1. Chapter 21 Magnetic Forces and Magnetic Fields

5. Chapter 21: Magnetic Forces and Magnetic Fields Section 1: Magnetic Fields

8. The needle of a compass is permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other.

9. The behavior of magnetic poles is similar to that of like and unlike electric charges.

10. Magnetic Fields Surrounding a magnet there is a magnetic field . The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point.

12. Magnetic Field Lines The magnetic field lines and pattern of iron filings in the vicinity of a bar magnet and the magnetic field lines in the gap of a horseshoe magnet.

13. Earth’s Magnetic Field Lines

14. 21.1.1. Consider the two rectangular areas shown with a point P located at the midpoint between the two areas. The rectangular area on the left contains a bar magnet with the south pole near point P. The rectangle on the right is initially empty. How will the magnetic field at P change, if at all, when a second bar magnet is placed on the right rectangle with its south pole near point P? a) The direction of the magnetic field will not change, but its magnitude will decrease. b) The direction of the magnetic field will not change, but its magnitude will increase. c) The magnetic field at P will be zero tesla. d) The direction of the magnetic field will change and its magnitude will increase. e) The direction of the magnetic field will change and its magnitude will decrease.

15. 21.1.2. Consider the two rectangular areas shown with a point P located at the midpoint between the two areas. The rectangular area on the left contains a bar magnet with the south pole near point P. The rectangle on the right is initially empty. How will the magnetic field at P change, if at all, when a second bar magnet is placed on the right rectangle with its north pole near point P? a) The direction of the magnetic field will not change, but its magnitude will decrease. b) The direction of the magnetic field will not change, but its magnitude will increase. c) The magnetic field at P will be zero tesla. d) The direction of the magnetic field will change and its magnitude will increase. e) The direction of the magnetic field will change and its magnitude will decrease.

16. 21.1.3. What is the direction of the magnetic field at the point P, directly below a point at the center of the magnet? The numbered arrows represent various directions. Direction “1” is to the right, “2” to the left, “3” is upward, “4” is downward, and “5” is toward you. a) 1 b) 2 c) 3 d) 4 e) 5

17. 21.1.4. Two rods are resting on a table. Although they appear to be identical, one is a permanent magnet and the other is made from soft iron and is not permanently magnetized. Which one of the following methods is most likely to reveal which rod is the magnet and which is the soft iron? a) Take one of the rods and touch it to each end of the other rod. b) Use a magnetic monopole to find the end of one of the rods that repels it. c) Move a compass along each rod to see if the compass needle behaves as it should in a magnetic field. d) There is no way to tell the difference between the two rods.

18. 21.1.5. You are given a bar magnet, but the poles are not labeled. Using which of the following items can you determine which end is a north pole and which is a south pole? a) a voltmeter b) a bottle of iron particles c) a charged rubber rod d) a compass e) a steel rod

19. Chapter 21: Magnetic Forces and Magnetic Fields Section 2: The Force That a Magnetic Field Exerts on a Moving Charge

21. The Force That a Magnetic Field Exerts on a Charge When a charge is placed in an electric field, it experiences a force, according to

25. Example 1 Magnetic Forces on Charged Particles A proton in a particle accelerator has a speed of 5.0x10 6 m/s. The proton encounters a magnetic field whose magnitude is 0.40 T and whose direction makes and angle of 30.0 degrees with respect to the proton’s velocity (see part (c) of the figure). Find (a) the magnitude and direction of the force on the proton and (b) the acceleration of the proton. (c) What would be the force and acceleration of the particle were an electron? (a) (b) (c) Magnitude of the force is the same, but direction is opposite.

26. 21.2.1. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true? a) The magnitude of the force is largest when the particle is not moving. b) The force is zero if the particle moves perpendicular to the field. c) The magnitude of the force is largest when the particle moves parallel to the direction of the magnetic field. d) The force depends on the component of the particle's velocity that is perpendicular to the field. e) The force acts in the direction of motion for a positively charged particle.

27. 21.2.2. An electron traveling due east in a region that contains only a magnetic field experiences a vertically downward force, toward the surface of the earth. What is the direction of the magnetic field? a) upward, away from the earth b) downward, toward the earth c) due north d) due west e) due south

28. 21.2.3. A charged particle is moving through a constant magnetic field. Does the magnetic field do work on the charged particle? a) yes, because the force is acting as the particle is moving through some distance b) no, because the magnetic force is always perpendicular to the velocity of the particle c) no, because the magnetic field is a vector and work is a scalar quantity d) no, because the magnetic field is conservative e) no, because the magnetic force is a velocity-dependent force

29. Chapter 21: Magnetic Forces and Magnetic Fields Section 3: The Motion of a Charged Particle in a Magnetic Field

33. Particle Motion in E & M Fields Charged particle in an electric field. Charged particle in a magnetic field.

34. Conceptual Example 2 A Velocity Selector A velocity selector is a device for measuring the velocity of a charged particle. The device operates by applying electric and magnetic forces to the particle in such a way that these forces balance. How should an electric field be applied so that the force it applies to the particle can balance the magnetic force? Using the right hand rule and looking only at the force created by the magnetic field, the particle would be directed: up Therefore the electric field must be directed: down

35. Work on particles The electrical force can do work on a charged particle. The magnetic force cannot do work on a charged particle.

36. Radius of circular motion The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path.

38. 21.3.1. An alpha particle (a helium nucleus which has a net positive charge) is moving due east when it enters a magnetic field that is directed due north. Which one of the following statements best describes the motion of the alpha particle after entering the magnetic field? a) The particle decelerates while traveling along a straight line until it stops. b) The particle continues at a constant speed, but its direction changes as it follows a circular path. c) The particle continues at a constant speed, but its direction changes as it follows a parabolic path. d) The particle slows and changes direction to accelerate to move due north. e) The particle slows and changes direction to accelerate to move directly upward.

39. 21.3.2. An electron is traveling due south in a region of space at a constant speed. What can you conclude from this situation regarding the presence any electric and/or magnetic fields? a) The electric field must be zero, but the magnetic field might be non-zero in the region. b) The magnetic field must be zero, but the electric field might be non-zero in the region. c) Both the electric and magnetic field might be non-zero, but they are perpendicular to each other in the region. d) Both the electric and magnetic field might be non-zero, but they point in opposite directions in the region. e) Both the electric and magnetic field must be zero in the region.

40. 21.3.3. A positively-charged particle is stationary in a constant magnetic field within a region of space. Which one of the following statements concerning the particle is true? a) The particle will not move. b) The particle will accelerate in the direction perpendicular to the field. c) The particle will accelerate in the direction parallel to the field. d) The particle will accelerate in the direction opposite to the field. e) The particle will move with constant velocity in the direction of the field.

41. 21.3.4. A negatively-charged particle travels parallel to magnetic field lines within a region of space. Which one of the following statements concerning the force exerted on the particle is true? a) The force is directed perpendicular to the magnetic field. b) The force is perpendicular to the direction in which the particle is moving. c) The force slows the particle. d) The force accelerates the particle. e) The force has a magnitude of zero newtons.

42. Chapter 21: Magnetic Forces and Magnetic Fields Section 4: The Mass Spectrometer (Not AP-B)

43. magnitude of electron charge KE=PE

44. Mass Spectrometer The mass spectrum of naturally occurring neon, showing three isotopes.

45. 21.4.1. For the mass spectrometer described in the text, the magnetic field is varied to allow ions of varying mass to reach the detector. A different method would be to maintain a constant magnetic field and vary the accelerating potential difference V . Assuming the magnetic field is held at B = 0.250 T and that r = 0.0750 m, in which of the following ranges of voltages could one detect both oxygen molecules ( m = 2.656  10  26 kg) and nitrogen molecules ( m = 2.325  10  26 kg). a) 4200 to 4900 V b) 3300 to 4500 V c) 5100 to 6000 V d) 2100 to 3100 V e) 4800 to 5700 V

46. 21.4.2. What must the initial state of motion of a charged particle be if it will follow a helical path in a magnetic field? a) It must be moving at an angle that is neither parallel to nor perpendicular to the magnetic field. b) It must be moving parallel to the magnetic field. c) It must be moving perpendicular to the magnetic field. d) It must be moving in the direction opposite to the magnetic field. e) It must be initially at rest when it is placed in the magnetic field.

47. Chapter 21: Magnetic Forces and Magnetic Fields Section 5: The Force on a Current in a Magnetic Field

49. Force on Current Carrying Wire The magnetic force on the moving charges pushes the wire to the right.

50. Example 5 The Force and Acceleration in a Loudspeaker The voice coil of a speaker has a diameter of 0.0025 m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A. (a) Determine the magnetic force that acts on the coil and the cone. (b) The voice coil and cone have a combined mass of 0.0200 kg. Find their acceleration. (a) (b)

51. 21.5.1. Three long, straight, identical wires are inserted one at a time into a magnetic field directed due east. Wire A carries a current of 2 A in the direction of 45  south of east. Wire B carries a current of 8 A, due north. Wire C carries a current of 10 A, due west. Rank the wires in terms of the magnitude of the magnetic force on each wire, with the largest force listed first and the smallest force listed last. a) A > B > C b) B > A > C c) C > B > A d) A > C > B e) B > C > A

52. 21.5.2. A portion of a loop of wire passes between the poles of a magnet as shown. We are viewing the circuit from above. When the switch is closed and a current passes through the circuit, what is the movement, if any, of the wire between the poles of the magnet? a) The wire moves toward the north pole of the magnet. b) The wire moves toward the south pole of the magnet. c) The wire moves upward (toward us). d) The wire moves downward (away from us). e) The wire doesn’t move.

53. Chapter 21: Magnetic Forces and Magnetic Fields Section 6: The Torque on a Current-Carrying Coil (Not AP-B)

54. Torque on Current Carrying Coil The two forces on the loop have equal magnitude but an application of RHR-1 shows that they are opposite in direction.

55. Torque on Current Carrying Coil The loop tends to rotate such that its normal becomes aligned with the magnetic field.

56. Torque on Current Carrying Coil number of turns of wire

58. Torque on Current Carrying Coil The basic components of a dc motor.

60. 21.6.1. Small charged disks are inserted into a larger, insulating disk. A compass is placed near the larger disk and points due north as shown. The larger disk is then rotated uniformly counterclockwise (as viewed from above). What, if anything, will happen? a) The north end of the compass will move toward the large disk as it rotates. b) The north end of the compass will move away from the large disk as it rotates. c) The compass will not be affected by the motion of the large disk. d) The north end of the compass will oscillate toward and away from the large disk as it rotates.

61. 21.6.2. A circular loop of wire is placed in a magnetic field such that the plane of the loop is perpendicular to the magnetic field. The loop is then connected to a battery and a current then flows through the loop. Which one of the following statements concerning this situation is true? a) The magnetic force exerts a net torque on the loop. b) The magnetic force exerts a net force on the loop. c) The magnetic force exerts both a net force and a net torque on the loop. d) The magnetic field has no affect on the loop.

62. Chapter 21: Magnetic Forces and Magnetic Fields Section 7: Magnetic Fields Produced by Currents (Straight Wires Only)

64. Right Hand Rule for Straight Currents Right-Hand Rule No. 2. Curl the fingers of the right hand into the shape of a half-circle. Point the thumb in the direction of the conventional current, and the tips of the fingers will point in the direction of the magnetic field.

65. Magnitude of Magnetic Field A LONG, STRAIGHT WIRE permeability of free space r : radius from center of wire

66. Example 7 A Current Exerts a Magnetic Force on a Moving Charge The long straight wire carries a current of 3.0 A. A particle has a charge of +6.5x10 -6 C and is moving parallel to the wire at a distance of 0.050 m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force on the particle.

67. Multiple Wires Current carrying wires can exert forces on each other.

70. Conceptual Example 9 The Net Force That a Current-Carrying Wire Exerts on a Current Carrying Coil Is the coil attracted to, or repelled by the wire? Coil would be attracted to the wire

71. Magnetic Field A SINGLE LOOP OF WIRE center of circular loop

72. Example 10 Finding the Net Magnetic Field A long straight wire carries a current of 8.0 A and a circular loop of wire carries a current of 2.0 A and has a radius of 0.030 m. Find the magnitude and direction of the magnetic field at the center of the loop.

73. Magnetic Fields Produced by Currents The field lines around the bar magnet resemble those around the loop.

75. A Solenoid Interior of a solenoid number of turns per unit length

76. A Cathode Ray Tube

77. 21.7.1. The drawing represents a device called Roget’s Spiral. A coil of wire hangs vertically and its windings are parallel to one another. One end of the coil is connected by a wire to a terminal of a battery. The other end of the coil is slightly submerged below the surface of a cup of mercury. Mercury is a liquid metal at room temperature. The bottom of the cup is also metallic and connected by a wire to a switch. A wire from the switch to the battery completes the circuit. What is the behavior of this circuit after the switch is closed? a) When current flows in the circuit, the coils of the wire move apart and the wire is extended further into the mercury. b) Nothing happens to the coil because there will not be a current in this circuit. c) A current passes through the circuit until all of the mercury is boiled away. d) When current flows in the circuit, the coils of the wire move together, causing the circuit to break at the surface of the mercury. The coil then extends and the process begins again when the circuit is once again complete.

78. 21.7.2. Three very long, parallel wires (a small portion of each is shown in the drawing) are resting on a flat surface. The distance between wire B, which has a 15 mA current to the left, and its neighbors is 0.0015 m. Wire A carries a 10 mA current toward the right; and wire C carries a 5 mA current toward the right. Rank the wires in order of the magnitude of the net magnetic force on each, with the largest value first and the lowest value last. a) A > B > C b) B > A > C c) C > B > A d) A > C > B e) B > C > A

79. 21.7.3. The drawing shows a rectangular wire loop that has one side passing through the center of a solenoid. Which one of the following statements describes the force, if any, that acts on the rectangular loop when a current is passing through the solenoid. a) The magnetic force causes the loop to move upward. b) The magnetic force causes the loop to move downward. c) The magnetic force causes the loop to move to the right. d) The magnetic force causes the loop to move to the left. e) The loop is not affected by the current passing through the solenoid or the magnetic field resulting from it.

80. 21.7.4. The coils of a solenoid are stretched so that the length of the solenoid is twice its original length. Assuming the same current is passed though the solenoid before and after it is stretched, how does the magnetic field inside the solenoid change, if at all, as a result of the stretching? a) The magnetic field after the stretching is one-fourth the value it was before stretching. b) The magnetic field after the stretching is one-half the value it was before stretching. c) The magnetic field after the stretching is the same as the value it was before stretching. d) The magnetic field after the stretching is twice the value it was before stretching. e) The magnetic field after the stretching is four times the value it was before stretching.

81. 21.7.5. The equation for the magnetic field of a straight, current carrying wire is given by , but the magnetic field at the center of a single closed circular loop is given by . Although these equations look similar, there is an important difference between these two equations, other that the factor of  . What is it? a) The µ 0 factor is different for the two situations. b) The variable R represents two different lengths. c) The I represents two different types of current.

82. 21.7.6. Complete the following statement: The magnetic field around a current-carrying, circular loop is most like that of a) the Earth. b) a current-carrying, rectangular loop c) a short bar magnet. d) a long, straight, current-carrying wire. e) two long, straight wires that carry currents in opposite directions.

83. 21.7.7. Two parallel wires have currents that have the same direction, but differing magnitude. The current in wire A is I ; and the current in wire B is 2 I . Which one of the following statements concerning this situation is true? a) Wire A attracts wire B with half the force that wire B attracts wire A. b) Wire A attracts wire B with twice the force that wire B attracts wire A. c) Both wires attract each other with the same amount of force. d) Wire A repels wire B with half the force that wire B attracts wire A. e) Wire A repels wire B with twice the force that wire B attracts wire A.

84. 21.7.8. Two parallel wires have currents that are in opposite directions and have differing magnitudes. The current in wire A is I ; and the current in wire B is 2 I . Which one of the following statements concerning this situation is true? a) Wire A attracts wire B with half the force that wire B attracts wire A. b) Wire A attracts wire B with twice the force that wire B attracts wire A. c) Both wires attract each other with the same amount of force. d) Wire A repels wire B with half the force that wire B attracts wire A. e) Wire A repels wire B with twice the force that wire B attracts wire A.

85. 21.7.9. The drawing shows two long, straight wires that are parallel to each other and carry a current of magnitude I toward you. The wires are separated by a distance d ; and the centers of the wires are a distance d from the y axis. 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) zero tesla

86. Chapter 21: Magnetic Forces and Magnetic Fields Section 8: Amp è re’s Law (Not AP-B)

87. AMPERE’S LAW FOR STATIC MAGNETIC FIELDS For any current geometry that produces a magnetic field that does not change in time, net current passing through surface bounded by path

88. Example 11 An Infinitely Long, Straight, Current-Carrying Wire Use Ampere’s law to obtain the magnetic field.

89. Chapter 21: Magnetic Forces and Magnetic Fields Section 9: Magnetic Materials (Not AP-B)

90. Magnetic Materials The intrinsic “spin” and orbital motion of electrons gives rise to the magnetic properties of materials. In ferromagnetic materials groups of neighboring atoms, forming magnetic domains, the spins of electrons are naturally aligned with each other.

91. Magnetic Materials

92. Magnetic Materials

93. 21.9.1. An initially unmagnetized iron bar is placed next to a solenoid. Which one of the following statements describes the iron bar after the solenoid is connected to the battery? a) A magnetic force accelerates the bar to the right. b) Since the bar is unmagnetized, there will not be any affect on the bar. c) The magnetic field of the solenoid will cause a current to flow in a loop that extends from one end of the bar to the other and that continues until the battery is disconnected from the solenoid. d) The magnetic field of the solenoid induces magnetism in the bar with the bar’s north pole nearest to the solenoid. e) The magnetic field of the solenoid induces magnetism in the bar with the bar’s south pole nearest to the solenoid.

94. END