CollegePhysics2e-SSM-Ch23

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OpenStax College Physics 2e Student Solutions Manual Chapter 23 CHAPTER 23: ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES 23.1 INDUCED EMF AND MAGNETIC FLUX 1. What is the value of the magnetic flux at coil 2 in Figure 23.53 due to coil 1? Solution Using the equation , we can calculate the flux through coil 2, since the coils are perpendicular: 23.2 FARADAY’S LAW OF INDUCTION: LENZ’S LAW 3. Referring to Figure 23.54 (a), what is the direction of the current induced in coil 2: (a) If the current in coil 1 increases? (b) If the current in coil 1 decreases? (c) If the current in coil 1 is constant? Explicitly show how you follow the steps in the Problem-Solving Strategy for Lenz's Law . Solution (a) CCW (b) CW (c) no current in coil 2 5. Referring to Figure 23.55 , what are the directions of the currents in coils 1, 2, and 3 (assume that the coils are lying in the plane of the circuit): (a) When the switch is first closed? (b) When the switch has been closed for a long time? (c) Just after the switch is opened? Solution (a) (i) CCW (ii) CCW (iii) CW (b) (i) no current (ii) no current (iii) no current (c) (i) CW (ii) CW (iii) CCW 9. (a) An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner’s 2.00 T field with his fingers pointing in the direction of the field. Find the average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) Discuss whether this current would significantly change the temperature of the ring.

OpenStax College Physics 2e Student Solutions Manual Chapter 23 Solution (a) (b) Since power goes as , the smaller the resistance the larger the power and the more heat transferred to the ring. So, as a lower limit on the ring, estimate . In this case, the power would be: . This power exists for of a second, so the heat transferred will be: . This is not a significant amount of heat. 11. An emf is induced by rotating a 1000-turn, 20.0 cm diameter coil in the Earth’s magnetic field. What average emf is induced, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in 10.0 ms? Solution 13. Approximately how does the emf induced in the loop in Figure 23.54 (b) depend on the distance of the center of the loop from the wire? Solution The magnetic field due to an infinite straight wire is , so the flux and hence the emf induced in the loop will be proportional to , where r is the distance from the wire. 23.3 MOTIONAL EMF 17. (a) A jet airplane with a 75.0 m wingspan is flying at 280 m/s. What emf is induced between wing tips if the vertical component of the Earth’s field is ? (b) Is an emf of this magnitude likely to have any consequences? Explain. Solution (a) (b) No , this is a very small emf. 18. (a) A nonferrous screwdriver is being used in a 2.00 T magnetic field. What maximum emf can be induced along its 12.0 cm length when it moves at 6.00 m/s? (b) Is it likely that this emf will have any consequences or even be noticed? Solution (a) (b) No. 19. At what speed must the sliding rod in Figure 23.10 move to produce an emf of 1.00 V in a 1.50 T field, given the rod’s length is 30.0 cm? Solution

OpenStax College Physics 2e Student Solutions Manual Chapter 23 25. Integrated Concepts The Tethered Satellite discussed in this module is producing 5.00 kV, and a current of 10.0 A flows. (a) What magnetic drag force does this produce if the system is moving at 7.80 km/s? (b) How much kinetic energy is removed from the system in 1.00 h, neglecting any change in altitude or velocity during that time? (c) What is the change in velocity if the mass of the system is 100,000 kg? (d) Discuss the long term consequences (say, a week-long mission) on the space shuttle’s orbit, noting what effect a decrease in velocity has and assessing the magnitude of the effect. Solution (a) (b) (c) Note that five digits are needed to see the difference between and . (d) For a week-long mission (168 hours), the change in velocity will be 60 m/s, or approximately 1%. In general, a decrease in velocity would cause the orbit to start spiraling inward because the velocity would no longer be sufficient to keep the circular orbit. The long term consequences are that the shuttle would require a little more fuel to maintain the desired speed, otherwise the orbit would spiral slightly inward. 23.5 ELECTRIC GENERATORS 28. Calculate the peak voltage of a generator that rotates its 200-turn, 0.100 m diameter coil at 3600 rpm in a 0.800 T field. Solution 30. What is the peak emf generated by rotating a 1000-turn, 20.0 cm diameter coil in the Earth’s magnetic field, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in 10.0 ms? Solution

OpenStax College Physics 2e Student Solutions Manual Chapter 23 32. (a) A bicycle generator rotates at 1875 rad/s, producing an 18.0 V peak emf. It has a 1.00 by 3.00 cm rectangular coil in a 0.640 T field. How many turns are in the coil? (b) Is this number of turns of wire practical for a 1.00 by 3.00 cm coil? Solution (a) (b) Yes , 50 turns is practical for a coil of this size. 34. (a) A car generator turns at 400 rpm when the engine is idling. Its 300-turn, 5.00 by 8.00 cm rectangular coil rotates in an adjustable magnetic field so that it can produce sufficient voltage even at low rpms. What is the field strength needed to produce a 24.0 V peak emf? (b) Discuss how this required field strength compares to those available in permanent and electromagnets. Solution (a) (b) This field strength is small enough that it can be obtained using either a permanent magnet or an electromagnet. 36. A 75-turn, 10.0 cm diameter coil rotates at an angular velocity of 8.00 rad/s in a 1.25 T field, starting with the plane of the coil parallel to the field. (a) What is the peak emf? (b) At what time is the peak emf first reached? (c) At what time is the emf first at its most negative? (d) What is the period of the AC voltage output? Solution (a) (b) We know this is the correct expression for since must change sign when peak emf is when (just after the generator is turned on). (c)

OpenStax College Physics 2e Student Solutions Manual Chapter 23 (d) 38. Unreasonable Results A 500-turn coil with a area is spun in the Earth’s field, producing a 12.0 kV maximum emf. (a) At what angular velocity must the coil be spun? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible? Solution (a) (b) This angular velocity is unreasonably high, higher than can be obtained for any mechanical system. (c) The assumption that a voltage as great as 12.0 kV could be obtained is unreasonable. 23.6 BACK EMF 39. Suppose a motor connected to a 120 V source draws 10.0 A when it first starts. (a) What is its resistance? (b) What current does it draw at its normal operating speed when it develops a 100 V back emf? Solution (a) (b) 41. What is the back emf of a 120 V motor that draws 8.00 A at its normal speed and 20.0 A when first starting? Solution 43. Integrated Concepts The motor in a toy car is powered by four batteries in series, which produce a total emf of 6.00 V. The motor draws 3.00 A and develops a 4.50 V back emf at normal speed. Each battery has a internal resistance. What is the resistance of the motor? Solution Since the resistors are in series, we know the total internal resistance of the batteries is . Therefore, 23.7 TRANSFORMERS

OpenStax College Physics 2e Student Solutions Manual Chapter 23 44. A plug-in transformer, like that in Figure 23.25 , supplies 9.00 V to a video game system. (a) How many turns are in its secondary coil, if its input voltage is 120 V and the primary coil has 400 turns? (b) What is its input current when its output is 1.30 A? Solution (a) (b) 46. A cassette recorder uses a plug-in transformer to convert 120 V to 12.0 V, with a maximum current output of 200 mA. (a) What is the current input? (b) What is the power input? (c) Is this amount of power reasonable for a small appliance? Solution (a) (b) (c) Yes , this amount of power is quite reasonable for a small appliance. 48. (a) The plug-in transformer for a laptop computer puts out 7.50 V and can supply a maximum current of 2.00 A. What is the maximum input current if the input voltage is 240 V? Assume 100% efficiency. (b) If the actual efficiency is less than 100%, would the input current need to be greater or smaller? Explain. Solution (a) (b) If the efficiency is less than 100%, the input current would need to be greater because more power would need to be input into the transformer to produce the required power output. 50. A large power plant generates electricity at 12.0 kV. Its old transformer once converted the voltage to 335 kV. The secondary of this transformer is being replaced so that its output can be 750 kV for more efficient cross-country transmission on upgraded transmission lines. (a) What is the ratio of turns in the new secondary compared with the old secondary? (b) What is the ratio of new current output to old output (at 335 kV) for the same power? (c) If the upgraded transmission lines have the same resistance, what is the ratio of new line power loss to old?

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