PHYS102 Previous Exam Problems. Induction

PHYS102 Previous Exam Problems CHAPTER 30 Induction Magnetic flux Induced emf (Faraday s law) Lenz law Motional emf 1. A circuit is pulled to the right at constant speed in a uniform magnetic field with a 16-N force, as shown in figure 2. As the circuit moves, a 6.0-A current flows through the 4.0-Ω resistor. With what speed does the circuit move? (Ans: 9.0 m/s) 2. A 2.0-m long copper wire, with a resistance of 5.0 Ω, is shaped into a square loop and placed perpendicular to a uniform magnetic field that is increasing at the constant rate of 1.0 10-2 T/s. At what rate is thermal energy generated in the loop? (Ans: 1.3 10-6 W) 3. A long solenoid has 10 turns per cm and carries a 4-A current. A circular coil with a cross sectional area of 8 cm 2 has 4 turns and lies within the solenoid with its axis parallel to the axis of the solenoid. Find the magnitude of the induced emf if the current increases uniformly from 0 to 4 A in 0.1 s. (Ans: 1.6 10-4 V) 4. A uniform magnetic field B = (2.0 î + 4.0 ĵ + 5.0 kˆ ) T intersects a circular surface of radius 2.0 cm lying in the yz plane. What is the magnetic flux through this surface? (Ans: 2.5 10-3 T.m 2 ) 5. A circular loop of radius R = 10 cm is placed so that its plane is perpendicular to a magnetic field that is increasing at a constant rate of 50 mt/s. What is the magnitude of the induced emf in the loop? (Ans: 1.6 mv) 6. Consider a rectangular conducting loop of length a = 20 cm, width b = 10 cm and resistance R = 10 Ω, as shown in figure 3. The loop is moving out of a uniform magnetic field region, at a constant speed of 5.0 m/s. The magnetic field B is into the page and has a magnitude of 0.50 T. What is the magnitude and direction of the induced current? (Ans: 25 ma, clockwise) 7. In figure 4, a very long straight wire is in the plane of a circular conducting loop of radius R = 2.0 cm. The wire carries a current of 1.0 A, and has a resistance of 2.0 Ω. The loop starts moving parallel to the wire with a speed of 10 m/s as shown. What is the induced current during the motion of the loop? (Ans: zero) 8. In figure 6, the magnetic field decreases from 1.0 T to 0.40 T in 1.2 s. A 3.0-cm radius conducting loop with a resistance of 0.010 Ω is perpendicular to B. What are the size and the direction of the current induced in the loop? (Ans: 140 ma, and current is clockwise) 9. Figure 7 shows a conducting loop consisting of a half circle of radius 0.20 m and three straight sections. The loop lies in a uniform magnetic field that is directed as shown in the figure, and is given by the expression: B = 4.5t 2-10t, where B is in tesla and t is in seconds. What is the magnitude of the induced emf at t = 10 s? (Ans: 8.2 V) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 1

10. A 1.7-T uniform magnetic field makes an angle of 30 0 with the z axis. What is the magnetic flux through an area of 4.0 m 2 lying in the xy plane? (Ans: 5.9 Wb) 11. Each turn of a 150-turn coil, encloses an area of 0.8 m 2. What should be the rate of change of a magnetic field parallel to its axis in order to induce a current of 0.1 A in the coil? [The resistance of the coil is 600 Ω] (Ans: 0.5 T/s) 12. A constant magnetic flux of 4.0 10-5 Wb is maintained through a coil for 0.5 s. What emf is induced in the coil by this flux during that period? (Ans: zero) 13. Figure 8 shows a metal rod of length 25 cm moving at a constant velocity along two parallel metal rails. If the magnetic field is 0.35 T into the page, and the induced emf is 15 mv, calculate the speed of the metal bar. (Ans: 17 cm/s) 14. A long straight wire carries a current that increases at a rate of 6 10 4 A/s. The wire passes through the center of a circular loop of radius 5 cm, as shown in figure 10. What is the induced emf in the loop? (Ans: zero) 15. A flat circular coil has 80 turns of diameter 20 cm with a total resistance of 40 Ω. The plane of the coil is perpendicular to a uniform magnetic field. At what rate should the magnetic field change for the power dissipated in the coil to be 2.0 W? (Ans: 3.6 T/s) 16. A 2.0-T uniform magnetic field makes an angle of 60 o with the xy plane. What is the magnetic flux through an area of 3.0 m 2 portion of the xy plane? (Ans: 5.2 Wb) 17. A metal bar is free to move over a U-shaped metal rail, as shown in figure 11. At t = 0, the external field is 0.40 T directed out of the page and is increasing at a rate of 0.20 T/s. What will be the velocity of the metal bar such that the induced emf is zero at x = 5.0 cm and t = 0? Take L = 5.0 cm. (Ans: 0.025 m/s, along - x direction) 18. A square coil of side 20 cm is rotating about the y-axis. It is oriented as shown in figure 12. The external field is B = 0.5 T is along the positive x axis. What is the change in the magnetic flux through the coil if the angle θ changes from 37 o to 53 o? (Ans: +4 mwb) 19. A small circular loop of area 0.50 cm 2 is placed in the plane of, and concentric with, a large circular loop of radius 2.0 m. The current in the large loop is changed uniformly from +100 A to 100 A in a time of 0.50 s. Find the emf induced in the small loop in this time interval (Assume the field is uniform through the smaller loop). (Ans: 6.3 10-9 V) 20. A circular wire loop, with an area of 0.10 m 2, is initially oriented so that its plane is perpendicular to a 0.40-T magnetic field. When the loop is rotated so that its plane is parallel to the field, a 25-V average potential difference is induced across the loop. What is the time required to make this rotation of the loop? (Ans: 1.6 10-3 s) 21. A circular wire loop of area 0.5 m 2 is perpendicular to a magnetic field of 0.8 T. If the coil is removed completely from the field in 0.1 s, what is the magnitude of the average emf induced in the loop? (Ans: 4.0 V) 22. A single turn plane loop of wire, of cross sectional area 40 cm 2, is perpendicular to a magnetic field that increases uniformly in magnitude from 0.50 T to 5.5 T in 2.0 s. What is the resistance of the wire if the induced current has a value of 1.0 ma? (Ans: 10 Ω) 23. A magnet is taken towards a metallic ring in such a way that a constant current of 10-2 A is induced in it. The total resistance of the ring is 0.25 Ω. How much does the flux of the magnetic field through the ring change in 10 s? (Ans: 2.5 10-2 Wb) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 2

24. Consider a circular loop of wire within which the magnetic flux, Φ, is given as a function of time, t, by the equation: Φ = a.t 2 + b, where a and b are constants. If the induced emf is measured as 48 V at t = 3.0 s, what is the value of a? (Ans: - 8.0 V/s) 25. Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5.0 Wb. If the page is turned by 30 around an edge, what will be the flux through it? (Ans: 4.3 Wb) 26. A circular wire loop of radius 15.0 cm is located in a uniform magnetic field that changes in magnitude as shown in figure 17. The plane of the loop is perpendicular to the magnetic field. What is the magnitude of the emf induced in the loop during the time interval t = 0 to t = 2.00 s? (Ans: 17.7 mv) 27. A uniform magnetic field passes through two areas, A 1 and A 2. The angles between the magnetic field and the normals of areas A 1 and A 2 are 30 and 60, respectively. If the magnetic flux through the two areas is the same, what is the ratio A 1/A 2? (Ans: 0.58) 28. A circular coil of wire has 25 turns and a radius of 0.075 m. The coil is located in a variable magnetic field whose behavior is shown on the graph of figure 18. At all times, the magnetic field is directed perpendicular to the plane of a loop. What is the magnitude of the emf induced in the coil in the time interval from t = 5.0 s to 7.5 s? (Ans: 71 mv) 29. In Dhahran, the total magnetic field of the Earth has been measured to be 0.54 10-4 T and it points downward at an angle of 53 o below the horizontal. What is the magnetic flux through 1.0 m 2 of ground in Dhahran due to the Earth magnetic field? (Ans: 0.43 10-4 Wb) 30. Figure 19 shows a bar being moved to the right on two parallel rails at a constant speed of 3.0 m/s in a uniform magnetic field of 0.50 T, directed into the page. If the induced current is 1.5 A, find the power dissipated in the resistor? Neglect the mass of the bar, friction, and the resistance of the bar and rails. (Ans: 2.7 W) 31. In figure 22, the magnetic flux through the loop increases according to the relation Φ = 2.0t 6 + 7, where t is in seconds and Φ is in Wb. What are the magnitude and direction of the current through the resistor R = 24 Ω at t = 1.0 s? (Ans: 0.50 A, counterclockwise) 32. A 10-m long conductor is formed into a circular loop in the xy-plane. A uniform magnetic field B = (9.0 î + 12 ĵ ) T exists in the region of the conductor. Find the magnetic flux through the loop. (Ans: zero) 33. A 10-cm-long conducting rod of negligible resistance moves on two horizontal frictionless conducting rails, as shown in figure 28. The magnetic field in the region is uniform and is directed perpendicular to the plane of the rails (out of the page). If a constant force of 0.60 N moves the bar at a constant speed of 2.0 m/s, what is the current through 12-Ω resistor? (Ans: 0.32 A) 34. The wing span (tip to tip) of a Boeing 747 airplane is 59 m. The plane is flying horizontally at a speed of 220 m/s. The vertical component of the earth s magnetic field is 50 μt. Find the induced emf between the tips. (Ans: 0.65 V) 35. A 5-turn square coil (10 cm along a side, resistance = 4.0 Ω) is placed in a magnetic field that makes an angle of 30 o with the plane of the coil. The magnitude of this field varies with time according to B = 0.50 t 2, where t is measured in s and B in Tesla. What is the induced current in the coil at t = 4.0 s? (Ans: 25 ma) 36. The normal to a certain plane with an area of 1.0-m 2 makes an angle of 60 with a uniform magnetic field. The magnetic flux through this plane is the same as the flux through a second plane whose area is perpendicular to the magnetic field. What is the area of the second plane? (Ans: 0.50 m 2 ) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 3

37. A square loop of wire is held in a uniform 0.24 T magnetic field directed perpendicular to the plane of the loop. The length of each side of the loop is decreasing at a constant rate of 5.0 cm/s. What is the emf induced in the loop at the instant the length is 12 cm? (Ans: 2.9 mv) 38. A circular loop of wire of radius 14 cm is placed in the xy plane in a magnetic field that makes an angle of 30 o with the normal to the plane of the loop, as shown in figure 30. The magnitude of this field increases at constant rate from 30 mt to 60 mt in 15 ms. If the loop has a resistance of 5.0 Ω, what is the current induced in the loop, looking from the top? (Ans: 21 ma, clockwise) 39. A 10.0-m long copper wire, with a resistance of 5.00 Ω, is formed into a square loop and placed with its plane perpendicular to an external uniform magnetic field that is increasing at the constant rate of 10.0 mt/s, at what rate is thermal energy generated in the loop? (Ans: 0.780 mw) 40. A 50-turrn coil is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 60 o with the direction of the magnetic field. When the magnetic field is increased uniformly from 200 μt to 600 μt in 0.40 s, an emf of magnitude 80 mv is induced in the coil. What is the cross sectional area of the coil? (Ans: 3.2 m 2 ) 41. A 200 turn coil of radius 2.2 cm and resistance 5.5 Ω is coaxial with a solenoid of 300 turns/cm and radius 1.6 cm (see figure 31). The solenoid current drops from 1.5 A to 0.50 A in 20 ms. What is the current induced in the coil during this time interval? (Ans: 0.055 A) 42. A flexible loop has a radius of 12.0 cm and is placed with its plane perpendicular to a uniform magnetic field of magnitude 0.150 T, as shown in figure 33. The loop is grasped at points A and B and stretched until its area is zero. If it takes 0.300 s to stretch the loop, what is the magnitude of the induced emf during this time interval? (Ans: 22.6 mv) 43. Figure 34 shows a 50-turn coil, with a diameter of 1.0-cm, inside a solenoid with a diameter of 2.0 cm. The solenoid is 8.0 cm long, has 1200 turns, and carries the current shown on the right in the figure. What is the magnetic flux through the coil at time t = 0? (Ans: 3.7 10-5 Wb) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 4

A B C D E Conceptual Problems 1. A long straight wire is in the plane of two circular conducting loops. The straight wire carries a constant current I in the direction shown in figure 1. The circular loop 1 is moved to the right while the loop 2 is moved to the left with the same speed, v. The induced current directions in the circular loops 1 and 2 are respectively: A. Clockwise, counterclockwise B. Clockwise, clockwise C. Counterclockwise, clockwise D. Counterclockwise, counterclockwise E. No current in both the loops 2. Figure 5 shows a conducting loop that is placed perpendicular to an external magnetic field that points into the page. Which of the following changes will induce a counterclockwise current? A. Increasing the magnitude of the magnetic field. B. Decreasing the magnitude of the magnetic field. C. Decreasing the area of the loop. D. Sliding the loop out of the field. E. Rotating the loop around an axis through its center perpendicular to the page. 3. Figure 9 shows a long straight wire carrying current I in the plane of a rectangular conducting loop. Which of the following statements is correct? A. No current will be induced if the loop is moved up parallel to the wire. B. No current will be induced in the loop as the current in the straight wire decreases gradually. C. A counterclockwise current is induced if the loop is moved away from the wire. D. A clockwise current is induced if the loop is moved toward the wire. E. The induced current in the loop decreases gradually as the current in the straight wire gradually increases. 4. A long straight wire is in the plane of a circular conducting loop, as shown in figure 13. The straight wire carries a constant current I in the direction shown. The circular loop starts moving to the left. The induced current in the circular loop is: A. Counterclockwise B. Clockwise C. 2I D. 4I E. zero 5. A long straight wire, carrying a constant current I, is in the plane of a circular conducting loop, as shown in figure 14. If the wire is moved away from the loop toward point A, what current is induced in the loop? A. clockwise. B. counterclockwise. C. zero. D. into the page. E. out of the page. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 5

6. A long straight wire is in the plane of a rectangular conducting loop, as shown in Figure 15. The straight wire carries an increasing current i in the direction shown. The current in the rectangular loop is: A. counterclockwise B. clockwise. C. zero. D. clockwise in the left side and counter clockwise in the right side. E. counter clockwise in the left side and clockwise in the right side. 7. Figure 16 shows a bar moving to the right on two conducting rails. To make an induced current in the direction indicated, a constant magnetic field in region A should be in what direction? A. Into the page. B. Out of the page. C. Left. D. Right. E. Impossible; this cannot be done with a constant magnetic field. 8. Faraday's law states that an induced emf is proportional to: A. the rate of change of magnetic flux. B. the rate of change of magnetic field. C. the rate of change of electric flux. D. the rate of change of electric field. E. the rate of change of gravitational field. 9. Figure 20 shows two loops and a long straight wire lying in the same plane. If the current in the straight wire is increased, then A. The induced current in loop 1 is counterclockwise and in loop 2 is clockwise. B. The induced current in loop 1 is clockwise and in loop 2 is counterclockwise. C. In both loops, the induced current is clockwise. D. In both loops, the induced current is counterclockwise. E. In both loops, there is no induced current. 10. A square loop of copper wire, figure 21, is pulled at constant velocity v through a region of magnetic field. Which statement about the magnitude of the pulling force F1, F2, F3 and F4 is true? A. F2 = F4 > F1 = F3. B. F3 > F2 = F4 > F1. C. F3 > F4 > F2 > F1. D. F4 > F2 > F3 > F1. E. F1 = F2 = F3 = F4. 11. A square loop of wire lies in the plane of the page. A decreasing magnetic field is directed into the page. The induced current in the loop: A. is clockwise. B. is counterclockwise. C. is zero. D. depends upon whether or not B is decreasing at a constant rate. E. is clockwise in two of the loop sides and counterclockwise in the other two. 12. In figure 23, a copper ring passes through a rectangular region where a constant magnetic field is directed into the page. In which position is the induced current through the ring clockwise? A. 4 B. 2 C. 5 D. 1 E. 3 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 6

13. Figure 24 shows four wire loops, with edge lengths of either L or 2L. All four wires move toward a region of uniform magnetic field B (directed out the page) at the same constant velocity. As they enter the magnetic field, in which loop(s) is the greatest induced emf? A. 1 and 2 B. 3 and 4 C. 3 only D. 1 only E. 2 only 14. Figure 25 shows the magnetic field as a function of time through a circular coil whose normal is parallel to the direction of the field. The induced current is: A. Maximum in the interval 0 to t1 B. Maximum in the interval t1 to t2 C. Maximum in the interval t2 to t3 D. Minimum in the interval 0 to t1 E. Minimum in the interval t2 to t3 15. A metallic rod moves at constant speed in the positive x direction inside a uniform magnetic field as shown in figure 26. Positive and negative charges build up on the rod as indicated. What is the direction of the magnetic field? A. Along the negative z-axis B. Along the negative y-axis C. Along the negative x-axis D. Along the positive y-axis E. Along the positive z-axis 16. The wire in figure 27 carries a current I that is increasing with time at a constant rate. Which one of the following statements is correct? A. The induced current is clockwise in loop A, zero in loop B and counterclockwise in loop C. B. No current is induced in any loop. C. The induced current is counterclockwise in all loops. D. The induced current is counterclockwise in loop A, zero in loop B and clockwise in loop C. E. The induced current is clockwise in loop A, clockwise in loop B and clockwise in loop C. 17. A bar magnet is dropped from above and falls through the loop of wire shown in figure 29. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct? A. The current in the loop flows first in a counterclockwise direction, then in a clockwise direction. B. The current in the loop always flows in a clockwise direction. C. The current in the loop always flows in a counterclockwise direction. D. The current in the loop flows first in a clockwise direction, then in a counterclockwise direction. E. No current flows in the loop because both ends of the magnet move through the loop. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 7

18. A conducting loop is held in a uniform magnetic field, with the plane of the loop perpendicular to the field lines. Which of the following will NOT cause a current to be induced in the loop? A. Keeping the orientation of the loop fixed and moving it within the field. B. Shrinking the loop. C. Changing the shape of the loop. D. Rotating the loop about an axis perpendicular to the field lines. E. Pulling the loop out of the field. 19. A rectangular loop of wire is placed midway between two long straight parallel conductors as in figure 32. The conductors carry currents i 1 and i 2 which are antiparallel to each other. The magnitudes of the currents are increasing with time at the same rate. Which one of the following statements is TRUE? A. The net induced current in the loop is counterclockwise. B. The net induced current in the loop is clockwise. C. The net induced current in the loop is zero. D. The net induced magnetic field in the loop is into the page E. The net induced magnetic field in the loop is zero. 20. A force F is applied to pull a conducting rod out of a magnetic field at constant speed v and power input P, as shown in figure 35. The rod moves on conducting rails. The force is increased so that the constant speed of the rod is doubled to 2v. What are the new force and power input? A. 2F and 4P B. 2F and 2P C. 4F and 2P D. 4F and 4P E. 2F and P 21. Two rectangular loops of wire lie in the same plane as shown in figure 36. If the current I in the outer loop is counterclockwise and increases with time, which of the following statements is CORRECT about the current induced in the inner loop? A) It is clockwise. B) It is counterclockwise. C) It is zero. D) Its direction depends on the dimensions of the loop. E) Its direction is fluctuating with time. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 8

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 9

Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Figure 32 Figure 33 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 10

Figure 34 Figure 35 Figure 36 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 30 Page 11