Exam 3 2003 - PH 132 Exam 3 Spring 2003 Student Name 5 OLA...

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Unformatted text preview: PH 132 Exam 3 Spring 2003 Student Name 5 OLA)?! O M 3 Student Number La'ofRecitation Section Number (11,...,35) Instructions: 1. Fill out all the information above. Write your name on each page. 2. Clearly indicate your final answers for all multiple-choice questions in the space provided. 3. Present neat and orderly solutions to each problem. Clearly indicate your method of solution by including equations used for each part. Final answers should be circled or bored. 4. Be sure to include appropriate units with all answers. |\J 5. Permittivity of free space: so = 8.85 x 10—12 Permeability of free space: #0 = 1.26 X 10—6 Multiple Choiceuw Problem 1 Problem 2 Total Multiple Choice (2 pts. each) 1) A closed rectangular loop of wire is formed with flexible wires and placed in a uniform gagnetic field, as shown. The magnetic field is directed into the page and is perpendicular to the plane of the loop. Ifthe rectangular loop resides in a frictionless environment, then when a current I flows in the clockwise digetion, the loop will 8 __h f2=f£x5 7?? z/fix-g zflBAL‘OO 3 O A) flip over and bunch together; F: B) flip over and spread out into a circle; C) flip over and remain rectangular; D) not flip over but bunch together; E) not flip over but spread out into a circle; P) not flip over but remain rectangular. Answer 5 2) A wire is formed into a shape that mimics four sides of a pentagon. Each side has length L. The wire carries a current I from point a to point I) and resides in a tactical mmp fieldz directed to the lefi as shown. The direction of the netforce acting on this wire is A) into the page; B) out of the page; C) upward and to the right; D) downward and to the left. Answer A 3) You conduct several experiments in which you send a proton (m = 1.67r x 10—27 kg) into a aniform magnetic field, with its velocity vector perpendicular to the direction of the field. Each time, you change the strength of the magnetic field and observe the radius of the proton’s circular trajectory. The veiocity is always the same. On a graph you plot the radius (r) of the trajectory versus the inverse of the field’s magnitude (3*! ) , as shown. From your graph, you verify that the speed of the proton was N012: .. r — ?£_ {woe-sano" _ : 1 : : : F '- E) s” " 5 " I) 023 ’ ' ' ' swan: .— 0.6 ... 3 2H0 7mq— 0.4 : 50w: raR- v". 0.2 0 l t I i I _ o 1.0 2.0 3.0 4.0 5.0 B;1 (T4) A) 12 mis; B) 19 mis; C) 26 mfs; D) 52 mis. Answer B 4) A positive charge (+q) moves with velocity (it) through a region of space where a uniform electric fieid is directed into the page and a uniform magnetic field is directed to the right. This particle will experience no net force if the velocity vector has a magnitude of: A) v = E / B and points in the positive y-direction; B) v = E/ B and points in the negative y-direction; C) v = B/ E and points in the positive y-direction; Answer 3 D) V = B/ E and points in the negative y—direction. 5) The figure below shows three circuits consisting of concentric circular arcs (either quarter, Q half, or three-quarter circles of radii r and Zr) and radial lengths. The circuits carry the some current. Rank them according to the magnitude of the magnetic field produced at the center of curvature (the dot), greatest first. a b c A) a, b, c; B) a, c, b; C) b, a, c; D) b, c, a; E) c, a, b; F) c, b, a. . -___ _/:_ Answer Sixteen long paraliel wires carry equal currents I in the directions shown. Rank the Ampedan loops (labeled a through (1) according to the magnitude of til-5" - d3 along each, greatest first. The wn'es are drawn in cross-section. %3. as = H 1.5% Act-0 _,_.. --I Aim-6L" 3"- .T-fzuc. 5 = 0 J1me 4 = J. fine; .2 2.2.. A)¢hmm B) a, d, c, 13; C)¢amm D) a, b, d, 0. Answer B Evaluate the magnitude of 53-3 0 d5" for the square Amperian loop (shown as a dotted line) of side 1J2, located inside a wire with a square cross-section of side L and carrying a current I. Assume the current is uniformly distributed across the cross-section of the wire. A) 211101, B) ref/2; C) flOI/4, D) 4;:0I Answer C 8) The magnetic field outside of an infinitely long ideal solenoid (carrying a constant current): A) decreases in the radial direction; B) increases in the radial direction; C) is constant in the radial direction; D) is infinite; E) is zero. Answer g 9) A closed conducting triangular loop is pulled away from a uniform magnetic field (directed out of the page), as shown. The boundary of the magnetic field is shown with a dotted line. Which of the following is true? 3 o I O —r B o 0 OUT 9 o O I A) 1(1) 3 I T in time and the induced current is clockwise; B) [(1) Bl T in time and the induced current is counterclockwise; C) lfl) 8| Jr in time and the induced current is ciockwise; D) ltl) Bl Jr in time and the induced current is counterclockwise; Answer D 10) Consider a circuit with an emf applied to a resistor (with resistance R) and a capacitor (with capacitance C) connected in series. The “time constant” for this circuit is RC, which represents the time it takes the current in the ci uit to d ase .I _ a “4’ M A) zero. " B) approximately 37% of its initial value; “’95”: Tat C) approximately 63% of its initial value; i- : Q 0 3 > D) approximately 73% of its initial value; 3- ( 7 Answer B Problem 1 Two long straight wires of length L are parallel to each other and carry equal currents of magnitudes I in opposite directions (as shown in cross-section). Each wire has a mass m and is supported by a string of length d. The wires hang in equilibrium and the mass of each string is negligible. Use appropriate unit vector notation according to the reference frame given. Y M __ - a) Find an expression for the magne reforce F B acting on the leftmost wire due to the rightmost wire. (5 pts.) b) Draw and label all forces acting on the leftmost wire. Find a simplified expression for the separation distance X between the wires. Assume that 9 is so small that tam? can be replaced by Sint9 . (10 pts.) c) Evaluate the separation distance and magneticforce for the following values: I =1_.00><102 A, d = 1.0 m, L =1.0 m, and mg=l.0 N. (2 pts.) (1) An extemal uniform magnetic field E is turned on in the positive y-direction. Find a new expression for the net magnetic force acting on the leftmost wire. (3 pts.) BONUS: Evaluate the new separation distance from part d if the external field has a magnitude of 5610 1.1T (approximately equivalent to the earth’s magnetic field near the surface). M- . 2___ ZAILBX #231371. ’X “*3 z-vawg sat/E @uAbiAWc. gag Lag VALuES' GWEM'. ‘2— x _. (5),on —(o.c9037’) :O x': 0.5)! I («.mchV-41""?qu3 :: 0.06? :0 Problem 2 A circular conducting ring is made to expand in a unifonn magnetic field 3’ . The field is directed out of the page and oriented perpendicular to the plane of the ring. The radius of the ring increases linearly with time as r(t) = are + a: i , where r0 is the initial radius and a is a positive parameter describing the growth rate. 0 t a) Find expressions for the area, the magnetic flux, and the magnitude of the induced emf in the ring, as fiinctions of time. (10 pts.) b) Sketch a plot of the magnitude of the induced emf on the graph above. Find the initial emf 80 at t.‘ =08 if B = 0.12 T, r0 =10 cm, and a =0.01mfs. (5 pts.) c) Find the current through the ring and the power dissipated by the ring at i = 5.0 s . Assume the resistance in the ring is 0.18 1119. Indicate whether the current is clockwise or connierciockwise. (5 pts.) BONUS: As the ring expands in circumference, it grows thinner, but the vlu e o t e wire alwazs remains the same. Find an expression for the resistance of the wire as a function of time, in terms of the resistivity p , the initial diameter of the wire d a , the initial radius-of the ring r0 , and the parameter a: . (3 pts.) ...
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This note was uploaded on 09/30/2010 for the course PHYSICS PH 131 taught by Professor Wick during the Fall '10 term at Clarkson University .

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Exam 3 2003 - PH 132 Exam 3 Spring 2003 Student Name 5 OLA...

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