placed at vertex :5: of the tetrahedron. The electric flux through face abc Q IS 3. Which of the following statements is FALSE for a conductor in electrostatic equilibrium? (A) The electric field E just outside is perpendicular to the surface. (B) (E! just outside decreases with decreasing radius of curvature. (C) The net electric flux through a closed surface inside the conductor is always zero. (D) The electric potential difference between two points on the surface does not depend on the distance between the points. answrar i continued on next page. U1 l")ll_\f§-§lt'H ll‘illli Point A is at the centre of a square with charges at each corner, as illustrated. Al. point A, A) Both the electric field and electric potential are zero. 13] Neither the electric field nor the electric potential is zero. C) The electric field is zero, the electric potential is not zero. D) The electric potential is zero, the electric field is not zero‘ ( ( ( ( eu'aswer i For the three points a, b, and (1 shown in a uniform electric field E, which of points a and cl and so on.) the following statements is true? (VaC means the potential difference between _"b.— l Page 3 ol' 1? pagen + _. q.I____. .___. .___, q A' _ q; ------------------- of q (A) iVm’Jl > ivorfl [Bl E‘v’iml > lVacl (Cl lVabl : ll/arl (D) [Van = 0 answer C Two spheres of equal radius R and separatimi D > R hold charges +Q and —Q. The capacitance of the pair ol' spheres (A) depends upon R, D and Q. (B) depends upon R and D. l I-l { l C 1 depends upon R and Q. J depends upon D and Q. answer B continued on next page... Physics ll‘lllil _ __ Page -1 of 1? pages The ends of a coil of wire are attached to a power supply so that a current. I [lows through the coil. As the current is increased at a constant rate, (A) the inductance of the coil increases. (B) the inductance of the coil decreases. (C) the emf generated by the coil increases. (D) the emf generated by the coil decreases. [3 E] None of the above. [finswer [U . A factory uses IUUMW of electrical power, which is supplied by a power station through transniissimi cables with a total resistance of 5.0 Q. The voltage at the factory is 200 kV. How large is the power loss in the cables? (A) 1.25 MW. I F MW : goo/7L (13) 8 x109w. ’ 2m) k v (C) 1.0 MW. (D) 100 Mw. 2 Z- R: /1<’00€/O W answer 4 When the switch is closed, the current through the resistors in the figure changes with a time constant equal to / R 'u s {X _" RC: 5 (, C ._ answer 1 '1 E . continued on next page... Physics llfltlli Page 5 ol' 1'? pages 10. A particle with charge q moving in a magnetic field B, with no other fields present. will (A) Iriaintain constant kinetic energy and speed. /I (15) experience an inerez-ise in electric potential. 7’ (C) always move in :1 circular path. X (D) accelerate iii a direction parallel to the lield. \Z answer ii 11. An electron with velocity v : 2.0 x 10"i im/s enters a region with electric field E = 2UUjV/1‘n. Because there is also a magnetic field present, the electron follows a straight—line path at constant velocity. The magnetic field could he FF.) —-:) (A)B=(—1x104k)'r 62% B + E : (.3 (8)13 : (4 >< 108 k) T (C) B :{1x10—4jj’1‘ 4‘) V (D)B=(1xio 4km" ”U”? )4. g = _ 200: 1; 12. A long} straight, solid cylindrical wire of radius a carries current I, distributed uniformlyr across the cross-section of the wire. Which graph below best represents the magnitude B of the magnetic field: as a function of the distance T" from the central axis of the wire? (A) (B) (C) (D) :I.11.~<\\"t‘1' a. R_7zr1:l‘ rfot continued on llr'.\'l page... Physics lL‘HlIi . ._ _ l Ag: (i (1! l7} 1)}I§_‘;['H 13. A thin conducting ring a lies directly below a coil b. When the switch is I: closed I _‘:'/'—"/’\) 1111?, o. is pulled upwards towards I). O ling o. is pushed downwards away from b. l l l l [ ’) ring a. experiences no not magnetic force. (D) ring a moves horizontally to the right. >¢ E Z Asp/(r WW ' fl; ' ”r. / I’IIL- \- ‘M-Wivx O. ((49% Lfivz’s Lag") ljna . hi 9 may (/wa-‘é 14. The switch 5' is closed at time t = 0. After a long time has passed, and the circuit has reached a steady state, what is the current through the inductor? 15. The displacement of points on a string is given (in SI units) by Mm, r) = (0.005) sin(3{}{)?rt) sine * 20m) . This represents: £1. wave travelling to the right on the x axis. _ £1. wave travelling to the left on the x axis. ’1} Bl C] E]. standing wave. D) none of the above. :ii'iswer ('tJIllllllI('(l on nr-xr page... l’hysitis l-Eilii .. _. Page T of 17 pages 16. A pair of slits separated by 0.2411111: is illuminated by light containing two wavelengths, Al _— 418011111 and A2 : 96011111. What. is the smallest non—zero angle at which there is a maximum in the interim-1mm pattern for both w;‘welengths at the same location?- 1’1 , 0.002 radian ) 0.00]. degree _ _ ) 0.001 radian 0 r” 1 d W 9 r M ‘ >l ' m L >‘ L l 0.004 radian [. (B (C (o l _P‘kc/L: wit—L) M1,: _ . 1 El! IS t\-'(-.‘I' D t 460““ _ )4 €60M‘m ___—l 7;) 9V6: Jfirazfzmm- I in .5) 9,5,9: @,004 {1:9 17. When a parallel beam of light is incident on a narrow slit, the central maximum of the difiraetion pattern on a distant. screen is 1 cm wide. To increase this width to 2 cm, we could: ( l (B) reduce the wavelength of the light by half. X (C) reduce the width of the slit by half. I/ (D) double the width of the slit, >1 Tnswer C. 18. A piano tuner hears 11 beats in 5 seconds when she compares the “A” note on a piano to a standard 440 Hr. tone. By what fraction should she change the tension on the piano string so that it will vibrate at 440 Hz? continued on lli'Xl [mar-___ 7 (PO 19. Physics USU-'5 _ _. . Page 8 ol l? page.» .l’art. B (problems): Write a clear solution showing how your answer was obtained. Belch problem is worth 3 marks. The electric field inside a. thick charged insulating 111:1l.eri:1l is in the 2; direction, and its strength varies with position according to E —- (a + bx) R, with (i. : BOON/C and b : ”1000 NC} IIn '1. Using Gauss’s Law" calculate the charge inside a 1~crn cube with one corner at the origin, and edges along the 3; go: and z axes. --—l ii \a. \l ‘Il I Q—" + I04 2 :5 Q 14 f \../ p4 ’\ “a. X. 9 D 3 \_/ D i ‘5: D "X o m if; ‘5 m) K 31 I; (B answer: i 4.43M0'M C {T(Jlll.lllllt.'tl on waI page... Viinit'H li‘llii ._ ._ Page SJ ul' 1? pagt‘s 20. Charges +q, —3q, and +291 are placed at three corners of a. square of Side + q . -‘_ . .—-—I~=I'.- x = [1.300111 as shown. Calculate how much work IS dm‘ie by an external force ;a _ b in moving the charge ~—q I'i‘mii its original position a to the empty corner of the Hqueu‘u. 1’). Take 4!; ; ZUUpC. Indicate whether tilt: antiwar is positive 01' mega.— 5'; [.ivu. a x a f . m. “ 3%" + 2g; 1| H *4: 7‘5" ‘ Vb m 0. HQ ' ”F U" I I xii) . N ‘1‘ \./ iN N 3°/ EU“ I 1 C3 1 L ,4“ Y“ + \/ \/(\/ 1'! 9 \J M\ A H ansWizr 0m T continued 011 11i',\'[ pagr... Physit's llCllii | n"! Page lll of 17 pa. 21. A capacitor Cl -1- 4.0;iF is connected to a, l2-volt battery and allowed to charge up completely, The battery is then removed and C1 is connected to an initially uncharged capacitor C2 = 6.0;iF‘. What is the, final charge 12 V and voltage on C] e-tftcr tlic capeujitrgirs hewo i'oeuilmt'l (zt'iiiilibrium? _ C.‘ l 2 i-Liiswoi‘ l4) “wt-6v timiliimml um III'XI. Inigo... rl' 105- 3}, 22. Tum/{Hm (W: T5 -— I, — 1'1: (54 I1}1}.'Hi(-5 iii-[H _. _. _ _ _ _ ljélgt’ ll :in 1T |IF1;_’,'I‘.H The (IllI‘I‘t’Ilt I] through the 4.0052 resistor is 2.50A, and the current. {2 through the resistor R. is 1.00 A. Calculate the resistance R. 9 11/): Q14 43CI4+MMB =97, +?-w/4 r x 2" I; I '-.. mutinuvd on mm I):l.'_"l'.. i’llvHieH ll‘lllii l’ftgn 12 ol lT pages 23. A long straight horizontal wire rests on a. table, in a uniform Iiiagnetio x x x XB X x lielrl B 013.5 T', directed into the page on the diagram. If the mews per unit I length of the wire is (1030 kg/m. detc'rririine the magnitude and direction. of the minimum current that will cause the wire to lift off the table. X L 84 MW a (t % filM \“fi <1tmli11umlon llE'Xf page. Physim 11303 i’ngt‘ .133 (:i' [T JieLguH 24. A long, win: carrying current I : 3.0A is straight except for a single circular 100]) of radius R = 0.040111. Calculate the Irmgnitudc of the magnetic field at the ("ranro of the loop, and give its direc— tirm. [07x7 (fit? ‘- T3, -‘-‘ i -. emf r- 1/5 P _S LA“ _:> __ 4) A R:f:l—Lffl ) P=R 14/7 FL 2’ ”:3. _ :\ 312/40}! 1.111% JOJD/W ElIISWGI‘ (ml/#7” I'Unliillimi mi m-xl lmgv. [’h}:§:it's 11303 Page lil ui' IT’ linger; 25. Two radio antenneu“. located 011 the 3: axis at :1: : —5.0111, and _1.- :1: : +5.flni. transmit. in phase with equal an'iplitudes at a wavelength )5 = 25.0111. Each anti-3111121, transrnitting alone, would produce an ampli— tude Uf‘iiLU ,rr\-"'fni Eli. a distant receiver on the +3: axis. Calculate the phase .. 5 m diffigrence between the two signals. and the amplitude of the combined sig— nal. at the receiver when both antennae are transmitting. A: floawz J 5.: agape/)1. O. 8 7L rut/«.3 h' H O .. 2?: gr .3 1/Ly’ _/.._ >‘ 2.7" :2 /¥/0 : 0’40 570651144 ...._.—-—— ' answer ' effi W", 10.2 : )Q’K I" {J JR. (tuntinuml nan III‘XI. page... l’llyfilt'H llflll'i .. _ Pélgt‘ lit {ll' l7 Iguana; 26. Two small lt‘nldspeakcrs are mounted on a wall, with one speaker 48 cm \rcrticalljy {-Llflfwe the other. A microphone is placed 55 cm directly in front of the lower Hpeakcr (at the same height as the lower Sl'ieaker). The two speakers :ch driven in phase [row a variable—frequency source. If the speed 48 cm \I of sound in air is 340 m/s, find the lower-".1. frequency at which there is g a. minimum in the sound intensity at the microphone due to destructive interferon“). 5 —§s $4—— 55 cm —+>{:L —% ElIISWUI‘ l 744 We ")1; -_ _.r 11.. continued on hex: page... ...
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