# Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation.

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1 Use the following to answer question 1. Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation. 1. Which combination of charges would yield the greatest repulsive force between the charges? A) 2q and 4q B) +1q and 3q C) 1q and 4q D) 2q and +4q E) +1q and +7q 2. A laser emits a single, 2.0-ms pulse of light that has a frequency of Hz and a total power of W. How many photons are in the pulse? A) B) C) D) E) Use the following to answer question 3. Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation. 3. Which combination of charges will yield zero electric field at the point x? A) +1q and 1q B) +2q and 3q C) +1q and 4q D) 1q and +4q E) +4q and +4q

2 Use the following to answer questions 4-6. A solid, conducting sphere of radius a carries an excess charge of +6 µc. This sphere is located at the center of a hollow, conducting sphere with an inner radius of b and an outer radius of c as shown. The hollow sphere also carries a total excess charge of +6 µc. 4. Determine the excess charge on the inner surface of the outer sphere (a distance b from the center of the system). A) zero coulombs B) 6?C C) +6?C D) +12?C E) 12?C 5. Determine the excess charge on the outer surface of the outer sphere (a distance c from the center of the system). A) zero coulombs B) 6?C C) +6?C D) +12?C E) 12?C 6. Which one of the following figures shows a qualitatively accurate sketch of the electric field lines in and around this system?

3 7. A charged conductor is brought near an uncharged insulator. Which one of the following statements is true? A) Both objects will repel each other. B) Both objects will attract each other. C) Neither object exerts an electrical force on the other. D) The objects will repel each other only if the conductor has a negative charge. E) The objects will attract each other only if the conductor has a positive charge. 8. Three charged particles A, B, and C are located near one another. Both the magnitude and direction of the force that particle A exerts on particle B is independent of A) the sign of charge B. B) the sign of charge A. C) the distance between C and B. D) the distance between A and B. E) the magnitude of the charge on B. 9. Two positive point charges Q and 2Q are separated by a distance R. If the charge Q experiences a force of magnitude F when the separation is R, what is the magnitude of the force on the charge 2Q when the separation is 2R? A) F/4 B) F/2 C) F D) 2F E) 4F

4 10. Four point charges are held fixed at the corners of a square as shown in the figure. Which of the five arrows shown below most accurately shows the direction of the net force on the charge Q due to the presence of the three other charges? A) B) C) D) E) 11. Which one of the following statements is true concerning the magnitude of the electric field at a point in space? A) It is a measure of the total charge on the object. B) It is a measure of the electric force on any charged object. C) It is a measure of the ratio of the charge on an object to its mass. D) It is a measure of the electric force per unit mass on a test charge. E) It is a measure of the electric force per unit charge on a test charge. 12. At which point (or points) is the electric field zero N/C for the two point charges shown on the x axis? A) The electric field is never zero in the vicinity of these charges. B) The electric field is zero somewhere on the x axis to the left of the +4q charge. C) The electric field is zero somewhere on the x axis to the right of the 2q charge. D) The electric field is zero somewhere on the x axis between the two charges, but this point is nearer to the 2q charge. E) The electric field is zero at two points along the x axis; one such point is to the right of the 2q charge and the other is to the left of the +4q charge.

5 13. Which one of the following statements is true concerning the strength of the electric field between two oppositely charged parallel plates? A) It is zero midway between the plates. B) It is a maximum midway between the plates. C) It is a maximum near the positively charged plate. D) It is a maximum near the negatively charged plate. E) It is constant between the plates except near the edges. 14. Complete the following statement: The magnitude of the electric field at a point in space does not depend upon A) the distance from the charge causing the field. B) the sign of the charge causing the field. C) the magnitude of the charge causing the field. D) the force that a unit positive charge will experience at that point. E) the force that a unit negative charge will experience at that point. 15. Which one of the following statements best explains why it is possible to define an electrostatic potential in a region of space that contains an electrostatic field? A) Work must be done to bring two positive charges closer together. B) Like charges repel one another and unlike charges attract one another. C) A positive charge will gain kinetic energy as it approaches a negative charge. D) The work required to bring two charges together is independent of the path taken. E) A negative charge will gain kinetic energy as it moves away from another negative charge. 16. The electric potential at a certain point is space is 12 V. What is the electric potential energy of a 3.0?C charge placed at that point? A) +4?J B) 4?J C) +36?J D) 36?J E) zero µj 17. Two positive point charges are separated by a distance R. If the distance between the charges is reduced to R/2, what happens to the total electric potential energy of the system? A) It is doubled. B) It remains the same. C) It increases by a factor of 4. D) It is reduced to one-half of its original value. E) It is reduced to one-fourth of its original value.

6 18. Two point charges are arranged along the x axis as shown in the figure. At which of the following values of x is the electric potential equal to zero? Note: At infinity, the electric potential is zero. A) m B) m C) m D) m E) m 19. Three point charges Q, Q, and +3Q are arranged along a line as shown in the sketch. What is the electric potential at the point P? A) +kq/r B) 2kQ/R C) 1.6kQ/R D) +1.6kQ/R E) +4.4kQ/R 20. If the work required to move a C charge from point A to point B is +125 J, what is the potential difference between the two points? A) zero volts B) 44 V C) 88 V D) 180 V E) 360 V

7 Use the following to answer questions Four point charges are individually brought from infinity and placed at the corners of a square as shown in the figure. Each charge has the identical value +Q. The length of the diagonal of the square is 2a. 21. What is the magnitude of the electric field at P, the center of the square? A) kq/a2 B) 2kQ/a2 C) 4kQ/a2 D) kq/4a2 E) zero V/m 22. What is the electric potential at P, the center of the square? A) kq/a B) 2kQ/a C) 4kQ/a D) kq/4a E) zero volts Use the following to answer questions Two charges of opposite sign and equal magnitude Q = 2.0 C are held 2.0 m apart as shown in the figure. 23. Determine the magnitude of the electric field at the point P. A) V/m B) V/m C) V/m D) V/m E) zero V/m

8 24. Determine the electric potential at the point P. A) V B) V C) V D) V E) zero volts 25. Which one of the following statements concerning electrostatic situations is false? A) E is zero everywhere inside a conductor. B) Equipotential surfaces are always perpendicular to E. C) It takes zero work to move a charge along an equipotential surface. D) If V is constant throughout a region of space then E must be zero in that region. E) No force component acts along the path of a charge as it is moved along an equipotential surface. 26. The magnitude of the charge on the plates of an isolated parallel plate capacitor is doubled. Which one of the following statements is true concerning the capacitance of this parallel-plate system? A) The capacitance is decreased to one half of its original value. B) The capacitance is increased to twice its original value. C) The capacitance remains unchanged. D) The capacitance depends on the electric field between the plates. E) The capacitance depends on the potential difference across the plates. 27. A parallel plate capacitor with plates of area A and plate separation d is charged so that the potential difference between its plates is V. If the capacitor is then isolated and its plate separation is decreased to d/2, what happens to the potential difference between the plates? A) The potential difference is increased by a factor of four. B) The potential difference is twice it original value. C) The potential difference is one half of its original value. D) The potential difference is one fourth of its original value. E) The potential difference is unchanged. 28. Which one of the following changes will necessarily increase the capacitance of a capacitor? A) decreasing the charge on the plates B) increasing the charge on the plates C) placing a dielectric between the plates D) increasing the potential difference between the plates E) decreasing the potential difference between the plates

9 29. A potential difference of 120 V is established between two parallel metal plates. The magnitude of the charge on each plate is C. What is the capacitance of this capacitor? A) 170 µc B) 24 µc C) 7.2 µc D) 0.12 C E) 2.4 C Use the following to answer questions Two positive charges are located at points A and B as shown in the figure. The distance from each charge to the point P is a = 2.0 m. 30. Which statement is true concerning the direction of the electric field at P? A) The direction is toward A. B) The direction is toward B. C) The direction is directly away from A. D) The direction makes a 45 angle above the horizontal direction. E) The direction makes a 135 angle below the horizontal direction. 31. Determine the electric potential at the point P. A) V B) V C) V D) V E) V 32. Which one of the following circuits has the largest resistance?

10 33. Which one of the following statements concerning resistance is true? A) The resistance of a semiconductor increases with temperature. B) Resistance is a property of resistors, but not conductors. C) The resistance of a metal wire changes with temperature. D) The resistance is the same for all samples of the same material. E) The resistance of a wire is inversely proportional to the length of the wire. 34. Complete the following statement: The unit kilowatt hour measures A) current. B) energy. C) power. D) potential drop. E) voltage. 35. Which one of the following quantities can be converted to kilowatt hours (kwh)? A) 2.0 A B) 8.3 V C) 5.8 J D) 9.6 W E) 6.2 C/V 36. A 40-W and a 60-W light bulb are designed for use with the same voltage. What is the ratio of the resistance of the 60-W bulb to the resistance of the 40-W bulb? A) 1.5 B) 0.67 C) 2.3 D) 0.44 E) A 220-? resistor is connected across an ac voltage source V = (150 V) sin [2?(60 Hz)t]. What is the average power delivered to this circuit? A) 51 W B) 110 W C) 280 W D) 320 W E) 550 W

11 Use the following to answer questions The figure shows variation of the current through the heating element with time in an iron when it is plugged into a standard 120 V, 60 Hz outlet. 38. What is the peak voltage? A) 10 V B) 60 V C) 120 V D) 170 V E) 240 V 39. What is the rms value of the current in this circuit? A) 1.4 A B) 7.1 A C) 11 A D) 14 A E) 18 A 40. What is the approximate average power dissipated in the iron? A) 450 W B) 600 W C) 850 W D) 1200 W E) 1700 W 41. Which one of the following statements concerning resistors in series is true? A) The voltage across each resistor is the same. B) The current through each resistor is the same. C) The power dissipated by each resistor is the same. D) The rate at which charge flows through each resistor depends on its resistance. E) The total current through the resistors is the sum of the current through each resistor.

12 42. Some light bulbs are connected in parallel to a 120 V source as shown in the figure. Each bulb dissipates an average power of 60 W. The circuit has a fuse F that burns out when the current in the circuit exceeds 9 A. Determine the largest number of bulbs, which can be used in this circuit without burning out the fuse. A) 9 B) 17 C) 25 D) 34 E) 36 Use the following to answer questions Three resistors are connected as shown in the figure. The potential difference between points A and B is 26 V. 43. How much current flows through the 3-? resistor? A) 2.0 A B) 4.0 A C) 6.0 A D) 8.7 A E) 10.0 A 44. How much current flows through the 2-? resistor? A) 2.0 A B) 4.0 A C) 6.0 A D) 8.7 A E) 10.0 A

13 Use the following to answer questions Three resistors are placed in a circuit as shown. The potential difference between points A and B is 30 V. 45. What is the equivalent resistance between the points A and B? A) 10? B) 20? C) 30? D) 50? E) 100? 46. What is the potential drop across the 30-? resistor? A) 10 V B) 20 V C) 30 V D) 60 V E) 100 V 47. How much energy is stored in the combination of capacitors shown? A) 0.01 J B) 0.02 J C) 0.03 J D) 0.04 J E) 0.05 J

14 Use the following to answer question 48. The figure shows a simple RC circuit consisting of a V battery in series with a 10.0-µF capacitor and a resistor. Initially, the switch S is open and the capacitor is uncharged. Two seconds after the switch is closed, the voltage across the resistor is 37 V. 48. How much charge is on the capacitor 2.0 s after the switch is closed? A) C B) C C) C D) C E) C 49. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true? A) It is a maximum if the particle is stationary. B) It is zero if the particle moves perpendicular to the field. C) It is a maximum if the particle moves parallel to the field. D) It acts in the direction of motion for a positively charged particle. E) It depends on the component of the particle's velocity that is perpendicular to the field. 50. Complete the following statement: The magnitude of the magnetic force that acts on a charged particle in a magnetic field is independent of A) the sign of the charge. B) the magnitude of the charge. C) the magnitude of the magnetic field. D) the direction of motion of the particle. E) the velocity components of the particle. 51. Which one of the following will not generate electromagnetic waves or pulses? A) a steady direct current B) an accelerating electron C) a proton in simple harmonic motion D) an alternating current E) charged particles traveling in a circular path in a mass spectrometer

15 52. Which one of the following statements best explains why a constant magnetic field can do no work on a moving charged particle? A) The magnetic field is conservative. B) The magnetic force is a velocity dependent force. C) The magnetic field is a vector and work is a scalar quantity. D) The magnetic force is always perpendicular to the velocity of the particle. E) The electric field associated with the particle cancels the effect of the magnetic field on the particle. 53. An electron traveling horizontally enters a region where a uniform magnetic field is directed into the plane of the paper as shown. Which one of the following phrases most accurately describes the motion of the electron once it has entered the field? A) upward and parabolic B) upward and circular C) downward and circular D) upward, along a straight line E) downward and parabolic 54. An electron enters a region that contains a magnetic field directed into the page as shown. The velocity vector of the electron makes an angle of 30 with the +y axis. What is the direction of the magnetic force on the electron when it enters the field? A) up, out of the page B) at an angle of 30 below the positive x axis C) at an angle of 30 above the positive x axis D) at an angle of 60 below the positive x axis E) at an angle of 60 above the positive x axis

16 55. A current-carrying, rectangular coil of wire is placed in a magnetic field. The magnitude of the torque on the coil is not dependent upon which one of the following quantities? A) the magnitude of the current in the loop B) the direction of the current in the loop C) the length of the sides of the loop D) the area of the loop E) the orientation of the loop 56. A long, straight wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what is the magnitude of the magnetic field at a distance 2d from the wire? A) B/2 B) B/4 C) 2B D) 4B E) 8B 57. Two long, straight wires are perpendicular to the plane of the paper as shown in the drawing. Each wire carries a current of magnitude I. The currents are directed out of the paper toward you. Which one of the following expressions correctly gives the magnitude of the total magnetic field at the origin of the x, y coordinate system? A) B) C) D) E)

17 Use the following to answer questions A wire is bent into the shape of a circle of radius r = 0.10 m and carries a 20.0-A current in the direction shown. 58. What is the direction of the magnetic field at the center of the loop? A) to the right of the page B) to the left of the page C) toward the top of the page D) into the plane of the paper E) out of the plane of the paper 59. What is the magnitude of the magnetic field at the center of the loop? A) T B) T C) T D) T E) zero tesla 60. Determine the magnetic moment of the loop. A) 0.20 A m2 B) 0.40 A m2 C) 0.63 A m2 D) 0.84 A m2 E) 1.3 A m2 61. A conducting loop of wire is placed in a magnetic field that is normal to the plane of the loop. Which one of the following actions will not result in an induced current in the loop? A) Rotate the loop about an axis that is parallel to the field and passes through the center of the loop. B) Increase the strength of the magnetic field. C) Decrease the area of the loop. D) Decrease the strength of the magnetic field. E) Rotate the loop about an axis that is perpendicular to the field and passes through the center of the loop.

18 62. A 0.50-T magnetic field is directed perpendicular to the plane of a circular loop of radius 0.25 m. What is the magnitude of the magnetic flux through the loop? A) Wb B) Wb C) 0.20 Wb D) 0.39 Wb E) zero Wb 63. A long, straight wire is in the same plane as a rectangular, conducting loop. The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop? A) There will be no induced emf and no induced current. B) There will be an induced emf, but no induced current. C) There will be an induced current that is clockwise around the loop. D) There will be an induced current that is counterclockwise around the loop. E) There will be an induced electric field that is clockwise around the loop. Use the following to answer questions A circuit is pulled with a 16-N force toward the right to maintain a constant speed v. At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. As the circuit moves, a 6.0-A current flows through a 4.0-? resistor. 64. Which one of the following statements concerning this situation is true? A) The temperature of the circuit remains constant. B) The induced current flows clockwise around the circuit. C) Since the circuit moves with constant speed, the force F does zero work. D) If the circuit were replaced with a wooden loop, there would be no induced emf. E) As the circuit moves through the field, the field does work to produce the current.

19 65. With what speed does the circuit move? A) 1.5 m/s B) 3.0 m/s C) 6.4 m/s D) 9.0 m/s E) 12 m/s 66. Determine the energy stored in a 95-mH inductor that carries a 1.4-A current. A) 0.38 J B) 0.27 J C) 0.19 J D) J E) J 67. Two coils share a common axis as shown in the figure. The mutual inductance of this pair of coils is 6.0 mh. If the current in coil 1 is changing at the rate of 3.5 A/s, what is the magnitude of the emf generated in coil 2? A) V B) V C) V D) V E) V

20 Use the following to answer questions Two coils, 1 and 2, with iron cores are positioned as shown in the figure. Coil 1 is part of a circuit with a battery and a switch. 68. Immediately after the switch S is closed, which one of the following statements is true? A) An induced current will flow from right to left in R. B) An induced current will flow from left to right in r. C) A magnetic field that points toward B appears inside coil 1. D) An induced magnetic field that points toward B appears inside coil 2. E) A current will pass through r, but there will be no current through R. 69. Assume the switch S has been closed for a long time. Which one of the following statements is true? A) An induced current will flow from right to left in R. B) An induced current will flow from left to right in r. C) A magnetic field that points toward B appears inside coil 1. D) An induced magnetic field that points toward B appears inside coil 2. E) A current will pass through r, but there will be no current through R. 70. In the drawing, a coil of wire is wrapped around a cylinder from which an iron core

21 extends upward. The ends of the coil are connected to an ac voltage source. After the alternating current is established in the coil, an aluminum ring of resistance R is placed onto the iron core and released. Which one of the following statements concerning this situation is false? A) The induced current in the ring is an alternating current. B) The temperature of the ring will increase. C) At any instant, the direction of the induced current in the ring is in the same direction as that in the coil. D) The induced magnetic field in the ring may by directed either upward or downward at an instant when the direction of the magnetic field generated by the current in the coil is upward. E) The ring may remain suspended at the position shown with no vertical movement of its center of mass. 71. A transformer changes 120 V across the primary to 1200 V across the secondary. If the secondary coil has 800 turns, how many turns does the primary coil have? A) 40 B) 80 C) 100 D) 400 E) 4000

22 Use the following to answer questions A loop with a resistance of 2.0? is pushed to the left at a constant speed of 4.0 m/s by a 32 N force. At the instant shown in the figure, the loop is partially in and partially out of a uniform magnetic field. An induced current flows from left to right through the resistor. The length and width of the loop are 2.0 m and 1.0 m, respectively. 72. What is the direction of the magnetic field? A) to the left B) to the right C) out of the paper D) into the paper E) toward the top of the page 73. Determine the magnitude of the induced current through the resistor. A) 2.0 A B) 4.0 A C) 8.0 A D) 16 A E) 32 A Use the following to answer question 74. A flexible, circular conducting loop of radius 0.15 m and resistance 4.0? lies in a uniform magnetic field of 0.25 T. The loop is pulled on opposite sides by equal forces and stretched until its enclosed area is essentially zero m2, as suggested in the drawings. It takes 0.30 s to close the loop. 74. Which one of the following phrases best describes the direction of the induced magnetic field generated by the current induced in the loop while the loop is being stretched? A) clockwise B) counterclockwise C) into the page D) out of the page E) The induced field is zero.

23 75. An ac voltage source that has a frequency f is connected across the terminals of a capacitor. Which one of the following statements correctly indicates the effect on the capacitive reactance when the frequency is increased to 4f? A) The capacitive reactance increases by a factor of four. B) The capacitive reactance increases by a factor of eight. C) The capacitive reactance is unchanged. D) The capacitive reactance decreases by a factor of eight. E) The capacitive reactance decreases by a factor of four. 76. The current in a certain ac circuit is independent of the frequency at a given voltage. Which combination of elements is most likely to comprise the circuit? A) resistors only B) inductors only C) capacitors only D) a combination of inductors and resistors E) a combination of inductors and capacitors Use the following to answer questions The graph shows the voltage across and the current through a single circuit element connected to an ac generator. 77. Determine the frequency of the generator. A) 0.14 Hz B) 7.14 Hz C) 12.5 Hz D) 25.0 Hz E) 50.0 Hz 78. Determine the rms voltage across this element. A) 49.5 V B) 70.0 V C) 112 V D) 140 V E) 170 V

24 79. Determine the rms current through this element. A) 1.4 A B) 2.0 A C) 3.4 A D) 3.9 A E) 5.6 A 80. What is the reactance of this element? A) 20? B) 25? C) 30? D) 35? E) 40? 81. Identify the circuit element. A) The element is a 25-? resistor. B) The element is a 35-? resistor. C) The element is a 0.45-H inductor. D) The element is a 360-µF capacitor. E) The element is a 510-µF capacitor. 82. Note the following circuit elements: (1) resistors, (2) capacitors, and (3) inductors. Which of these elements uses no energy, on average, in an ac circuit? A) 1 only B) 2 only C) 3 only D) both 2 and 3 E) both 1 and A 7.70-µF capacitor and a 1250-? resistor are connected in series to a generator operating at 50.0 Hz and producing an rms voltage of 208 V. What is the average power dissipated in this circuit? A) 346 W B) 31.2 W C) 19.7 W D) 1.66 W E) zero watts 84. A series RCL circuit contains a 222-? resistor, a 1.40-µF capacitor, and a H inductor. The 444-Hz ac generator in the circuit has an rms voltage of 208 V. What is the average electric power dissipated by the circuit? A) 135 W B) 81 W C) 166 W D) 191 W E) 102 W

25 85. The electric field E of an electromagnetic wave traveling the positive x direction is illustrated in the figure. This is the wave of the radiation field of an antenna. What is the direction and the phase relative to the electric field of the magnetic field at a point where the electric field is in the negative y direction? Note: The wave is shown in a region of space that is a large distance from its source. A) +y direction, in phase B) z direction, 90 out of phase C) +z direction, 90 out of phase D) z direction, in phase E) +z direction, in phase 86. A television station broadcasts at a frequency of 86 MHz. The circuit contains an inductor with an inductance L = H and a variable-capacitance C. Determine the value of C that allows this television station to be tuned in. A) F B) F C) F D) F E) F 87. Which one of the following types of wave is intrinsically different from the other four? A) radio waves B) sound waves C) gamma rays D) ultraviolet radiation E) visible light 88. Which one of the following statements concerning electromagnetic waves is false? A) Electromagnetic waves carry energy. B) X-rays have longer wavelengths than radio waves. C) In vacuum, all electromagnetic waves travel at the same speed. D) Lower frequency electromagnetic waves can be produced by oscillating circuits. E) They consist of mutually perpendicular electric and magnetic fields that oscillate perpendicular to the direction of propagation.

26 89. Which one of the following statements concerning the wavelength of an electromagnetic wave in a vacuum is true? A) The wavelength is independent of the speed of the wave for a fixed frequency. B) The wavelength is inversely proportional to the speed of the wave. C) The wavelength is the same for all types of electromagnetic waves. D) The wavelength is directly proportional to the frequency of the wave. E) The wavelength is inversely proportional to the frequency of the wave. 90. Complete the following sentence: The various colors of visible light differ in A) frequency only. B) wavelength only. C) their speeds in a vacuum. D) frequency and wavelength. E) frequency and their speed in a vacuum. 91. When a radio telescope observes a region of space between two stars, it detects electromagnetic radiation that has a wavelength of 0.21 m. This radiation was emitted by hydrogen atoms in the gas and dust located in that region. What is the frequency of this radiation? A) Hz B) Hz C) Hz D) Hz E) Hz 92. A radio wave sent from the surface of the earth reflects from the surface of the moon and returns to the earth. The elapsed time between the generation of the wave and the detection of the reflected wave is s. Determine the distance from the surface of the earth to the surface of the moon. Note: The speed of light is m/s. A) m B) m C) m D) m E) m 93. An electromagnetic wave has an electric field with peak value N/C. What is the average energy delivered to a surface with area 2.00 m2 by this wave in one minute? A) 83.1 J B) 166 J C) 2490 J D) 4980 J E) 9960 J

27 94. An incandescent light bulb radiates uniformly in all directions with a total average power of W. What is the maximum value of the magnetic field at a distance of 0.50 m from the bulb? A) T B) T C) T D) T E) zero tesla 95. Electromagnetic waves are radiated uniformly in all directions from a source. The rms electric field of the waves is measured 35 km from the source to have an rms value of 0.42 N/C. Determine the average total power radiated by the source. A) W B) W C) W D) W E) W 96. The most convincing evidence that electromagnetic waves are transverse waves is that A) they can be polarized. B) they carry energy through space. C) they can travel through a material substance. D) they do not require a physical medium for propagation. E) all electromagnetic waves travel with the same speed through vacuum. 97. Two polarizing sheets have their transmission axes parallel so that the intensity of unpolarized light transmitted through both of them is a maximum. Through what angle must either sheet be rotated if the transmitted intensity is 25 % of the incident intensity? A) 15 B) 30 C) 45 D) 60 E) 75

28 Use the following to answer questions The figure shows the time variation of the magnitude of the electric field of an electromagnetic wave produced by a wire antenna. 98. Determine the rms value of the electric field magnitude. A) 7.1 N/C B) 12 N/C C) 14 N/C D) 19 N/C E) 28 N/C 99. What is the rms value of the magnitude of the magnetic field? A) T B) T C) T D) T E) T 100. Determine the frequency of the wave. A) Hz B) Hz C) Hz D) Hz E) Hz 101. Determine the wavelength of the wave. A) 0.30 m B) 0.60 m C) 0.79 m D) 1.2 m E) 2.3 m 102. What is the average intensity of this electromagnetic wave? A) 0.13 W/m2 B) 0.26 W/m2 C) 0.33 W/m2 D) 0.36 W/m2 E) 0.54 W/m The speed of light in material A is 1.25 times as large as it is in material B. What is the ratio of the refractive indices, na/nb, of these materials? A) 1.50 B) 1.25 C) 1.00 D) 0.90 E) 0.800

29 104. A beam of light passes from air into water. Which is necessarily true? A) The frequency is unchanged and the wavelength increases. B) The frequency is unchanged and the wavelength decreases. C) The wavelength is unchanged and the frequency decreases. D) Both the wavelength and frequency increase. E) Both the wavelength and frequency decrease Complete the following statement: Fiber optics make use of A) total internal reflection. B) polarization. C) chromatic aberration. D) Brewster's angle. E) dispersion A glass block with an index of refraction of 1.7 is immersed in an unknown liquid. A ray of light inside the block undergoes total internal reflection as shown in the figure. Which one of the following relations best indicates what may be concluded concerning the index of refraction of the liquid, nl? A) nl < 1.0 B) nl > 1.1 C) nl > 1.3 D) nl < 1.1 E) nl < A child is looking at a reflection of the sun in a pool of water. When she puts on a pair of Polaroid sunglasses with a vertical transmission axis, she can no longer see the reflection. At what angle is she looking at the pool of water? A) 45.0 B) 48.8 C) 53.1 D) 61.6 E) 77.3

### A) m B) m C) m D) m E) m. 5. Which one of the following circuits has the largest resistance?

Use the following to answer question 1. Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation. 1. Which combination of charges would yield

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