Quantum Physics

A.24 Answers to Quick Quizzes, Odd-Numbered Conceptual Questions and Problems15. No. The wire will emit electromagnetic waves only if thecurrent varies in time. The radiation is the result of acceleratingcharges, which can occur only when the current isnot constant.17. The resonance frequency is determined by the inductanceand the capacitance in the circuit. If both L and C are doubled,the resonance frequency is reduced by a factor of two.19. It is far more economical to transmit power at a highvoltage than at a low voltage because the I 2 R loss on thetransmission line is significantly lower at high voltage.Transmitting power at high voltage permits the use ofstep-down transformers to make “low” voltages and highcurrents available to the end user.21. No. A voltage is induced in the secondary coil only if theflux through the core changes with time.PROBLEMS1. (a) 141 V (b) 20.0 A (c) 28.3 A (d) 2.00 kW3. 70.7 V, 2.95 A5. 6.76 W9. 4.0 10 2 Hz11. 17 F15. 3.14 A17. 0.450 T m 219. (a) 0.361 A (b) 18.1 V (c) 23.9 V (d) 53.0°21. (a) 1.4 k (b) 0.10 A (c) 51° (d) voltage leads current23. (a) 89.6 V (b) 108 V25. 1.88 V27. (a) 103 V (b) 150 V (c) 127 V (d) 23.6 V29. (a) 208 (b) 40.0 (c) 0.541 H31. (a) 1.8 10 2 (b) 0.71 H33. 2.29 H35. C min 4.9 nF, C max 51 nF37. 0.242 J39. 0.18% is lost41. (a) 1.1 10 3 kW (b) 3.1 10 2 A (c) 8.3 10 3 A43. 1 000 km; there will always be better use for tax money.45. f red 4.55 10 14 Hz, f IR 3.19 10 14 Hz,E max,f /E max,i 0.5747. 2.94 10 8 m/s49. E max 1.01 10 3 V/m, B max 3.35 10 6 T51. (a) 188 m to 556 m (b) 2.78 m to 3.4 m53. 5.2 10 13 Hz, 5.8 m55. 4.299 999 84 10 14 Hz; 1.6 10 7 Hz(the frequency decreases)57. 99.6 mH59. 1.7 cents61. (a) resistor and inductor (b) R 10 , L 30 mH63. (a) 6.7 10 16 T (b) 5.3 10 17 W/m 2(c) 1.7 10 14 W65. (a) 0.536 N (b) 8.93 10 5 m/s 2 (c) 33.9 days67. 4.47 10 9 JChapter 22QUICK QUIZZES1. (a)2. Beams 2 and 4 are reflected; beams 3 and 5 are refracted.3. (b)4. (c)CONCEPTUAL QUESTIONS1. Sound radiated upward at an acute angle with the horizontalis bent back toward Earth by refraction. This meansthat the sound can reach the listener by this path as wellas by a direct path. Thus, the sound is louder.3. The color will not change, for two reasons. First, despitethe popular statement that color depends on wavelength,it actually depends on the frequency of the light, whichdoes not change under water. Second, when the light entersthe eye, it travels through the fluid within. Thus, evenif color did depend on wavelength, the important wavelengthis that of the light in the ocular fluid, which doesnot depend on the medium through which the light traveledto reach the eye.5. (a) Away from the normal (b) increases (c) remains thesame7. No, the information in the catalog is incorrect. The indexof refraction is given by n c/v, where c is the speed oflight in a vacuum and v is the speed of light in the material.Because light travels faster in a vacuum than in anyother material, it is impossible for the index of refractionof any material to have a value less than 1.9. There is no dependence of the angle of reflection on wavelength,because the light does not enter deeply into thematerial during reflection—it reflects from the surface.11. On the one hand, a ball covered with mirrors sparkles byreflecting light from its surface. On the other hand, afaceted diamond lets in light at the top, reflects it by totalinternal reflection in the bottom half, and sends the lightout through the top again. Because of its high index ofrefraction, the critical angle for diamond in air for totalinternal reflection, namely c sin 1 (n air /n diamond ), issmall. Thus, light rays enter through a large area and exitthrough a very small area with a much higher intensity.When a diamond is immersed in carbon disulfide, thecritical angle is increased to c sin 1 (n carbon disulfide /n diamond ). As a result, the light is emitted from the diamondover a larger area and appears less intense.13. The index of refraction of water is 1.333, quite differentfrom that of air, which has an index of refraction of about 1.The boundary between the air and water is therefore easy todetect, because of the differing diffraction effects above andbelow the boundary. (Try looking at a glass half full ofwater.) The index of refraction of liquid helium, however,happens to be much closer to that of air. Consequently,the defractive differences above and below the helium-airboundary are harder to see.15. The diamond acts like a prism, dispersing the light into itsspectral components. Different colors are observed as aconsequence of the manner in which the index of refractionvaries with the wavelength.17. Light travels through a vacuum at a speed of 3 10 8 m/s.Thus, an image we see from a distant star or galaxy musthave been generated some time ago. For example, thestar Altair is 16 lightyears away; if we look at an image ofAltair today, we know only what Altair looked like 16 yearsago. This may not initially seem significant; however,astronomers who look at other galaxies can get an idea ofwhat galaxies looked like when they were much younger.Thus, it does make sense to speak of “looking backward intime.”PROBLEMS1. 3.00 10 8 m/s3. 114 rad/s for a maximum intensity of returning light5. (b) 3.000 10 8 m/s