PHYSICS 253 SAMPLE FINAL EXAM. Student Number. The last two pages of the exam have some equations and some physical constants.

Transcription

1 PHYSICS 253 SAMPLE FINAL EXAM Name Student Number CHECK ONE: Instructor 1 10:00 Instructor 2 1:00 Note that problems 1-19 are worth 2 points each, while problem 20 is worth 15 points and problems 21 and 22 are worth 10 points each. There is only one correct answer for each of questions For numeric questions choose the closest answer given. For questions 20-22, for full credit explain what you are doing, round your final answer to three significant figures and give the units. The last two pages of the exam have some equations and some physical constants. PUT YOUR ANSWERS TO QUESTIONS 1-19 IN THE BOXES BELOW THIS LINE PLEASE DO NOT WRITE BELOW THIS LINE total for 1-19 score for 20 score for 21 score for 22 total for exam 1

2 Please put the letter of the correct answer for each question in the numbered box on the first page. 1. The electrostatic potential as a function of distance along a certain line in space is shown in graph (1). Which of the curves in graph (2) is most likely to represent the electric field as a function of distance along the same line? A) 1 B) 2 C) 3 D) 4 E) 5 2. An electric dipole that has a positive charge of C is separated from a negative charge of the same magnitude by m. The electric potential at a point m from each of the two charges is A) 9.4 V B) zero C) 4.2 V D) V E) 1.7 V 3. A metal ball of charge +Q is lowered into an insulated, uncharged metal shell and allowed to rest on the bottom of the shell. When the charges reach equilibrium, (a) the outside of the shell has a charge of Q and the ball has a charge of +Q. (b) the outside of the shell has a charge of +Q and the ball has a charge of +Q. (c) the outside of the shell has a charge of zero and the ball has a charge of +Q. (d) the outside of the shell has a charge of +Q and the ball has zero charge. (e) the outside of the shell has a charge of +Q and the ball has a charge of Q. 2

3 4. You connect three capacitors as shown in the diagram. C 1 = 5.0 :F, C 2 = 4.0 :F, and C 3 = 3.0 :F. What is the capacitance across A and B. A) 3.10 :F B) 0.56 :F C) 1.27 :F D) 2.25 :F E) 12.0 :F 5. Two identical capacitors A and B are connected across a battery, as shown. If mica (k = 5.4) is inserted in B, A) both capacitors will retain the same charge. B) B will have the larger charge. C) A will have the larger charge. D) the potential difference across B will increase. E) the potential difference across A will increase. 6. The current in a wire varies with time according to the relation I = 4+ 3t 2 where I is in amperes and t is in seconds. The number of coulombs of charge that pass a cross section of the wire between t = 3 s and t = 5 s is A) 12 B) 48 C) 52 D) 106 E) In this circuit, the current I through the battery is approximately A) 1.7 A B) 4.4 A C) 0.36 A D) 0.60 A E) 3.4 A 3

4 8. The region of space around a moving proton contains A) a gravitational field only. B) a magnetic field only. C) an electric field only. D) both an electric and a magnetic field. E) neither an electric nor a magnetic field. 9. The radius of the orbit of an electron moving with a speed of 6x10 7 m/s perpendicular to a magnetic field of 5.0x10 3 T is approximately A) 1.1 m B) m C) 0.34 m D) m E) 8.9 m 10. A wire rod rolls with a speed of 30 m/s on two metallic rails, 2.0 m apart, that form a closed loop. If the magnetic field is 1.5 T into the page, the power dissipated in the resistor R and the current direction are, respectively, A) 33 mw, clockwise. B) 33 mw, counterclockwise. C) 220 mw, counterclockwise. D) 686 mw, clockwise. E) 686 mw, counterclockwise. 11. Two identical bar magnets are dropped from equal heights. Magnet A is dropped over bare earth and magnet B over a metal plate. Which magnet strikes first? A) magnet A B) magnet B C) both strike at the same time D) whichever has its N pole toward the ground E) whichever has its S pole toward the ground 4

5 12. Maxwell's equations: (a) imply that the electric field due to a point charge varies inversely as the square of the distance from the charge. (b) describe how electric field lines diverge from a positive charge and converge on a negative charge. (c) assert that the flux of the magnetic field vector is zero through any closed surface. (d) describe the experimental observation that magnetic field lines do not diverge from any point space or converge to any point. E) All of these are correct. 13. An air prism is immersed in water. A ray of monochromatic light strikes one face as shown. The emerging ray is A) 1 B) 2 C) 3 D) 4 E) An object is placed 10 inches in front of a concave mirror that has a radius of curvature of 8 inches. The image is located A) 4.75 inches in front of the mirror. B) 4.75 inches behind the mirror. C) 3 inches behind the mirror. D) 6.67 inches behind the mirror. E) 6.67 inches in front of the mirror. 15. A converging lens and a screen are so arranged that an image of the sun falls on the screen. The distance from the lens to the screen is A) the focal length. B) the object distance. C) the magnifying power. D) one-half the radius of curvature of one of the lens faces. E) the average radius of curvature of the two lens faces. 5

6 16. The minimum path difference that will produce a phase difference of 180º for light of wavelength 600 nm is A) 600 nm B) 500 nm C) 300 nm D) 200 nm E) 100 nm 17. In an experiment to demonstrate interference of light, it is essential that A) coherent sources of light be used. B) the light paths differ by not more than one-half wavelength. C) the light be monochromatic. D) the beam of light be a parallel beam. E) there be no difference in light paths. 18. You illuminate two slits 0.50 mm apart with light of wavelength 555 nm and observe interference fringes on a screen 6.0 m away. What is the spacing between the fringes on the screen? A) 4.5 mm B) 3.3 mm C) 6.7 mm D) 10 mm E) 5.0 mm 19. When a parallel beam of light is diffracted at a single slit, A) the shadow is always sharp. B) the narrower the slit, the narrower the central diffraction maximum. C) the narrower the slit, the wider the central diffraction maximum. D) the width of the central diffraction maximum is independent of the width of the slit. E) None of these is correct. 6

7 ROUND ALL NUMERICAL ANSWERS TO 3 SIGNIFICANT FIGURES AND GIVE THE UNITS FOR FULL CREDIT EXPLAIN WHAT YOU ARE DOING Indicate your answer for EACH part clearly 15 points 20. A tomato seed is placed in front of a combination of two symmetrical lenses, 1 and 2. The focal points for lens 1 are 3 cm from the lens, and those for lens 2 are 6 cm from the lens. Lens 1 is converging and lens 2 is diverging. The separation of the lenses is 8.5 cm, and the seed is located 9 cm to the left of Lens 1. (a) Where does the system of 2 lenses produce an image of the seed? (b) Draw a ray diagram with two well know rays for each lens to verify your answer. lens 1 lens 2 (c) Is the final image real or virtual for an observer far to the right of Lens 2? Explain. (d) Is the final image inverted or not with respect to the original object? (e) The seed has a height of h = 2mm. What is the height of the image? 7

8 ROUND ALL NUMERICAL ANSWERS TO 3 SIGNIFICANT FIGURES AND GIVE THE UNITS FOR FULL CREDIT EXPLAIN WHAT YOU ARE DOING Indicate your answer for EACH part clearly 10 points 21. An electromagnetic wave is propagating in the x-direction. An electric dipole antenna is placed in the path of the wave and is oriented so that it points in the y-direction. By measuring the emf in the antenna we determine that the electric field has a maximum size of 50 V/m. (a) What is the maximum magnetic field associated with this wave? What is the direction of this magnetic field? (b) What is the maximum value of the Poynting vector? What is its direction? (c) What is the rms intensity of this wave? (d) Suppose that we now replace the antenna with a circular black disk of area 0.5 square meters, which completely absorbs the electromagnetic radiation that falls on it. What is the total force on this disk due to the wave? 8

9 ROUND ALL NUMERICAL ANSWERS TO 3 SIGNIFICANT FIGURES AND GIVE THE UNITS FOR FULL CREDIT EXPLAIN WHAT YOU ARE DOING Indicate your answer for EACH part clearly 10 points 22. The diameters of fine wires can be accurately measured using interference patterns. Two optically flat pieces of glass of length L are arranged with the wire between, as shown. The setup is illuminated by monochromatic light, and the resulting interference fringes are detected. d L Explain why a dark line or fringe appears near the point where the glass plates just touch each other. Suppose L = 20 cm and yellow sodium light with a wavelength of 590 nm is used for illumination. If 19 bright fringes are seen along this 20 cm distance, what are the limits on the diameter of the wire? 9