4. An electron moving in the positive x direction experiences a magnetic force in the positive z direction. If B x

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1 Magnetic Fields 3. A particle (q = 4.0 µc, m = 5.0 mg) moves in a uniform magnetic field with a velocity having a magnitude of 2.0 km/s and a direction that is 50 away from that of the magnetic field. The particle is observed to have an acceleration with a magnitude of 5.8 m/s 2. What is the magnitude of the magnetic field? a. 5.3 mt b. 4.9 mt c. 5.1 mt d. 4.7 mt e. 3.6 mt 4. An electron moving in the positive x direction experiences a magnetic force in the positive z direction. If B x = 0, what is the direction of the magnetic field? a. negative y direction b. positive y direction c. negative z direction d. positive z direction e. negative x direction 9. A positively charged particle has a velocity in the negative z direction at point P. The magnetic force on the particle at this point is in the negative y direction. Which one of the following statements about the magnetic field at point P can be determined from this data? a. B x is positive. b. B z is positive. c. B y is negative. d. B y is positive. e. B x is negative. 10. A charged particle (mass = 4.0 µg, charge = 5.0 µc) moves in a region where the only force on it is magnetic. What is the magnitude of the acceleration of the particle at a point where the speed of the particle is 5.0 km/s, the magnitude of the magnetic field is 8.0 mt, and the angle between the direction of the magnetic field and the velocity of the particle is 60? a. 39 km/s 2 b. 43 km/s 2 c. 48 km/s 2 d. 52 km/s 2 e. 25 km/s A charged particle (mass = M, charge = Q > 0) moves in a region of space where the magnetic field has a constant magnitude of B and a downward direction. What is the magnetic force on the particle at an instant when it is moving horizontally toward the north with speed V? a. QVB toward the east b. Zero c. QVB toward the west d. QVB upward e. QVB toward the south 13. A straight wire carries a current of 40 A in a uniform magnetic field (magnitude = 80 mt). If the force per unit length on this wire is 2.0 N/m, determine the angle between the wire and the magnetic field. a. either 39 or 141 b. either 25 or 155 c. either 70 or 110 d. either 42 or 138 e. either 65 or 115 1

2 2 CHAPTER A segment of wire carries a current of 25 A along the x axis from x = 2.0 m to x = 0 and then along the y axis from y = 0 to y = 3.0 m. In this region of space, the magnetic field is equal to 40 mt in the positive z direction. What is the magnitude of the force on this segment of wire? a. 2.0 N b. 5.0 N c. 1.0 N d. 3.6 N e. 3.0 N 17. What is the magnitude of the magnetic force on a charged particle (Q = 5.0 µc) moving with a speed of 80 km/s in the positive x direction at a point where B x = 5.0 T, B y = 4.0 T, and B z = 3.0 T? a. 2.8 N b. 1.6 N c. 1.2 N d. 2.0 N e. 0.4 N 18. A straight wire of length L carries a current I in the positive z direction in a region where the magnetic field is uniform and specified by B x = 3B, B y = 2B, and B z = B, where B is a constant. What is the magnitude of the magnetic force on the wire? a. 3.2 ILB b. 5.0 ILB c. 4.2 ILB d. 3.6 ILB e. 1.0 ILB 21. What is the magnetic force on a 2.0-m length of (straight) wire carrying a current of 30 A in a region where a uniform magnetic field has a magnitude of 55 mt and is directed at an angle of 20 away from the wire? a. 1.5 N b. 1.3 N c. 1.1 N d. 1.7 N e. 3.1 N 23. A current of 4.0 A is maintained in a single circular loop having a circumference of 80 cm. An external magnetic field of 2.0 T is directed so that the angle between the field and the plane of the loop is 20. Determine the magnitude of the torque exerted on the loop by the magnetic forces acting upon it. a N m b N m c N m d N m e N m 25. What current must be maintained in a square loop (50 cm on a side) to create a torque of 1.0 N m about an axis through its center and parallel to one of its sides when a magnetic field of magnitude 70 mt is directed at 40 to the plane of the loop? a. 66 A b. 89 A c. 61 A d. 75 A e. 37 A 29. A square loop (L = 0.20 m) consists of 50 closely wrapped turns, each carrying a current of 0.50 A. The loop is oriented as shown in a uniform magnetic field of 0.40 T directed in the positive y direction. What is the magnitude of the torque on the loop? a N m b N m c N m d N m e N m

3 Magnetic Fields A rectangular coil (0.20 m 0.80 m) has 200 turns and is in a uniform magnetic field of 0.30 T. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is N m. What is the current in the coil? a. 5.0 ma b. 1.7 A c. 8.3 ma d. 1.0 A e. 42 ma 31. A circular coil (radius = 0.40 m) has 160 turns and is in a uniform magnetic field. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is 0.16 N m when the current in the coil is 4.0 ma. What is the magnitude of the magnetic field? a T b. 1.6 T c T d. 1.2 T e. 2.5 T 33. A deuteron is accelerated from rest through a 10-kV potential difference and then moves perpendicularly to a uniform magnetic field with B = 1.6 T. What is the radius of the resulting circular path? (deuteron: m = kg, q = C) a. 19 mm b. 16 mm c mm d. 10 mm e. 9.0 mm 35. A 500-eV electron and a 300-eV electron trapped in a uniform magnetic field move in circular paths in a plane perpendicular to the magnetic field. What is the ratio of the radii of their orbits? a. 2.8 b. 1.7 c. 1.3 d. 4.0 e A proton moves around a circular path (radius = 2.0 mm) in a uniform 0.25-T magnetic field. What total distance does this proton travel during a 1.0-s time interval? ( m kg, q C ) a. 82 km b. 59 km c. 71 km d. 48 km e. 7.5 km 46. An electron follows a circular path (radius = 15 cm) in a uniform magnetic field (magnitude = 3.0 G). What is the period of this motion? a µs b. 1.2 ms c µs d. 1.8 ms e. 1.8 µs 47. A proton with a kinetic energy of 0.20 kev follows a circular path in a region where the magnetic field is uniform and has a magnitude of 60 mt. What is the radius of this path? a. 4.1 cm b. 2.9 cm c. 3.4 cm d. 5.1 cm e. 2.4 cm

4 4 CHAPTER A proton is accelerated from rest through a potential difference of 150 V. It then enters a region of uniform magnetic field and moves in a circular path (radius = 12 cm). What is the magnitude of the magnetic field in this region? a. 18 mt b. 12 mt c. 15 mt d. 22 mt e. 10 mt 49. A proton is accelerated from rest through a potential difference of 2.5 kv and then moves perpendicularly through a uniform 0.60-T magnetic field. What is the radius of the resulting path? a. 15 mm b. 12 mm c. 18 mm d. 24 mm e. 8.5 mm 54. Equal charges, one at rest, the other having a velocity of 10 4 m/s, are released in a uniform magnetic field. Which charge has the largest force exerted on it by the magnetic field? a. The charge that is at rest. b. The charge that is moving, if its velocity is parallel to the magnetic field direction when it is released. c. The charge that is moving if its velocity makes an angle of 45 o with the direction of the magnetic field when it is released. d. The charge that is moving if its velocity is perpendicular to the magnetic field direction when it is released. e. All the charges above experience equal forces when released in the same magnetic field. 56. One reason why we know that magnetic fields are not the same as electric fields is because the force exerted on a charge +q a. is in opposite directions in electric and magnetic fields. b. is in the same direction in electric and magnetic fields. c. is parallel to a magnetic field and perpendicular to an electric field. d. is parallel to an electric field and perpendicular to a magnetic field. e. is zero in both if the charge is not moving. 57. You stand near the earth s equator. A positively charged particle that starts moving parallel to the surface of the earth in a straight line directed east is initially deflected upwards. If you know there are no electric fields in the vicinity, a possible reason why the particle does not initially acquire a downward component of velocity is because near the equator the magnetic field lines of the earth are directed a. upward. b. downward. c. from south to north. d. from north to south. e. from east to west. 59. A magnetic field is directed out of the page. Two charged particles enter from the top and take the paths shown in the figure. Which statement is correct? a. Particle 1 has a positive charge and particle 2 has a negative charge. b. Both particles are positively charged. c. Both particles are negatively charged. d. Particle one has a negative charge and particle 2 has a positive charge. e. The direction of the paths depends on the magnitude of the velocity, not on the sign of the charge.

5 Magnetic Fields The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. 69. The magnetic field in a region of space is parallel to the surface of a long flat table. Imagine that this page is lying flat on the table. When current is present in the coil, which is lying on the table, the coil tends to rotate so that the left side moves up and the right side moves down. The magnetic field is When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is a. A. b. B. c. C. d. D. e. E. 65. The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T that are perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed up out of the page, the direction of the magnetic field at P is closest to the direction of a. directed parallel to the page and downwards. b. directed parallel to the page and upwards. c. directed parallel to the page and to the right. d. directed parallel to the page and to the left. e. in a direction that cannot be determined in this experiment 71. A magnetic field of 2.0 T is applied to a bubble chamber to make the tracks of protons and other charged particles identifiable by the radius of the circles they move in. If a high-energy proton moves along an arc of a 3.3-m circle, what is the momentum of the proton? [q = C, m = kg] a. E. b. F. c. G. d. H. e. A

6 Sources of the Magnetic Field 3. d 4. a 9. a 10. b 11. c 13. a 14. d 17. d 18. d 21. c 23. c 25. d 29. c 30. c 31. c 33. c 35. c 37. d 46. a 47. c 48. c 49. b 54. d 56. d 57. c 59. a 61. c 65. e 69. c C kg m/s 6

7 Sources of the Magnetic Field 7 1. One long wire carries a current of 30 A along the entire x axis. A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0, 4, 0) m. What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis? a. 4.0 µt b. 5.0 µt c. 3.0 µt d. 7.0 µt e. 1.0 µt 2. Two long parallel wires each carry a current of 5.0 A directed to the east. The two wires are separated by 8.0 cm. What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires? a. 72 µt b. 48 µt c. 24 µt d. 96 µt e. 32 µt 6. Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions. What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire? a. 51 µt b. 33 µt c. 72 µt d. 64 µt e. 46 µt 7. Two long parallel wires carry unequal currents in the same direction. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 µt. What is the larger of the two currents? a. 5.3 A b. 3.8 A c. 4.5 A d. 3.0 A e. 0.5 A 15. Two long parallel wires carry unequal currents in opposite directions. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 µt. What is the larger of the two currents? a. 0.5 A b. 1.0 A c. 1.5 A d. 2.0 A e. 3.0 A 17. A segment of wire of total length 2.0 m is formed into a circular loop having 5.0 turns. If the wire carries a 1.2-A current, determine the magnitude of the magnetic field at the center of the loop. a. 79 µt b. 69 µt c. 59 µt d. 89 µt e. 9.4 µt 25. What is the magnitude of the magnetic field at point P if a = R and b = 2R? a. b. c. d. e. 3µ 0 I 4R µ 0 I 4R 2µ 0 I 3R µ 0 I 3R 3µ 0 I 4R

8 8 CHAPTER What is the magnitude of the magnetic field at point P in the figure if a = 2.0 cm, b = 4.5 cm, and I = 5.0 A? a. 87 µt, into the paper b. 87 µt, out of the paper c mt, out of the paper d mt, into the paper e. 23 µt, into the paper 28. Three long, straight, parallel wires each carry a current of 10 A in the positive x direction. If the distance between each wire and the other two is 10 cm, what is the magnitude of the magnetic force on a 20-cm length of either of the wires? a. 57 µn b. 40 µn c. 69 µn d. 50 µn e. 20 µn 29. Two long parallel wires are separated by 6.0 mm. The current in one of the wires is twice the other current. If the magnitude of the force on a 3.0-m length of one of the wires is equal to 8.0 µn, what is the greater of the two currents? a A b A c. 40 ma d. 20 ma e A 32. Two long parallel wires are separated by 4.0 cm. One of the wires carries a current of 20 A and the other carries a 30-A current. Determine the magnitude of the magnetic force on a 2.0-m length of the wire carrying the greater current. a. 7.0 mn b. 6.0 mn c. 8.0 mn d. 9.0 mn e. 4.0 mn 33. The figure shows a cross section of three parallel wires each carrying a current of 5.0 A out of the paper. If the distance R = 6.0 mm, what is the magnitude of the magnetic force on a 2.0-m length of any one of the wires? a. 2.5 mn b. 3.3 mn c. 2.2 mn d. 2.9 mn e. 1.7 mn

9 Sources of the Magnetic Field The figure shows a cross section of three parallel wires each carrying a current of 15 A. The currents in wires A and C are out of the paper, while that in wire B is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 4.0-m length of wire C? a. 90 mn b. 54 mn c. 30 mn d. 18 mn e. 36 mn 51. A long solenoid (n = 1200 turns/m, radius = 2.0 cm) has a current of a 0.30 A in its winding. A long wire carrying a current of 20 A is parallel to and 1.0 cm from the axis of the solenoid. What is the magnitude of the resulting magnetic field at a point on the axis of the solenoid? a mt b mt c. 52 µt d mt e mt 53. A long solenoid (1000 turns/m) carries a current of 25 ma and has an inside radius of 2.0 cm. A long wire which is parallel to and 4.0 cm from the axis of the solenoid carries a current of 6.0 A. What is the magnitude of the magnetic field at a point on the axis of the solenoid? a. 51 µt b. 61 µt c. 43 µt d. 81 µt e. 1.4 µt 61. When the number of turns in a solenoid and its length are both doubled, the ratio of the magnitude of the new magnetic field inside to the magnitude of the original magnetic field inside is: a b c. 1 d. 2 e By using a compass to measure the magnetic field direction at various points adjacent to a long straight wire, you can show that the wire s magnetic field lines are a. straight lines in space that go from one magnetic charge to another. b. straight lines in space that are parallel to the wire. c. straight lines in space that are perpendicular to the wire. d. circles that have their centers on the wire and lie in planes perpendicular to the wire. e. circles that have the wire lying along a diameter of the circle. 63. The reason the north pole of a bar magnet free to rotate points north is because a. the south geographic pole of the earth is the earth s magnetic north pole. b. the south geographic pole of the earth is the earth s magnetic south pole. c. there is a net accumulation of negative magnetic charge at the earth s south geographic pole. d. there is a net accumulation of positive magnetic charge at the earth s north geographic pole. e. the north geographic pole of the earth is the earth s magnetic north pole.

10 10 CHAPTER At a point in space where the magnetic field is measured, the magnetic field produced by a current element a. points radially away in the direction from the current element to the point in space. b. points radially in the direction from the point in space towards the current element. c. points in a direction parallel to the current element. d. points in a direction parallel to but opposite in direction to the current element. e. points in a direction that is perpendicular to the current element and perpendicular to the radial direction. 67. A solenoid consists of 100 circular turns of copper wire. Parts of three turns, A, B and C, are shown below. When a current flows through the coil, a. both A and C are repelled by B. b. A is attracted to B; C is repelled by B. c. neither A nor C is attracted to or repelled by B. d. A is repelled by B; C is attracted to B. e. both A and C are attracted to B Two solenoids are each made of 2000 turns of copper wire per meter. Solenoid I is 2 m long, while solenoid II is 1 m long. When equal currents are present in the two solenoids, the ratio of the magnetic field B I along the axis of solenoid I to the magnetic field B II along the axis of solenoid II, B I /B II, is a. 1/4. b. 1/2. c. 1. d. 2 e Two solenoids of equal length are each made of 2000 turns of copper wire per meter. Solenoid I has a 5.00 cm radius; solenoid II a 10.0 cm radius. When equal currents are present in the two solenoids, the ratio of the magnitude of the magnetic field B I along the axis of solenoid I to the magnitude of the magnetic field B II along the axis of solenoid II, B I /B II, is a. 1/4. b. 1/2. c. 1. d. 2. e The magnetic field strength B within a solenoid with n turns per unit length (length = ) and current I has magnitude B equal to a. ni. b. 0nI. c. 1( 0) ni. d. e. ni. 0 ni.

11 Sources of the Magnetic Field Equal currents of magnitude I travel out of the page in wires M and N. Eight directions are indicated by letters A through H. The direction of the magnetic field at point P is a. E. b. F. c. G. d. H. e. A. 79. Equal currents of magnitude I travel into the page in wire M and out of the page in wire N. Eight directions are indicated by letters A through H. 82. Two wires, each having a weight per unit length of 10 4 N/m, are strung parallel, one 0.1 m above the other. If the wires carry the same current, though in opposite directions, how great must the current in each wire be for the magnetic field of the lower conductor to balance the weight of the upper conductor? 83. What current in a solenoid 15-cm long wound with 100 turns would produce a magnetic field equal to that of the Earth, T? 84. A superconducting wire carries a current of A. Find the magnetic field at a distance of 1.0 m from the wire. 85. The planetary model of the hydrogen atom consists of an electron in a circular orbit about a proton. The motion of the electron of charge C creates an electric current. The radius of the electron orbit is m and the electron s velocity is m/s. What is the magnetic field strength at the location of the proton? The direction of the magnetic field at point P is a. C. b. E. c. F. d. G. e. H. Open-Ended Problems 81. A long solenoid (n = 80 turns/cm) carries a current of 70 ma. If the interior of the solenoid is filled with a ferromagnetic material having a permeability k m of 650, determine the magnitude of the magnetic field before and after the ferromagnetic material is inserted.

12 12 CHAPTER b 2. c 6. b 7. d 15. c 17. c 25. a 27. a 28. c 29. b 32. b 33. d 35. d 51. a 53. c 61. c 62. d 63. a 65. e 67. e 70. c 72. c 75. a 77. e 79. d gauss, 0.46 T A ma T T

Physics 2401 Summer 2, 2008 Exam III

Physics 2401 Summer 2, 2008 Exam e = 1.60x10-19 C, m(electron) = 9.11x10-31 kg, ε 0 = 8.845x10-12 C 2 /Nm 2, k e = 9.0x10 9 Nm 2 /C 2, m(proton) = 1.67x10-27 kg. n = nano = 10-9, µ = micro = 10-6, m =