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Unformatted text preview: Husain, Zeena Homework 11 Due: Apr 12 2004, 6:00 pm Inst: Sonia Paban 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page find all choices before making your selection. The due time is Central time. 001 (part 1 of 1) 10 points Given: c = 2 . 99792 10 8 m / s . The distance from the Earth to Polaris is approximately 6 . 31 10 18 m. If the North Star, Polaris, were to burn out today, in how many years would it disappear from our vision? Correct answer: 667 . 425 years. Explanation: Since the light travels at a finite velocity c , the last ray of light going out from Polaris would travel t = d c = 6 . 31 10 18 m 2 . 99792 10 8 m / s = 2 . 10479 10 10 s seconds before arriving at the Earth. In years, this is t y = t 1 60 min / s 1 60 hr / min 1 24 day / hr 1 365 yr / day = 667 . 425 years . 002 (part 1 of 5) 10 points Given: c = 2 . 99792 10 8 m / s . Consider a monochromatic electromagnetic plane wave propagating in the x direction. At a particular point in space, the magnitude of the electric field has an instantaneous value of 625 V / m in the positive y-direction. The wave is traveling in the positive x-direction. x y z E wave propagation Compute the instantaneous magnitude of the magnetic field at the same point and time. Correct answer: 2 . 08478 10- 6 T. Explanation: For plane, electromagnetic waves, we know that the ratio of the instantaneous magni- tudes of the electric and magnetic fields is E B = c . This means that the instantaneous magnitude of the magnetic field is B = E c = 625 V / m 2 . 99792 10 8 m / s = 2 . 08478 10- 6 T . 003 (part 2 of 5) 10 points What is the instantaneous magnitude of the Poynting vector at the same point and time? Correct answer: 1036 . 88 W / m 2 . Explanation: The Poynting vector, ~ S , is given by ~ S = 1 ~ E ~ B . For a plane, electromagnetic wave, ~ E and ~ B are always perpendicular to each other and to the direction of propagation of the wave. In this case, the Poynting vector is in the direction of propagation and has magnitude S = E B = (625 V / m)(2 . 08478 10- 6 T) 1 . 25664 10- 6 N / A 2 = 1036 . 88 W / m 2 . 004 (part 3 of 5) 10 points What are the directions of the instantaneous magnetic field and the instantaneous Poynt- ing vector respectively? Husain, Zeena Homework 11 Due: Apr 12 2004, 6:00 pm Inst: Sonia Paban 2 1. b B = + k and b S = 2. b B = + and b S = k 3. b B = k and b S = correct 4. b B = k + and b S = 5. b B = and b S = 6. b B = k and b S = + 7. b B = k and b S = 8. b B = and b S = 9....
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