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HW09-solutions

# HW09-solutions - Munoz(gm7794 HW09 TSOI(92515 This...

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Munoz (gm7794) – HW09 – TSOI – (92515) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points A helium-neon laser intended for classroom produces 4 . 1 mW of light power. At a point where the cross section of the beam has an area of 2 . 1 mm 2 , what is the maximum value of the electric field E ? The permeability of free space is 1 . 25664 × 10 - 6 N / A 2 and the speed of light is 2 . 99792 × 10 8 m / s. Correct answer: 1212 . 87 N / C. Explanation: Let : P = 4 . 1 mW = 0 . 0041 W , A = 2 . 1 mm 2 = 2 . 1 × 10 - 6 m 2 , μ 0 = 1 . 25664 × 10 - 6 N / A 2 , and c = 2 . 99792 × 10 8 m / s . The intensity I of the beam is given by I = P A . LASER L face B face A This is related to the electric and magnetic field peak amplitudes by I = E max B max 2 μ 0 = E 2 max 2 μ 0 c , so E 2 max = 2 c μ 0 I = 2 μ 0 c P A and E max = 2 μ 0 c P A = 2 (1 . 25664 × 10 - 6 N / A 2 ) × 2 . 99792 × 10 8 m / s × 0 . 0041 W 2 . 1 × 10 - 6 m 2 = 1212 . 87 N / C . 002 (part 2 of 3) 10.0 points What is the electromagnetic energy in a beam of length 1 . 9 m? Correct answer: 2 . 59846 × 10 - 11 J. Explanation: The amount of energy that has passed through face A of a column is P t , after a time t . For t < L c , the energy passing through face A has not passed through face B . Hence, in this time interval all the energy that has passed through face A is within the column, so the energy stored in the column is U = P L c = (0 . 0041 W) (1 . 9 m) 2 . 99792 × 10 8 m / s = 2 . 59846 × 10 - 11 J . Alternate Solution: The amount of energy U in a column of light with volume V is U = u V where u is the energy per unit volume. For an electromagnetic wave u = 1 2 0 E 2 max , so the total energy is U = u V = 1 2 0 E 2 max A L = 1 2 (7 . 15207 × 10 22 C 2 / N · m 2 ) × (1212 . 87 N / C) 2 (2 . 1 mm 2 ) (1 . 9 m) = 2 . 59846 × 10 - 11 J . 003 (part 3 of 3) 10.0 points What is the corresponding momentum of the beam? Correct answer: 8 . 66754 × 10 - 20 J · s / m. Explanation: Let U be the energy. The momentum is p = U c = 2 . 59846 × 10 - 11 J 2 . 99792 × 10 8 m / s = 8 . 66754 × 10 - 20 J · s / m .

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Munoz (gm7794) – HW09 – TSOI – (92515) 2 004 (part 1 of 2) 10.0 points Lasers have been used to suspend spherical glass beads in the Earth’s gravitational field. A bead has a mass of 10 μ g and a density of 0 . 4 g / cm 3 . The laser beam is larger than the glass bead with a radius 1230 μ m and fully impinges on the bead. Assume complete absorption. The acceleration of gravity is 9 . 8 m / s 2 .
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HW09-solutions - Munoz(gm7794 HW09 TSOI(92515 This...

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