hw11sol

# hw11sol - Flores, Michael Homework 11 Due: Apr 12 2004,...

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Flores, Michael – 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 – fnd all choices be±ore making your selection. The due time is Central time. 001 (part 1 o± 1) 10 points Given: c = 2 . 99792 × 10 8 m / s . The distance ±rom the Earth to Polaris is approximately 6 . 24 × 10 18 m. I± the North Star, Polaris, were to burn out today, in how many years would it disappear ±rom our vision? Correct answer: 660 . 021 years. Explanation: Since the light travels at a fnite velocity c , the last ray o± light going out ±rom Polaris would travel t = d c = 6 . 24 × 10 18 m 2 . 99792 × 10 8 m / s = 2 . 08144 × 10 10 s seconds be±ore 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 = 660 . 021 years . 002 (part 1 o± 5) 10 points Given: c = 2 . 99792 × 10 8 m / s . Consider a monochromatic electromagnetic plane wave propagating in the z direction. At a particular point in space, the magnitude o± the electric feld has an instantaneous value o± 214 V / m in the positive x -direction. The wave is traveling in the positive z -direction. z x y E wave propagation Compute the instantaneous magnitude o± the magnetic feld at the same point and time. Correct answer: 7 . 13827 × 10 - 7 T. Explanation: For plane, electromagnetic waves, we know that the ratio o± the instantaneous magni- tudes o± the electric and magnetic felds is E B = c . This means that the instantaneous magnitude o± the magnetic feld is B = E c = 214 V / m 2 . 99792 × 10 8 m / s = 7 . 13827 × 10 - 7 T . 003 (part 2 o± 5) 10 points What is the instantaneous magnitude o± the Poynting vector at the same point and time? Correct answer: 121 . 562 W / m 2 . Explanation: The Poynting vector, ~ S , is given by ~ S = 1 μ 0 ~ E × ~ B . For a plane, electromagnetic wave, ~ E and ~ B are always perpendicular to each other and to the direction o± propagation o± the wave. In this case, the Poynting vector is in the direction o± propagation and has magnitude S = E B μ 0 = (214 V / m)(7 . 13827 × 10 - 7 T) 1 . 25664 × 10 - 6 N / A 2 = 121 . 562 W / m 2 . 004 (part 3 o± 5) 10 points What are the directions o± the instantaneous magnetic feld and the instantaneous Poynt- ing vector respectively?

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Flores, Michael – Homework 11 – Due: Apr 12 2004, 6:00 pm – Inst: Sonia Paban 2 1. b B = ˆ + ˆ k and b S ı 2. b B = ˆ and b S = ˆ k correct 3. b B ı and b S = ˆ 4. b B ı and b S = ˆ k 5. b B = ˆ and b S ı 6. b B = ˆ k and b S = ˆ 7. b B = ˆ and b S = ˆ k ı 8. b B ı and b S = ˆ k 9. b
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## This note was uploaded on 02/18/2010 for the course PHYS 303l taught by Professor Panab during the Spring '04 term at North Texas.

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hw11sol - Flores, Michael Homework 11 Due: Apr 12 2004,...

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