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AP Physics 2 Electromagnetic Induction HW due___________ Conceptual Questions 1. 2. 3. 4. 5. 6. An airplane flies horizontally toward the north pole. Is the induced emf from wing tip to wing tip greater when the plane is at the equator or when it is at the latitude of New York? Explain. Explain the difference between a magnetic field and a magnetic flux. You hold a circular loop of wire at the equator. Consider the magnetic flux through this loop due to the Earth’s magnetic field. Is this flux greater when the normal to the loop points north or when it points vertically upward? Explain. You hold a circular loop of wire at the north pole. Consider the magnetic flux through this loop due to the Earth’s magnetic field. Is this flux greater when the normal to the loop points horizontally or when it points vertically downward? Explain. Figure 1 shows two metal disks of the same size and material oscillating in and out of a region with a magnetic field. One disk is solid; the other has a series of slots. Is the retarding effect of eddy currents on the solid disk greater than, less than, or equal to the retarding effect on the slotted disk? Explain. Consider the solid disk in Figure 1. When this disk has swung to the right as far as it can go, is the induced current in it a maximum or a minimum? Explain. Figure 1 7. 8. 9. 10. 11. Figure 2 As the solid metal disk in Figure 1 swings to the right, from the region with no field into the region with a finite magnetic field, does the induced current in the disk circulate clockwise or counterclockwise? Explain. A metal ring with a break in its perimeter is dropped from a field-free region of space into a region with a magnetic field. What effect does the magnetic field have on the ring? Figure 2 shows a vertical iron rod with a wire coil of many turns wrapped around its base. A metal ring slides over the rod and rests on the wire coil. Initially the switch connecting the coil to a battery is open, but when it is closed the ring flies into the air. Explain why this happens. Referring to Question 9, suppose the metal ring has a break in its circumference. Describe what happens when the switch is closed in this case. In a common classroom demonstration, a magnet is dropped down a long, vertical copper tube. The magnet moves very slowly as it moves through the tube, taking several seconds to reach the bottom. Explain this behavior. Problems Magnetic Flux 1. A 0.055-T magnetic field passes through a circular ring of radius 2.1 cm at an angle of 12° with the normal. Find the magnitude of the magnetic flux through the ring. 2. Find the magnitude of the magnetic flux through the floor of a house that measures 22 m by 18 m. Assume that the Earth’s magnetic field at the location of the house has a horizontal component of 2.6 105 T pointing north, and a downward vertical component of 4.2 105 T. 3. At a certain location, the Earth’s magnetic field has a magnitude of 5.9 105 T and points in a direction that is 70° below the horizontal. Find the magnitude of the magnetic flux through the top of a desk at this location that measures 110 cm by 62 cm. Faraday’s Law of Induction 4. A 0.25-T magnetic field is perpendicular to a circular loop of wire with 50 turns and a radius of 15 cm. If the magnetic field is reduced to zero in 0.12 s, what is the magnitude of the induced emf? 5. shows the magnetic flux through a coil as a function of time. At what times shown in this plot do (a) the magnetic flux and (b) the induced emf have the greatest magnitude? Figure 3 Figure 3 6. 7. 8. 9. Figure 4 shows the magnetic flux through a single-loop coil as a function of time. What is the induced emf in the coil at (a) t 0.05 s, (b) t 0.15 s, and (c) t 0.5 s ? A single conducting loop of wire has an area of 7.4 102 m2 and a resistance of 110 . Perpendicular to the plane of the loop is a magnetic field of strength 0.18 T. At what rate (in T/s) must this field change if the induced current in the loop is to be 0.22 A? An emf is induced in a conducting loop of wire 1.12 m long as its shape is changed from square to circular. Find the average magnitude of the induced emf if the change in shape occurs in 4.25 s, and the local 0.105-T magnetic field is perpendicular to the plane of the loop. A magnetic field increases from 0 to 0.20 T in 1.5 s. How many turns of wire are needed in a circular coil 12 cm in diameter to produce an induced emf of 6.0 V? Figure 4 Lenz’s Law 10. A bar magnet with its north pole pointing downward is falling toward the center of a horizontal, conducting ring. As viewed from above, is the direction of the induced current in the ring clockwise or counterclockwise? Explain. 11. A loop of wire is dropped and allowed to fall between the poles of a horseshoe magnet, as shown in Figure 5. State whether the induced current in the loop is clockwise or counterclockwise when (a) the loop is above the magnet and (b) the loop is below the magnet. 12. Suppose we change the situation shown in Figure 5 as follows: Instead of allowing the loop to fall on its own, we attach a string to it and lower it with constant speed along the path indicated by the dashed line. Is the tension in the string greater than, less than, or equal to the weight of the loop? Give specific answers for times when (a) the loop is above the magnet and (b) the loop is below the magnet. Explain in each case. 13. Rather than letting the loop fall downward in Figure 5, suppose we attach a string to it and raise it upward with constant speed along the path indicated by the dashed line. Is the tension in the string greater than, less than, or equal to the weight of the loop? Give specific answers for times when (a) the loop is below the magnet and (b) the loop is above the magnet. Explain in each case. Figure 5 Figure 6 shows a current-carrying wire and a circuit containing a resistor R. (a) If the current in the wire is constant, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain. (b) If the current in the wire increases, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain. 15. Consider the physical system shown in Figure 6. If the current in the wire changes direction, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain. 14. Figure 6 shows a circuit containing a resistor and an uncharged capacitor. Pointing into the plane of the circuit is a uniform magnetic field B. If the magnetic field increases in magnitude with time, which plate of the capacitor (top or bottom) becomes positively charged? Explain. 17. Referring to Problem 16, which plate of the capacitor (top or bottom) becomes positively charged if the magnetic field reverses direction? 18. A long, straight, current-carrying wire passes through the center of a circular coil. The wire is perpendicular to the plane of the coil. (a) If the current in the wire is constant, is the induced emf in the coil zero or nonzero? Explain. (b) If the current in the wire increases, is the induced emf in the coil zero or nonzero? Explain. (c) Does your answer to part (b) change if the wire no longer passes through the center of the coil but is still perpendicular to its plane? Explain. 16. Figure 7 Figure 7 19. Figure 8 A wire with a current I is placed under a clear sheet of plastic, as shown in Figure 8. Three loops of wire, A, B, and C, are placed on the sheet of plastic at the indicated locations. If the current in the wire is increased, indicate whether the induced emf in each of the loops is clockwise, counterclockwise, or zero. Explain your answer for each loop. Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. = 7.5 x 105 Wb = 1.7 x 102 Wb = 4 x 105 Wb = 7.4 V (a) The magnetic flux has its greatest magnitude at t = 0 s, 0.2 s, 0.4 s, and 0.6 s . (b) The magnitude of the induced emf is greatest when the magnitude of the slope of the plot is greatest, which occurs at t = 0.1 s, 0.3 s, and 0.5 s . (a) = 0.1 kV (b) = 0, because the rate of flux change is zero. (c) = 0.04 kV B/t = 3.3 x 102 T/s = 5.29 x 104 V N = 4000 turns Remaining problems (#’s 10 - 19) are conceptual rather than numerical; answers may be found online as an extension of this file, and they will be discussed in class. 10. The current in the loop flows counterclockwise as viewed from above…explain. 11. (a) The current in the loop will oppose the increasing field by flowing clockwise …explain. (b) The current in the loop will oppose the decreasing field by flowing counterclockwise …explain. 12. The current in the loop opposes the loop’s change in position. (a) The loop resists moving downward toward the magnet. (The poles of the loop’s field line up with the magnet poles northto-north and south-to-south, causing repulsion.) So the string tension is less than the loop’s weight. (b) The loop resists moving downward away from the magnet. (The poles of the loop’s field line up with the magnet poles north-to-south and south-to-north, causing attraction.) So the string tension is again less than the loop’s weight. 13. The current in the loop opposes the loop’s change in position. (a) The loop resists moving upward toward the magnet. (The poles of the loop’s field line up with the magnet poles north-tonorth and south-to-south, causing repulsion.) So the string tension is greater than the loop’s weight. (b) The loop resists moving upward away from the magnet. (The poles of the loop’s field line up with the magnet poles north-to-south and south-to-north, causing attraction.) So the string tension is again greater than the loop’s weight. 14. (a) Since the current in the wire is constant, the magnetic field through the circuit does not vary with time, so the induced current is zero . (b) Since the current in the wire is increasing, the magnetic field through the circuit is increasing. And, since the magnetic field is directed out of the page, the induced current in the circuit will induce a magnetic field into the page. So, the current in the circuit flows clockwise . 15. If the current in the wire changes direction, the direction of the magnetic field is reversed, changing its direction from out of the page to into the page. According to Lenz’s law, the current induced in the circuit will oppose this change by flowing counterclockwise , generating a field which is directed out of the page. 16. Since the field is increasing and is directed into the page, the current in the circuit will flow counterclockwise to generate a field directed out of the page to oppose it. So, the bottom plate will become positively charged. 17. If the magnetic field changes direction, the current in the circuit will flow clockwise to generate a field to oppose the change. So, the top plate will become positively charged. 18. (a) The induced emf is zero because the magnetic field is parallel to the plane of the loop. (b) The induced emf is still zero because, although the field is varying in time, it is still parallel to the plane of the loop, so there is no time-varying flux through the loop to generate an emf. (c) The answer to part (b) does not change because the field is still parallel to the plane of the loop. 19. The increasing current in the wire generates an increasing magnetic field which is directed out of the page above the wire and into the page below. Loop A: The induced emf is clockwise . The field generated is into the page and opposes the outwardly directed field generated by the current in the wire. Loop B: Although the field through the loop is varying with time, the net flux through the plane of the loop is zero, so the induced emf is zero . Loop C: The induced emf is counterclockwise . The field generated is out of the page and opposes the inwardly directed field generated by the current in the wire.