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NYB Exam May 2005 with answers

NYB Exam May 2005 with answers - 311)[email protected]flfloge Emotes...

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Unformatted text preview: 311)an @oflfloge Emotes Efleclriefisy and! mam TOTAL MARKS: 100 May 20, 2005 TIME: 3 HOURS 9:30 a.m. to 12:30 pm. This examination is divided into two parts: PART I (30%) — Answer only six (6) out of the seven questions or problems in this section. Each question or problem is worth 5 %. PART II (70%) — Solve only seven (7) out of the eight problems in this section. Each problem is worth -10 %. Instructions: 1. Ifyou answer more than 6 questions in Part I, or solve more than 7 problems in Part 1], indicate which one(s) you want omitted. 2. Formulas and constants are given on the last page of this exam. Expressions not given on this last page should be derived. 3. Calculators are allowed. 4. You may answer two questions on the same page. However, solve every problem on a different page. . Write only on the light-hand pages of your booklet. Use the left-hand pages for your rough work. Show all your work, including diagrams, in the exam booklet. Give all numerical answers to a three-digit precision. . Do not tear any page(s) fiom the examination booklet. Ifyou use more than one booklet, number your booklet. When you hand in your examination, place booklet #2, 3, etc., inside booklet #1. 10. Write your name and the name of your teacher on each booklet. Physics NYB Final Exam 1’ May 20, 2005 PART 1 (30%) — Answer only six (6) out of the seven questions or problems in this section. 1. A bar magnet is dropped vertically downward and falls through a conducting loop, as shown in Figure 1. During the magnets entire motion, which of the following statement(s) is correct? Assume that you are looking downward into the loop. (a) The current in the loop always flows in a clockwise direction. (b) The current in the loop always flows in a counterclockwise direction. (c) The current in the loop flows first in a clockwise, then in a counterclockwise direction. (d) The current in the loop flows first in a counterclockwise, then in a clockw1se direction. Figure 1 (e) No current flows in the loop because both ends of the magnet move through the loop. 2. A circular coil has a cross sectional area lof 0.200 m2 and a resistance of 2.00 9. A uniform magnetic field directed perpendicular to the plane of the coil is turned on. Ifthe field through the coil increases linearly from zero to 1.50 T in 50 ms, determine (a) the magnitude of the induced emf in the coil while the field is changing, and (b) the induced current in the coil while the field is changing. 3. Draw a diagram showing two long wires, wire 1 and wire 2, separated by a certain distance d and carrying currents in the same direction. Determine whether the two wires attract or repel each other. Your diagram should include the appropriate magnetic field and force vectors to illustrate your answer. 4. If the net flux through a gaussian surface is zero, which of the following statements are true? (Note that more than one statement may be true.) (3.) There are no charges inside the surface. (b) The net charge inside the surface is zero. ‘ (c) The electric field is zero everywhere on the surface. (d) The number of electric field lines entering the surface equals the-number leaving the surface. (e) E - a2 = 0 everywhere on the surface. 5. (a) Reproduce Figure 2 in your exam booklet and add in this diagram a voltmeter connected so as to measure the potential difference across R}. (b) What should be the resistance of an ideal voltmeter? Why? Explain what problem(s) may arise if the voltmeter‘s resistance is not close to this value. Physics NYB Final Exam I May 20, 2005 . 3 6. (a) Suppose that the electric field is zero throughout some regiou of space. Can you conclude that the potential is also zero in this region? Explain. - (b) Suppose that the potential is zero throughout some region of space. Can you conclude that the electric field is also zero in this region? Explain. 7. Figure 3 represents three rectangular loops in a magnetic field E. The figure shows an edge View of each loop, that is, the plane of each loop is perpendicular to the plane of the page. The three loops each carry the same current I, with directions as shown in the figure, and have equal areas A. (a) Find the net force on each loop. (b) Find the magnitude of the net torque on each loop. (c) In each case determine whether the torque would rotate the loop clockwise or counterclockwise. Physics NYE Final Exam / May 20, 2005 4 PART E (70%) - Solve only seven (7) out of the eight problems in this section. 8.A hollow insulating sphere has a uniform charge density p. Its inner and outer radii are a and b, respectively. See Figure 4. Find expressions for the magnitude of the electric field in the regions (a)r<a, (b)a<r<b,and (c)r>b. 9.A uniform magnetic field of magnitude 1.50 x 10—3T is directed along the positive 3: axis. A positron (of charge +3, and same mass as an electron) moving with a speed of 5.00 x106 m/s enters the field along a direction that makes an angle of 850° with the x axis. See Figure 5. The motion of the particle is expected to he a helix. Calculate (a) the radius r of the trajectory, (b) the time it takes the positron to make one revolution, and (b) the pitch p. 10.(a) In the circuit shown in Figure 6, find the a C 1332-001X 6' currents I; and 12 and the emf 6‘]. State the directions of currents II, I2, and 13. R4=12.OQ (b) Prove, numerically, that the total power produced in the circuit equals the total power consumed. Figure 6 11. In the circuit shown in Figure 7, R1 = 6.00 k9, R2 = 18.0 kg, R3 = 12.0 kg, 8 = 12.0 V, and C = 2.00 pF. Suppose that the switch has been closed for a time sufficiently long for the capacitor to become fully charged. (a) Find the steady—state current through each of the three resistors, (b) Find the charge on the capacitor. Now, at t= 0, the switch is opened. (c) Find the time at which the charge on the capacitor is one- fiflh Of its original value. Figure 7 ((1) Find the current through the 12.0-kQ resistor (R3) at the same time as that of Part (0). Physics NYB Final Exam / May 20, 2005 5 12. Two long wires a distance d apart carry equal antiparallel currents I, as shown in Figure 8. Show that E at point P, which is equidistant fiom the T J’ wires is given by _‘ .. P B = 2t;oId 2 i d x fi(4}i d-d ) ‘""”"—___.R‘_‘___"“4 In your derivation, be sure to show every step i clearly. Figure 8 13. Consider a uniformly charged disk of radius a and charge per unit area (3. Assume that the disk is perpendicular to the xvaxis (on the y—z—plane) and that its center is at x = 0. (a) Prove that the electric potential at a point P located on the axis of the disk and at a distance x from the center of the disk is given by V = Zukecr N 3c2 + a2 — it]. Show a diagram and clearly explain every step in your derivation. (b) Use the result of Part (a! to find an expression for the magnitude of the electric field along the axis of the disk, a distance x fiom its center. What is the direction of the electric field? How do you know? 14. Capacitors C1 = 6.00 uF and C2 = 2.00 uF are first charged by connecting them in parallel across a 250—V battery. The capacitors are then disconnected from the battery and hem each other. They are then connected positive plate to negative plate and negative plate to positive plate, as shown in Figure 9. Calculate the resulting charge on each capacitor alter the switches are closed. . G Figgre 9 rilfi _ 51 d (:1 cg" '— ——-- ++++ bLfl/J . $2 15. (a) Consider a circular wire loop of radius R located in the y—z—plane and carrying a steady current I, as shown in Figure 10. Derive an expression for the magnitude and direction of the magnetic field at an axial point P a distance x from the center of the loop. Be sure to show a vector diagram to explain your work. I Z (b) Use the expression you found in Part (a) to determine the magnetic field (magnitude and direction) at the center of the coil, that is, at x = 0. Physics NYE Final Exam 1 May 20, 2005 6 Aux-m a; Mn and PM u. M Em mum M. 2005 (d) (a) |s|=6.00V; (b)I=3.00A The two wires attract each other. 03) 311101) . (a) The voltmeter must be connected in parallel across R1. (13) The resistance of a voltmeter should be very high. Ideally, it should be infinite, so that no current passes through the voltmeter. U‘PP’P!‘ 6. (a) No. For example, consider the case where four positive point charges, of the same magnitude, are at the corners of a square. The electric field at the center of the square is zero; however, the electric potential IS not. (b) No. For example, consider the case of two point charges of equal magnitude but opposite signs. The electric potential at the midpoint between the two charges IS zero; however, the electric field is not. 7. (a) The net force on any current loop carrying current in a magnetic field is zero. (b) The magnitude of the torque on the lefi-hand loop is 2' = 0; that on the middle loop is r =IABsin60°g and that on the right-hand loop is r =IAB (c) The left-hand loop would not rotate, the middle and the right—hand loop would rotate clockwise. 3 3 3_ (a')E- 0- (b)E=_p___(r__:§g_l_ (C)E=p_(b__-_c_1_)i 380 r 380 r2 9. (a) r= 1. 89 cm; (b) T=2 38 ><10'B s; (c)p= 1.04 cm 10. (a) £1=12.,0V I1=10.0,A Iz=8.;00A (b) The power produced in the circuit is PEl = 120 W, and the power consumed is also 120 W. 11. (a) I; = I; = 0.500 mA, 13 = 0; (b) Q; = 18.0 pC; (c) t= 9.66 x10"2 3; (d) I; = 13 = 60.0 uA, upward through the 12.04;!) resistor. 13. (b) E = 21tk80' [1— x ] . The electric field at P is in the positive x-direction. We know I 2 2 x +a this because the electric potential depends only on x (it is independent of y and z) and E = Ex: m—d—V is positive. ab: 14. Q1'= 750 pc and Q; = 250 pic 1R2 ~ II. “'0 121'; (b) B: “’0 2(JR2 +x )3 2R 15 (a) 13’: Physics NYB Final Exam / May 20, 2005 7 ...
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