PHYS 1112 In-Class Exam #3, Version A

Transcription

1 PHYS 1112 In-Class Eam #3, Version A Tue. April 15, 2014, 11:00am-12:15am This is a closed-book, closed-notes eam, but ou are permitted to bring and use a clean cop of the official Formula Sheet for this eam, which ou should have printed out from the PHYS1112 web page. The eam consists of 15 multiple-choice questions. Each question is worth one raw score point, without penalt for wrong answers. No partial credit will be given. Read all the questions at the start so that ou can allocate our time wisel. (Do eas questions first!) You ma use a scientific calculator for arithmetic onl; our calculator must be non-graphing, nonprogrammable, and non-algebraic. You are not allowed to share our calculator. The use of cell phones, pagers, PDAs, or an other electronic devices (besides calculators) is forbidden. Do not open the eam until ou are told to begin. When told to open the eam, ou ma tear off the last few sheets, marked WORKSPACE, as scratch paper. Make sure the scantron sheet has our name and our UGA Card ID ( ) number filled in. Make sure ou also have entered our name, UGA Card ID number and signature on the eam cover page (this page!) below. Make sure to enter our eam Version, A, B, C, D, or E, on our scantron as our answer to Problem 16. Without version ID, our eam can not be graded and ou will get a score of zero. At the end of the eam period ou must hand in both our scantron sheet and this entire eam paper, ecept for last few sheets of scratch paper, with cover page signed and with our name and UGA Card ID ( ) number filled-in on both scantron and cover page. Your eam will not be graded, and ou will receive a score of zero, if ou do not hand in all the foregoing required materials with name and ID information filled in. You will also receive a score of zero if ou talk to or otherwise communicate with anone during the eam, ecept for attending instructor and teaching assistants. You will also receive a score of zero if ou use an unauthorized materials or devices during the eam. You have until the end of the class period (i.e., until 10:45am for Period 2 Class, until 12:15pm for Period 3 Class) to finish the eam and hand in the required eam materials described above. B signing below, ou indicate that ou understand the instructions for this eam and agree to abide b them. You also certif that ou will uphold the universit standards of academic honest for this eam, and will not tolerate an violations of these standards b others. Name (please print): UGACard ID ( ) #: Signature: 1

2 Conceptual Problems Problem 1: Two ver thin circular rings, labeled 1 and 2 in the following, with radii R 1 and R 2, respectivel, and R 1 > R 2, are both centered at the coordinate origin O (0, 0, 0), as shown in Fig Ring 1 lies in the -plane with current I 1 flowing around the ring in the direction indicated in panel (B) of Fig Ring 2 lies in the z -plane with current I 2 flowing around the ring in the direction indicated in panel (C) of Fig Fig (A) (B) (C) 2 z 1 2 I 1 2 I 2 z 1 1 z z z z--plane View --Plane View z--plane View Let B 1 > 0 and B 2 > 0 denote the magnetic field strengths produced at the origin O b onl I 1 alone and onl I 2 alone, respectivel. The total magnetic field vector B (B, B, B z ) produced b both currents at the origin O is then given b: (A) (B, B, B z ) = (0, B 1 B 2, 0) (B) (B, B, B z ) = ( B 2, 0, +B 1 ) (C) (B, B, B z ) = (+B 2, 0, B 1 ) (D) (B, B, B z ) = ( B 2, 0, B 1 ) (E) (B, B, B z ) = (0, B 1 + B 2, 0) 2

3 Problem 2: A molecular ion beam containing four different tpes of ions, called P, Q, R and S here, enters a uniform magnetic field, as shown in Fig below, with B 0 above the lower horizontal line, and B perpendicular to, and pointing out of, the plane of the drawing. The incident beam, below the lower horizontal line, is in the plane of the drawing. Fig B (out) R Q P S B=0 The diameters of the semicircular ion trajectories in the B-field, denoted b d P, d Q, d R and d S, respectivel are observed to be in a ratio of d P : d Q : d R : d S = 1 : 2 : 3 : 4, as indicated in Fig Assume all four ion tpes carr the same absolute amount of charge per ion, q, and the all enter the B-field with the same kinetic energ K. What is the ratio of the four ion masses, denoted b m P, m Q, m R and m S, respectivel? (A) m P : m Q : m R : m S = 1 : 4 : 9 : 16. (B) m P : m Q : m R : m S = 1 : 2 : 3 : 4. (C) m P : m Q : m R : m S = 1 : 2 : 3 : 4. (D) m P : m Q : m R : m S = 1 : 1 : 1 : (E) m P : m Q : m R : m S = : 2 1 : 3 1 : 4. 3

4 Problem 3: Three different circuits, Z, Y and X, are built with the same three resistors, R 1 > 0, R 2 > 0, and R 3 > 0, and the same batter of batter voltage E, as shown in Fig Compare and rank the magnitude of the voltage drops V 1 across R 1, observed in the three different circuits. Fig I o I 3 R 3 I o I 1 R 1 I o I 2 R 2 E I 2 R 2 E I 2 R 2 E I 3 R 3 I 1 R 1 I 3 R 3 I 1 R 1 (Z) (Y) (X) (A) V 1 (Z) < V 1 (Y ) < V 1 (X) (B) V 1 (X) < V 1 (Z) < V 1 (Y ) (C) V 1 (X) < V 1 (Y ) < V 1 (Z) (D) V 1 (Y ) < V 1 (X) < V 1 (Z) (E) V 1 (Z) < V 1 (X) < V 1 (Y ) Problem 4: If a wire of some length L and with a circular cross-section of diameter D has a current I flowing through it, when connected to a batter of voltage E, what will be the current in a wire of length 15L and diameter 5D, made from the same material, at the same temperature, connected to the same batter. (A) 3 5 I (B) 45 I (C) 5 3 I (D) 3 I (E) 1 3 I 4

5 Problem 5: Two ver long thin straight wires running parallel to the z-ais carr currents I 1 (in zdirection) and I 2 (in +z-direction). The intersections of the wires with the -plane and point P form 3 corners of a square, as shown in Fig (C) (D) Fig I 1 (B) (E) (A) P I 2 --Plane View z Assuming I 1 > I 2, which arrow drawn at point P in the -plane could correctl represent the magnetic field vector B produced b I 1 and I 2 at P? (A) (B) (C) (D) (E) 5

6 Numerical Problems Problem 6: If a 30A current flows in a thin straight metal rod of length 4m through a uniform magnetic field of 30T and the direction of the current flow is at an angle of 145 o from the direction of the magnetic field vector, what is the strength of the magnetic force eerted on the rod? (A) 2949N (B) 2065N (C) 3600N (D) 1272N (E) 581N Problem 7: Two resistors, with resistances R 1 = 20Ω and R 2 = 160Ω, are connected in parallel in a circuit. Current flow generates heat at a rate of 80W in R 1. What is the current flowing through R 2? (A) 1.0A (B) 2.0A (C) 0.5A (D) 4.0A (E) 0.25A Problem 8: Suppose ou are on a strange planet where there is no gravit, no friction and no air resistance and the planet s magnetic field is 50T pointing horizontall eastward everwhere at and above the planet s surface. How fast and in which direction would ou have to throw a charged bowling ball of mass 4.80kg and charge 1.5mC so that it reaches a maimum height of 1600m directl above our head? (A) 25.0m/s, thrown westward (B) 25.0m/s, thrown northward (C) 12.5m/s, thrown northward (D) 12.5m/s, thrown southward (E) 25.0m/s, thrown upward Problem 9: Ions of tpe S in Fig (see Problem 2) have a mass of kg and an absolute value of charge of q = e = C. The enter the magnetic field with a speed of 36600m/s and leave it at a distance of 3.84m to the right of the point of entr. How strong is the magnetic field? (A) 8.90mT (B) 35.6mT (C) 71.2mT (D) 142.mT (E) 17.8mT 6

7 Problem 10: Two ver long thin straight wires running parallel to the z-ais and cutting through the -ais at 1 = 3m and through the -ais at 2 = 4m, respectivel, carr currents I 1 and I 2, both in the z-direction, as shown in Fig I 1 --Plane View P Fig z I 2 Assuming I 1 has 5 times the strength of I 2, what is the absolute value of the angle between the +direction and the total magnetic field vector produced b the two wires at point P (4m, 3m, 0m) in the -plane? (Hint: You onl need to calculate the ratio B 1 /B 2!) (A) 75.1 o (B) o (C) 14.9 o (D) 81.5 o (E) o Problem 11: In circuit Y in Fig.3.33 (Problem 3), two of the resistances are R 1 = 10 Ω and R 2 = 20 Ω; and two of the currents are I 1 = 5A and I 3 = 2A. What is the batter voltage E? (A) 90V (B) 110V (C) 200V (D) 10V (E) 190V 7

8 Problem 12: A wire is made of a poorl conducting allo, with a circular cross-section of 0.03mm diameter and a length of 1800m. When connected to a 20V batter for 20 hours, electrons will flow through this wire. What is the heating power of that wire when it is connected to a 40V batter? (A) 4.0 mw (B) 0.25 mw (C) 2.0 mw (D) 1.0 mw (E) 0.5 mw Problem 13: What is the resistivit of the allo in the wire described in the preceding problem? (A) Ωm (B) Ωm (C) Ωm (D) Ωm (E) Ωm Problem 14: Last time ou checked ou weighed in at 160kg. Also, some space alien frat brothers, as part of their annual hazing ritual, have implanted a point charge of 6 Coulomb in our head. Now, to make matters worse, the ve ordered ou to jog on a straight east-west track to become suspended against gravit b the magnetic force eerted on ou b planet earth s magnetic field. Just to be nice to ou, the ve cranked up earth s field to 110 Tesla with the field vector pointing horizontall at an angle α = 25 o east of due south, as shown in Fig But the left earth s value of g at 9.81m/s 2... Up Down N Fig W E α S B In case ou can still handle electromagnetic theor with all that electricit under our hairdo and ou still want to join that fraternit: How fast do ou have to run, and in which direction, to achieve levitation? (A) At least 5.53m/s, running westward (B) At least 5.53m/s, running eastward (C) At least 2.38m/s, running eastward (D) At least 2.62m/s, running westward (E) At least 2.62m/s, running eastward 8

9 Problem 15: In the circuit fragment shown in Fig. 3.44, given currents are I 1 = +7A and I 2 = +3A; and resistances are R b = 12 Ω and R c = 20 Ω. What is the electrical potential difference V cb V c V b between points c and b in the circuit? [Hint: V cb =(V c V a ) + (V a V b )] I 1 a I 3 R c c Fig I 2 R b b Arrows indicate positive current directions: I>0 if I flowing into arrow direction I<0 if I flowing against arrow direction (A) +236V (B) 116V (C) 44V (D) +44V (E) +116V Problem 16: Enter our eam Version, A, B, C, D or E, on our scantron as the answer to Problem 16!! Your eam version is printed in bold face on top of the cover page of this eam paper which ou signed. 9

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