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Physics 272 - Honors Physics 2 FINAL EXAM Wednesday, May 13, 2015 ⇒ ⇐ SIGN HERE NOW: 1. The exam will last from 3:40 - 4:30 p.m. Use a #2 pencil to make entries on the answer sheet. Enter ID information items 2-5, now, on the answer sheet before the exam starts. 2. In the section labeled NAME (Last, First, M.I.) enter your last name, then fill in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. 3. Under STUDENT # enter your 9-digit RUID Number. 4. Enter 272 under COURSE; you may ignore the section number. 5. Under CODE enter the exam code from the label above. 6. During the exam, you may use pencils, a calculator, and one 8.5 x 11 inch sheet (both sides) with formulas and notes. 7. There are 24 multiple-choice questions on the exam. For each question, mark only one answer on the answer sheet. There is no deduction of points for an incorrect answer, so even if you cannot work out the answer to a question, you should make an educated guess. At the end of the exam, hand in the answer sheet and this SIGNED exam. 8. When you are asked to open the exam, make sure that your copy contains all 24 questions. Raise your hand if this is not the case, and a proctor will help you. Also raise your hand during the exam if you have a question. 9. Please have your student ID ready to show to the proctor during the exam. 10. Possibly useful information: Possibly Useful numerical constants: Acceleration due to gravity g = 9.8 m/s2 Elementary charge e = 1.6 × 10−19 C Proton charge = 1.6 × 10−19 C Electron charge = −1.6 × 10−19 C 1 electron volt (eV ) = 1.6 × 10−19 J Proton mass = 1.673 × 10−27 kg = 938.3 MeV /c2 Electron mass = 9.11 × 10−31 kg = 0.511 MeV /c2 1/4π"0 = 9 × 109 N · m2 /C 2 µ0 = 4π × 10−7 T · m/A Powers of ten: femto(f) 10−15 centi(c) 10−2 pico(p) 10−12 kilo(k) 10+3 nano(n) 10−9 Mega(M) 10+6 micro(µ) 10−6 Giga(G) 10+9 milli(m) 10−3 Tera(T) 10+12 1. A ray of light goes from air into water. Which of the following is true? a) b) c) d) e) Its wavelength stays the same Its frequency decreases Its speed stays the same Its frequency increases None of the other statements is true 2. A beam of light in water (to the left, n = 1.333) in a fish tank is incident on the glass wall (to the right, n = 1.54) of the tank at some angle. Which picture is qualitatively correct? a) b) d) e) c) 3. You see swimming goggles at the bottom corner of a pool when you look down at a pool’s surface. The goggles appear to be 1.00 m underwater. How deep is the water? (nwater = 1.33) a) b) c) d) e) 1.00 2.03 0.49 0.75 1.33 m m m m m 4. A concave spherical mirror has a focal length f . At what position s of the object will the image have magnification M = −2? a) b) c) d) e) M = −2 is not possible. s = 3f /2 s = f /3 s = 3f s = −3f /2 5. In a double-slit experiment, the two slits are spaced 0.1 mm apart, and a screen is at a distance of 1.0 m. If yellow light with a wavelength of 600 nm is used, what will be the spacing between adjacent bright fringes? (Assume the angle is small.) a) b) c) d) e) 6 mm 12 mm 60 mm 1.0 mm 0.16 mm 6. Plane-polarized light is incident on a polarizer whose transmission axis makes an angle of 60◦ with the direction of the light’s electric field. What fraction of the incident light intensity is transmitted by the polarizer? a) b) c) d) e) Zero 12.5% 25% 50% 100% 7. A circular disk radar antenna on a navy ship radiates and receives electromagnetic waves of 0.020 m wavelength to detect two small boats located 9 km from the ship. If the small boats are 100 m apart from each other, what must be the minimum diameter of the antenna so that the boats can be distinguished as two objects, rather than as one small object? Important: for resolving power, circular disk radar antenna can be considered to behave just like a circular aperture. a) b) c) d) e) 0.45 m 0.27 m 1.1 m 1.4 m 2.2 m 8. Light traveling in glass, with a refractive index of 1.6 is reflected at a glassoil interface. The critical angle for total internal reflection is 60◦ . What is the index of refraction of the oil? a) b) c) d) e) 2 0.9 1.87 1.38 3 9. Plane monochromatic waves with wavelength 500 nm are incident normally on a plane transmission grating having 500 slits/mm. Find the angle of the m = 2 interference maximum. a) b) c) d) e) 60◦ 39◦ 30◦ 19◦ 15◦ 10. In vacuum the velocity of an electromagnetic wave (e.g./ light or radio wave) a) b) c) d) e) depends on its frequency. depends on its amplitude. is a universal constant. none of the others is true. depends upon its wavelength. 11. A long solenoid has a diameter of 12.0 cm. When a current i exists in its windings, a uniform magnetic field vector B = 31.0 mT is produced in its interior. By decreasing i, the field is caused to decrease at the rate of 5.20 mT/s. Calculate the magnitude of the induced electric field at 8.2 cm from the axis of the solenoid. a) b) c) d) e) 6.84 × 10−4 V/m 2.28 × 10−4 V/m 1.14 × 10−4 V/m 5.2 × 10−5 V/m 2.6 × 10−5 V/m 12. The wire in the figure consists of two straight sections that are radial from the center of the circle. The arc subtends an angle of 60o at a radius of 3 cm, and the wire carries a current of 4 Amps. The magnetic field at the center is: a) b) c) d) e) 3 µT 84 µT 0.15 mT 14 µT 0.50 mT i=4A 60o O 3 cm 13. An electromagnetic wave is traveling along the k direction. Which of the following sets are possible directions for the associated electric and magnetic fields at any one instant? • I: E along +i; B along +j • II: E along −j; B along +i • III E along −i; B along −j a) b) c) d) e) All three are possible None of the three is possible III is possible; I and II are not I and III are possible; II is not II and III are possible; I is not 14. An oil furnace uses a transformer to provide an arc for igniting the fuel. The primary winding has 40 turns and operates at 120 V and 0.5 A. If the secondary winding has 2000 turns, what are the secondary voltage and current respectively? a) b) c) d) e) 2.4 V and 0.01 A 2.4 V and 25 A 6000 V and 25 A 6000 V and 0.01 A 6000 V and 0.5 A 15. You walk 150 m directly towards a street lamp and find that the intensity increases to 1.5 times the intensity at your original position. Assuming that the lamp radiates uniformly in all directions, how far from it were you first standing? a) b) c) d) e) 1350 m 817 m 750 m 682 m 450 m 16. A bar magnet with its north end down is dropped through a circular loop of wire from far above. Magnetic field lines leave the magnet through its north end and enter the magnet through its south end. Seen from above, the direction of the current induced in the loop will S a) b) c) d) e) first be counterclockwise and later clockwise. none of these. always be counterclockwise. always be clockwise. first be clockwise and later counterclockwise. N 17. Two concentric, circular loops of wire lie in the plane of the paper. The outer loop carries a current I. Pick the correct answer. a) If I is clockwise and constant, the induced current in the inner loop will be counterclockwise. b) If I is clockwise and increasing, the induced current in the inner loop will be clockwise. c) If I is counterclockwise and decreasing, the induced current in the inner loop will be counterclockwise. d) If I is clockwise and decreasing, the induced current in the inner loop will be zero. e) If I is counterclockwise and constant, the induced current in the inner loop will be counterclockwise. R R E NT C U I 18. One long wire placed along the x-axis carries a current of 30 A in the +x direction. Another wire, perpendicular to the xy plane and passing through the point (0, 4, 0) m carries a current of 40 A in the +z direction. What is the magnitude of the magnetic field at the point P = (0, 2, 0) m. 40 A a) b) c) d) e) 4.0µ 5.0µ 3.0µ 7.0µ 1.0µ T T T T T P 30 A 19. A radio wave of frequency 107 Hz hits a perfectly absorbing planar surface that is perpendicular to the direction of propagation of the wave. The average power per unit area of the wave at the position where it is absorbed is 10 W/m2 . Calculate the radiation pressure on the surface. a) b) c) d) e) (3.3 × 10−8 ) N/m2 (18.6 × 10−4 ) N/m2 (3.3 × 10−9 ) N/m2 33 N/m2 18.6 N/m2 20. A proton (charge = e; mass = m) and a deuteron (charge = e; mass = 2m) have the same kinetic energy. They enter a magnetic field, and both move in circular paths. How are the radii of the paths related? a) b) c) d) e) rd rd rd rd rd =√ 2rp = 2rp = rp √ = rp / 2 = rp /2 21. The current in a solenoid increases steadily from 0 to 10 mA in 40 ms. If the induced emf across the solenoid is 0.8 mV, what is the solenoid’s inductance? a) 0.2 mH b) 3.2 mH c) 8.0 mH d) 0.8 mH e) Cannot be determined from the information given 22. A proton is traveling in the negative y direction. It enters a magnetic field pointing in the positive z direction. In which direction is the force on the proton? a) b) c) d) e) x y -z z none of the other responses 23. A square loop of wire is held in a uniform 0.22 T magnetic field directed perpendicular to the plane of the loop. The length of each side of the square is decreasing at a constant rate of 5.0 cm/s. What emf is induced in the loop when the length is 12 cm? a) b) c) d) e) 0.0052 0.0026 0.0013 0.0006 0.0003 V V V V V 24. The magnetic potential energy stored in a certain inductor is 40.0 mJ when the current in the inductor is 52.5 mA. What current is required for the stored energy to be 100 mJ? a) b) c) d) e) 166 mA 103 mA 83 mA 63 mA 32 mA