Final_Exam_12_11_07_Solns

# Final_Exam_12_11_07_Solns - PHYSICS 222 FALL 2007 FINAL...

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PHYSICS 222 FALL 2007 FINAL EXAM SOLUTIONS TUESDAY, DECEMBER 11, 2007 Problems 61-80 are worth 4 points each 61. An 80-turn circular coil of radius 5.00 cm carries a current of 5.00 Amperes and lies in the x-y plane as shown in the figure. As viewed from the top (i.e., from the positive z-axis), the current is circulating in the coil in the clockwise direction. The magnetic field at the center of the coil is ____ . x y z coil A. (100 mT) k ˆ B. (100 mT) k ˆ C. (5 mT) k ˆ D. (5 mT) k ˆ E. (50 mT) k ˆ From the circular right-hand rule, the direction of the magnetic field at the center of the coil is in the k ˆ direction. The magnitude of the field is B = µ o NI 2R = (4 π × 10 7 T·m/A)(80)(5.00 A) 2(0.0500 m) = 5.03 × 10 3 T = 5.03 mT . 62. An ac current flows through an ideal inductor with an inductance of 2.11 mH. The current through the inductor is given by i(t) = (2.50 A) cos[(380 rad/s)t], where t is the time in seconds. The amplitude of the ac voltage across the inductor is ____ Volts. A. 1 B. 2 C. 3 D. 4 E. 5 V L = IX L = I ω L = (2.50 A)(380 rad/s)(2.11 × 10 3 H) = 2.00 Volts

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63. The wave function of a transverse wave on a stretched string is given by y(x,t) = (1.00 mm) cos[(126 rad/m)x] cos[(500 rad/s)t] . The wave is a ____ wave with a wavelength of ____ . A. standing, 0.050 m B. traveling, 0.010 m C. standing, 0.10 m D. traveling, 0.20 m E. standing, 0.15 m From the form of the wave function where the x and t dependences are separated into two sinusoidal functions, the wave is a standing wave. The wavelength is λ = 2 π k = 2 π 126 rad/m = 0.050 m . 64. A plane electromagnetic traveling wave in vacuum is polarized along the x-axis, has a wavenumber k, and moves in the positive y direction. If the amplitude of the electric field wave is designated as E 0 , a possible wave function of the electric field wave in the electromagnetic wave is ____ . (x, y, and z are Cartesian coordinates, c is the speed of light in vacuum, and t is the time) A. E 0 cos(kx ct) i ˆ B. E 0 sin(kx + ct) j ˆ C. E 0 sin[k(y ct)] i ˆ D. E 0 cos[k(y + ct)] k ˆ E. E 0 cos(kz ct) k ˆ For a traveling plane wave moving in the +y direction, the argument of the sinusoidal function has to be (ky ω t), where here ω = ck. Thus the argument becomes [k(y ct)]. The electric field axis is the axis of polarization of the wave, which here is the x-axis. Therefore the answer is C. 65. A microscope has an objective lens with a focal length of 1.00 cm and an eyepiece with a focal length of 2.50 cm. A small object to be viewed is 1.20 cm in front of the objective lens. The angular magnification of the microscope is ____ . A. 20 B. 30 C. 40 D. 50 E. 60 1 s 1 ' = 1 f 1 s 1 = 1 1.00 cm 1 1.20 cm = 1 6.00 cm , so s 1 ' = 6.00 cm . M = (25 cm)s 1 ' f 1 f 2 = (25 cm)(6.0 cm) (1.00 cm)(2.50 cm) = 60 .
66. Monochromatic light of wavelength 500 nm is normally incident on a diffraction grating with 5000 lines per cm. The second-order diffraction peak occurs at a diffraction angle of ____ degrees. A. 30 B. 40 C. 50 D. 60 E. 70 d = 0.01 m 5000 = 2.00 × 10 6 m . sin θ = m λ d = 2(5.00 × 10 7 m) 2.00 × 10 6 m = 1 2 , so θ = 30˚ .

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## This note was uploaded on 02/11/2012 for the course PHYSICS 222 taught by Professor Ogilvie during the Fall '05 term at Iowa State.

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Final_Exam_12_11_07_Solns - PHYSICS 222 FALL 2007 FINAL...

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