A. τ 3 > τ 2 > τ 1 B. τ 3 > τ 1 = τ 2 C. τ 2 > τ 1 > τ 3 D. τ 1 = τ 2 = τ 3

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Kristian Shepherd
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1 2013 March 18 Exam 2 Physics 106 Circle the letter of the single best answer. Each question is worth 1 point Physical Constants: proton charge = e = C proton mass = m p = kg electron mass = m e = kg electron charge = e = C permittivity of free space = ǫ 0 = F/m permeability of free space = µ 0 = 4π 10 7 T m/a Coulomb constant = k e = N m 2 /C 2 Faraday constant = C speed of light = c = m/s 1. An electron moves horizontally toward a screen. The electron moves along the dotted path because of a magnetic force caused by a magnetic field. In what direction does that magnetic field point? q v B? 2. A current flowing clockwise around a square loop; additionally a current flowing to the left through a long straight wire that sits above the square. (The square loop and the wire sit in the plane of this sheet of paper as shown in the below figure.) The net force on the square is A. to the left B. out of the page C. up the page D. down the page 3. The below figure shows three different shape/size circuits that lie together in the plane of this sheet of paper; the same current I is flowing (as indicated) in each circuit. Rank the torque on these circuits if there is a uniform magnetic field in the plane of these circuits pointed to the right. (τ 1 denotes the magnitude of the torque in circuit #1, etc.) screen A. Toward the top of this page B. Toward the bottom of this page C. Into this page D. Out of this page A. τ 3 > τ 2 > τ 1 B. τ 3 > τ 1 = τ 2 C. τ 2 > τ 1 > τ 3 D. τ 1 = τ 2 = τ 3 4. Consider again the torques on the circuits of the previous problem, but now the magnetic field points directly out of this page. A. τ 3 > τ 2 > τ 1 B. τ 3 > τ 1 = τ 2 C. τ 2 > τ 1 > τ 3 D. τ 1 = τ 2 = τ 3

2 5. The below figure shows where infinitely long wires parallel to the z axis intersect the xy plane. The current in each wire is listed along with the flow direction: = out of page, = into page. Consider various amperian loop sums (L = B l) along three circles centered on the origin with radii as shown in the figure. Which of the below options best describes the relationship between the integrals. (L 1 denotes the loop sum for circle 1, etc. Negative numbers are smaller than any positive number.) y 6. A beam consists of an unknown mix of particles. All the particles have the same velocity. The beam directs the particles into a region of uniform magnetic field (pointing out of the page much like a mass spec). The following figure displays some possible paths for particles. Note the following names: proton (the positively charged nucleus of normal hydrogen), deuteron(the nucleus of an isotope of hydrogen: twice the mass of a proton, but with the same charge), α particle (He nucleus: four times the mass of a proton and twice the charge of a proton), electron (negatively charged particle orbiting the nucleus in Bohr s atom). 2 A 1 A 3 A 2 A x uniform magnetic field A. L 1 > L 3 > L 2 B. L 1 > L 2 > L 3 C. L 2 > L 3 > L 1 D. L 3 > L 2 > L beam source A. The proton, deuteron and α all follow different paths, with the more massive particles having the largest radius path. B. The proton and deuteron follow the same path; C. The deuteron and the α follow the same path. D. The radius of the electron s path is much larger than the radius of the proton s path and curves in the opposite direction.

3 100 V 100 V 1 V 100 V 1 Α 1 ma 1 Α 1 A 7. The below circuit shows a series LR circuit. Theswitch is closed at t = 0. Which graphbest represents how the current changes in time? 10 Ω 100 Ω 10 mh.033 µf A 1 ms C 1 ms 10 V 10 mh B 1 µs D 1 ms 8. A generator coil consists of 1000 square loops (turns) of wire each with a side of 2 cm. This coil is rotated about a diagonal at a frequency: f = 60 Hz. The axis of rotation is perpendicular to a 1 T magnetic field. Which of the below graphs best represents the voltage produced in the coil. A B 9. If an rms AC current of 0.3 A flows through the above circuit, the total electrical power converted to heat is most nearly: A. 1 W B. 10 W C. 100 W D. Can t say; depends on the frequency of the generator 10. The primary winding of a transformer has 1000 turns and is connected to a normal household receptacle. The secondary has 200 turns. The output (secondary) voltage is most nearly A. 600 V B. 120 V C. 25 V D. 5 V 11. Theacgenerator inthebelowcircuithasafixed output voltage (V) and frequency (f). We seek to maximize the current through the coil (which has inductance L). Compared to the simple circuit shown, the current through the coil could be increased by: 20ms 100 s C D A. Adding a resistor in parallel to L 3 ms 20 ms B. Adding a capacitor in series with L C. Adding an inductor in parallel with L D. It is not possible to increase the current through the coil by adding components.

4 Voltage (V) 12. Much like an oscilloscope, the below plot displays two voltages (solid and dotted) as functions of time. Which of the below phasor pairs is consistent with this plot? 14. Which of the below diagrams properly displays a light ray in air refracted at the interface between air and glass? A B air glass glass air A ωt B ωt C D air glass glass air C ωt D ωt 15. Which of the following list of types of light correctly orders the light in terms of increasing frequency? 13. The below plot similar to that of an oscilloscope displays voltage vs. time. Such signals may be characterized by the rms voltage (V rms ), the period (T), the frequency (f), and the angular frequency (ω). Which of the below is a good estimate of one of these quantities? A. visible, microwave, ultraviolet, X-ray B. ultraviolet, visible, infrared, radio C. infrared, microwave, ultraviolet, X-ray D. radio, microwave, infrared, visible 16. Consider sign convention for situation displayed in the below ray diagram. How many of the the following three quantities: f, p, q are positive? t (ms) Object A. f = 30 Hz B. V rms = 14 V C. T =.0015 s D. ω = 2000 rad/s A. 0 B. 1 C. 2 D. 3

5 The following questions are worth 10 pts each Record your steps! (Grade based on method displayed not just numerical result) 17. As shown below three long wires are arranged in an equilateral triangle with side 10 cm. The currents I 1 and I 3 come directly out of this page; I 2 goes into the page. We seek the magnetic field vector at the spot marked X (i.e., the midpoint of the horizontal segment). A. Directly on the diagram, draw (approximately) and label the magnetic field vector (including direction) at X due to each of the three currents. Label the magnetic field due to I 1 : B 1, etc. B. Draw (approximately) the sum of these three magnetic field vectors. Label an angle that describes the direction of this net magnetic field vector. C. Calculate the net magnetic field vector at the spot marked X, by finding its x and y components. D. Calculate the numerical value of the angle you labeled in part (B). I 3 = 3 A I 1 = 1 A s = 10 cm I 2 = 2 A

6 Secondary circuit Primary circuit 18. The below diagrams show three separate circuits. For each case, add an arrow directly on a wire showing the direction of the induced current in that wire. (Note that the bottom case of the long straight wire has two secondary circuits and hence two separate arrows are required.) S N The north pole of a bar magnet is approaching the solenoid The current shown flowing through the primary circuit is increasing A long straight wire and a square loop of wire sit in the plane of this sheet of paper. A circular loop of wire is centered on the long wire, but sits in a plane perpendicular to this sheet of paper. For several minutes there has been no current flowing in any wire. A battery (not shown) is connected and a current starts to flow to the right through the long straight wire.

7 19. Consider the below right LRC circuit, driven by a generator at a frequency of f = 20 khz A. What rms current flows through the circuit? B. What is the rms voltage across the inductor (V L )? Across the capacitor (V C )? Across the resistor (V R )? 8 mh C. Accurately draw a phasor diagram showing/labeling how the voltages: V L,V R,V C add to produce the total voltage of the source. D. On your phasor diagram label the angle φ that is used to find the power factor cosφ. (No need to calculate this angle, just label it.) E. Circle one: the total voltage leads the current the total voltage lags the current 50 Ω.01 µf 3 V rms 20. Find below two diagrams: a lens & object and a mirror & object. For each situation accurately draw the three principal rays described in our textbook. Follow the book s convention: dotted lines for rays extrapolated by the viewing eye and solid line for the actual rays. Draw an arrow accurately showing the size, location and orientation of the image. Object f = 15 Object f = +10

8 21. Consider the problem of designing a camera for a Venus rover: the Venusian atmosphere is about 100 times thicker than the Earth s atmosphere, so the index of refraction deviates noticeably from one: n = Thecameralens(n = 1.5) issupposedtotaketheparallel rays fromadistant sceneandfocus them on the electronic film. In this problem you will ray-trace rays that hit near the circumference of the R = 2 cm lens. As diagrammed below, that portion of the lens can be considered a 10 prism. A bit of geometry shows the following relations among the angles: a = 5, c = 10 b, and e = d 5. Tests in Earth s atmosphere find a focal length of cm; What do you calculate as the focal length in Venus s atmosphere? (Report your results for the angles a,b,c,d,e.) 10 a b c d R e focal length

104 Practice Exam 2-3/21/02

104 Practice Exam 2-3/21/02 1. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero