* 83. Calculate the peak output voltage of a simple

1. (I) The magnetic flux through a coil of wire containing two loops changes from 50Wb to +38 Wb in 0.42 s. What is the emf induced in the coil?

2. (I) The rectangular loop shown in Fig. 21-46 is pushed into the magnetic field which points inward. In what direction is the induced current?

3. (I) The north pole of the magnet in Fig. 21-47 is being inserted into the coil. In which direction is the induced current flowing through the resistor /??

4. (I) A 9.6-cm-diameter circular loop of wire is in a 1.10-T magnetic field. The loop is removed from the field in 0.15 s. What is the average induced emf?

5. (I) A 12.0-cm-diamcter loop of wire is initially oriented perpendicular to a 1.5-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.20 s. What is the average induced emf in the loop?

6. (II) A 10.2-cm-diameter wire coil is initially oriented so that its plane is perpendicular to a magnetic field of 0.63 T pointing up. During the course of 0.15 s, the field is changed to one of 0.25 T pointing down. What is the average induced emf in the coil?

7. (II) A 15-cm-diameler circular loop of wire is placed in a 0.50-T magnetic field, (a) When the plane of the loop is perpendicular to the field lines, what is the magnetic flux through the loop? (b) The plane of the loop is rotated until it makes a 35 angle with the field lines. What is the angle 6 in Eq. 211 for this situation? (c) What is the magnetic flux through the loop at this angle?

8. (II) (a) If the resistance of the resistor in Fig. 21-48 is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop? (b) What would it be if the small loop were placed outside the larger one, to the left?

9. (II) What is the direction of the induced current in the circular loop due to the current shown in each part of Fig. 21-49?

10. (II) If the solenoid in Fig. 21-50 is being pulled away from the loop shown, in what direction is the induced current in the loop?

11. (II) The magnetic field perpendicular to a circular wire loop 12.0 cm in diameter is changed from +0.52 T to -0.45 T in 180 ms. where + means the field points away from an observer and - toward the observer, (a) Calculate the induced emf. (b) In what direction does the induced current flow?

12. (II) The moving rod in Fig. 21-12 is 12.0 cm long and is pulled at a speed of 15.0 cm/s. If the magnetic field is 0.800 T. calculate (a) the emf developed, and (b) the electric field felt by electrons in the rod.

13. (II) A circular loop in the plane of the paper lies in a 0.75-T magnetic field pointing into the paper. If the loop's diameter changes from 20.0 cm to 6.0 cm in 0.50 s, (a) what is the direction of the induced current. (b) what is the magnitude of the average induced emf. and (c) if the coil resistance is 2.5 ft. what is the average induced current?

14. (II) The moving rod in Fig. 2112 is 13.2 cm long and generates an emf of 120 mV while moving in a 0.90-T magnetic field, (a) What is its speed? (/>) What is the electric field in the rod?

15. (II) Part of a single rectangular loop of wire with dimensions shown in Fig. 21-51 is situated inside a region of uniform magnetic field of 0.550 T. The total resistance of the loop is 0.230(1. Calculate the force required to pull the loop from the field (to the right) at a constant velocity of 3.40 m/s. Neglect gravity.

16. (II) A 500-turn solenoid. 25 cm long, has a diameter of 2.5 cm. A 10-turn coil is wound tightly around the center of the solenoid. If the current in the solenoid increases uniformly from 0 to 5.0 A in 0.60 s, what will be the induced emf in the short coil during this lime?

17. (II) In Fig. 21-12. the rod moves with a speed of 1.6 m/s, is 30.0 cm long, and has a resistance of 2.5(1. Hie magnetic field is 0.35 T. and the resistance of the U-shaped conductor is 25.0(1 at a given instant. Calculate (a) the induced emf, (b) the current in the U-shaped conductor, and (c) the external force needed to keep the rods velocity constant at that instant.

18. (Ill) A 22.0-cm-diameter coil consists of 20 turns of circular copper wire 2.6 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 8.65 X 10~ - T/s. Determine (a) the current in the loop, and (b) the rate at which thermal energy is produced.

19. (Ill) The magnetic field perpendicular to a single 13.2-cm-diameter circular loop of copper wire decreases uniformly from 0.750 T to zero. If the wire is 2.25 mm in diameter, how much charge moves past a point in the coil during this operation?

20. (I) A simple generator is used to generate a peak output voltage of 24.0 V. The square armature consists of windings that arc 6.0 cm on a side and rotates in a field of 0.420 T at a rate of 60.0rev/s. How many loops of wire should be wound on the square armature ?

21. (II) The generator of a car idling at 1100 rpm produces 12.4 V. What will the output be at a rotation speed of 2500 rpm. assuming nothing else changes?

22. (II) Show that the rms output_(Section 187) of an ac generator is Vrms = .\'ABa>/V2. where io = 2ttf.

23. (II) A simple generator has a 320-loop square coil 21.0 cm on a side. How fast must it turn in a 0.650-T field to produce a 120-V peak output?

24. (II) A 450-loop circular armature coil with a diameter of 8.0 cm rotates at 120rev/s in a uniform magnetic field of strength 0.55 T. (a) What is the rms voltage output of the generator? (b) What would you do to the rotation frequency in order to double the rms voltage output?

25. (II) A generator rotates at 85 Hz in a magnetic field of 0.030 T. It has 1000 turns and produces an rms voltage of 150 V and an rms current of 70.0 A. (d) What is the peak current produced? (6) What is the area of each turn of the coil?

26. (I) A motor has an armature resistance of 3.25 Cl. If it draws 8.20 A when running at full speed and connected to a 120-V line, how large is the back emf?

27. (I) The back emf in a motor is 72 V when operating at 1800 rpm. What would be the back emf at 2500 rpm if the magnetic field is unchanged?

28. (II) The back emf in a motor is 95 V when the motor is operating at 1000 rpm. How would you change the motors magnetic field if you wanted to reduce the back emf to 65 V when the motor was running at 2500 rpm?

29. (II) What will be the current in the motor of Example 21 -9 if the load causes it to run at half speed?

30. (I) A transformer is designed to change 120 V into 10.000 V. and there are 164 turns in the primary coil. How many turns are in the secondary coil?

31. (I) A transformer has 320 turns in the primary coil and 120 in the secondary coil. What kind of transformer is this, and by what factor does it change the voltage? By what factor docs it change the current?

32. (I) A step-up transformer increases 25 V' to 120 V. What is the current in the secondary coil as compared to the primary coil?

33. (I) Neon signs require 12 kV for their operation. To operate from a 240-V line, what must be the ratio of secondary to primary turns of the transformer? What would the voltage output be if the transformer were connected backward?

34. (II) A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 7.5 A to the train, (a) What voltage is present across the tracks? (b) Is the transformer step-up or step-down?

35. (II) TTie output voltage of a 95-W transformer is 12 V. and the input current is 22 A. (a) Is this a step-up or a step-down transformer? (b) By what factor is the voltage multiplied?

36. (II) A transformer has 330 primary turns and 1340 secondary turns. The input voltage is 120 V and the output current is 15.0 A. What are the output voltage and input current?

37. (II) If 30 MW of power at 45 kV (rms) arrives at a town from a generator via 4.0-il transmission lines, calculate (a) the emf at the generator end of the lines, and (b) the fraction of the power generated that is wasted in the lines.

38. (Ill) 65 kW is to arrive at a town over two 0.100-11 lines. Estimate how much powfer is saved if the voltage is stepped up from 120 V to 1200 V and then down again, rather than simply transmitting at 120 V. Assume the transformers are each 99%: efficient.

*39. (I) If the current in a 180-mH coil changes steadily from 25.0 A to 10.0 A in 350 ms. what is the magnitude of the induced emf?

* 40. (I) What is the inductance of a coil if the coil produces an emf of 2.50 V when the current in it changes from -28.0 mA to +31.0 mA in 12.0 ms?

*41. (I) What is the inductance L of a 0.60-m-long air-filled coil 2.9 cm in diameter containing 10,000 loops?

* 42. (I) How many turns of wire would be required to make a 130-mH inductance out of a 30.0-cm- long air-filled coil with a diameter of 5.2 cm?

* 43. (II) An air-filled cylindrical inductor has 2800 turns, and it is 2.5 cm in diameter and 28.2 cm long, (a) What is its inductance? (b) How many turns would you need to generate the same inductance if the core wrere iron-filled instead? Assume the magnetic permeability of iron is about 1200 times that of free space.

*44. (II) A coil has 2.25-Cl resistance and 440-mH inductance. If the current is 3.00 A and is increasing at a rate of 3.50 A/s, what is the potential difference across the coil at this moment?

*45. (Ill) A long thin solenoid of length / and cross-sectional area A contains closely packed turns of wire. Wrapped tightly around it is an insulated coil of turns. Fig. 21-52. Assume all the flux from coil 1 (the solenoid) passes through coil 2, and calculate the mutual inductance.

* 46. (Ill) The wire of a tightly wound solenoid is unwound and used to make another tightly wound solenoid of twice the diameter. By what factor docs the inductance change?

*47. (I) The magnetic field inside an air-filled solenoid 36 cm long and 2.0 cm in diameter is 0.80 T. Approximately how-much energy is stored in this field?

* 48. (II) At a given instant the current through an inductor is 50.0 m A and is increasing at the rate of 115 mA/s. What is the initial energy stored in the inductor if the inductance is known to be 60.0 mH, and how long does it take for the energy to increase by a factor of 10 from the initial value?

49. (II) Assuming the F.arth's magnetic field averages about 0.50 X 10-4T near the surface of the Earth, estimate the total energy stored in this field in the first 10 km above the Earths surface.

50. (II) Determine A//Af at / = 0 (when the battery is connected) for the LR circuit of Fig. 21-33 and show that if / continued to increase at this rate, it would reach its maximum value in one time constant.

51. (Ill) After how many time constants does the current in Fig. 21-33 reach within (a) 10%. (b) 1.0%. and (c) 0.1% of its maximum value?

52. (Ill) Two tightly wound solenoids have the same length and circular cross-sectional area. But solenoid 1 uses wire that is half as thick as solenoid 2. (a) What is the ratio of their inductances? (b) What is the ratio of their inductive time constants (assuming no other resistance in the circuits)?

53. (I) What is the reactance of a 7.20-^iF capacitor at a frequency of (a) 60.0 Hz. (b) l.OOMHz?

54. (I) At what frequency will a 22.0-mH inductor have a reactance of 66011?

55. (I) At what frequency will a 2.40-/xF capacitor have a reactance of 6.70 kll?

56. (II) Plot a graph of the reactance of a 1.0-juF capacitor as a function of frequency from 10 to 1000 Hz.

57. (II) Plot a graph of the reactance of a 1.0-mH inductor as a function of frequency from 100 to 10,000 Hz.

58. (II) Calculate the reactance of. and rms current in. a 160-mH radio coil connected to a 240-V (rms) 10.0-kHz ac line. Ignore resistance.

59. (II) An inductance coil operates at 240 V and 60.0 Hz. It draws 12.8 A. What is the coils inductance?

60. (II) (a) What is the reactance of a well-insulated 0.030-/xF capacitor connected to a 2.0-k V (rms) 720-Hz line? (b) What will be the peak value of the current?

*61. (I) A 30-kll resistor is in series with a 45-mH inductor and an ac source. Calculate the impedance of the circuit if the source frequency is (r/) 50 Hz. and (b) 3.0 x 104 Hz.

* 62. (I) A 3.5-kll resistor and a 4.0-yu.F capacitor are connected in series to an ac source. Calculate the impedance of the circuit if the source frequency is () 60 Hz, and (b) 60.000 Hz.

* 63. (I) For a 120-V rms 60-Hz voltage, an rms current of 70 mA passing through the human body for 1.0 s could be lethal. What must be the impedance of the body for this to occur?

64. (II) What is the resistance of a coil if its impedance is 23511 and its reactance is 13511?

*65. (II) What are the total impedance, phase angle, and rms current in an LRC circuit connected to a 10.0-kHz, 725-V (rms) source if L = 22.0 mH. R = 8.70 kll. and C = 6250 pF?

* 66. (Ill) A 2.5-kll resistor in series with a 420-mH inductor is driven by an ac power supply. At what frequency is the impedance double that of the impedance at 60 Hz?

* 67. (Ill) (n) What is the rms current in an RL circuit when a 60.0-Hz 120-V rms ac voltage is applied, where R = 1.80 kll, and L = 350 mH? (b) What is the phase angle between voltage and current? (c) What are the rms voltage readings across R and L?

*68. (Ill) (a) What is the rms current in an RC circuit if R = 8.80 kll. C = 1.80 ^iF. and the rms applied voltage is 120 V at 60.0 Hz? (b) What is the phase angle between voltage and current? (c) What are the voltmeter readings across R and C?

*69. (I) A 3500-pF capacitor is connected to a 55.0-^tH coil of resistance 3.0011. What is the resonant frequency of this circuit?

* 70. (I) The variable capacitor in the tuner of an AM radio has a capacitance of 2800 pF when the radio is tuned to a station at 580 kHz. (a) What must l>e the capacitance for a station at 1600 kHz? (b) What is the inductance (assumed constant)?

71. (II) An LRC circuit has L = 14.8 mH and R = 4.4011. (a) What value must C have to produce resonance at 3600 Hz? (b) What will be the maximum current at resonance if the peak external voltage is 150 V?

72. Suppose you are looking at two current loops in the plane of the page as shown in Fig. 21-53. When switch S is thrown in the left-hand coil, (a) what is the direction of the induced current in the other loop? (/?) What is the situation after a long time? (c) What is the direction of the induced current in the right-hand loop if that loop is quickly pulled horizontally to the right?

73. A square loop 24.0 cm on a side has a resistance of 5.2011. It is initially in a 0.665-T magnetic field, with its plane perpendicular to B, but is removed from the field in 40.0 ms. Calculate the electric energy dissipated in this process.

74. A high-intensity desk lamp is rated at 45 W but requires only 12 V. It contains a transformer that converts 120-V household voltage, (a) Is the transformer step-up or step-down? (/>) What is the current in the secondary coil when the lamp is on? (c) What is the current in the primary coil? (r/) What is the resistance of the bulb when on?

75. Power is generated at 24 kV at a generating plant located 118 km from a town that requires 50 MW of power at 12 kV. Two transmission lines from the plant to the town each have a resistance of 0.10 ll/'km. What should the output voltage of the transformer at the generating plant be for an overall transmission efficiency of 98.5%, assuming a perfect transformer?

76. The primary windings of a transformer which has an 80% efficiency are connected to 110-V ac. 'llie secondary windings are connected across a 2.4-11. 75-W lightbulb. (a) Calculate the current through the primary windings of the transformer. (/>) Calculate the ratio of the number of primary windings of the transformer to the number of secondary windings of the transformer.

77. A pair of power transmission lines each have a 0.80-11 resistance and carry 740 A over 9.0 km. If the rms input voltage is 42 kV. calculate (a) the voltage at the other end. (/>) the power input, (c) power loss in the lines, and (d) the power output.

78. Two resistanceless rails rest 32 cm apart on a 6.0U ramp. They are joined at the bottom by a 0.60-11 resistor. At the top a copper bar of mass 0.040 kg (ignore its resistance) is laid across the rails. The whole apparatus is immersed in a vertical 0.55-T field. What is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?

79. Show that the power loss in transmission lines. PL. is given by PL = (Pr)2 RL/V2, where Pr is the power transmitted to the user. V is the delivered voltage, and /?L is the resistance of the power lines.

80. A coil with 150 turns, a radius of 5.0cm, and a resistance of 1211 surrounds a solenoid with 230 turns/cm and a radius of 4.5 cm; sec Fig. 21-54. The current in the solenoid changes at a constant rate from 0 to 2.0 A in 0.10 s. Calculate the magnitude and direction of the induced current in the coil.

81. A certain electronic device needs to be protected against sudden surges in current. In particular, after the power is turned on the current should rise no more than 7.5 mA in the first 120 The device has resistance 15011 and is designed to operate at 55 mA. How would you protect this device?

82. A 25-turn 12.5-cm-diameter coil is placed between the pole pieces of an electromagnet. When the magnet is turned on. the flux through the coil changes, inducing an emf. At what rate (in T/s) must the field produced by the magnet change if the emf is to be 120 V?

* 83. Calculate the peak output voltage of a simple generator whose square armature windings are 6.60 cm on a side; the armature contains 155 loops and rotates in a field of 0.200 T at a rate of 120rev/s.

* 84. Typical large values for electric and magnetic fields attained in laboratories are about 1.0 x 104V/m and 2.0 T. (a) Determine the energy density for each field and compare. (b) What magnitude electric field would be needed to produce the same energy density as the 2.0-T magnetic field?

* 85. What is the inductance L of the primary of a transformer whose input is 220 V at 60.0 Hz if the current drawn is 5.8 A? Assume no current in the secondary.

* 86. A 130-mH coil whose resistance is 18.5 11 is connected to a capacitor C and a 1360-Hz source voltage. If the current and voltage are to be in phase, what value must C have?

* 87. An inductance coil draws 2.5-A dc when connected to a 36-V battery. When connected to a 60- Hz 120-V (rms) source, the current drawn is 3.8 A (rms). Determine the inductance and resistance of the coil.

*88. A 135-mH inductor with 2.0-11 resistance is connected in series to a 20-/xF capacitor and a 60- Hz. 45-V source. Calculate (a) the rms current, and (b) the phase angle.

* 89. The Q factor of a resonance circuit can be defined as the ratio of the voltage across the capacitor (or inductor) to the voltage across the resistor, at resonance. The larger the O factor, the sharper the resonance curve will be and the sharper the tuning. () Show that the Q factor is given by the equation Q = (l/R) VL/C. (b) At a resonant frequency /0 = 1.0 MHz, what must be the values of L and R to produce a Q factor of 550? Assume that C = O.OlOfiF.

The pivoted metal bar with slots in Fig. 21–45 falls much more quickly through a magnetic field than does a solid bar. Explain.

Given the two charges shown in Fig. , at what position(s) is the electric field zero? Is the field zero at any other points, not on the axis?

Problem 11P The magnetic field perpendicular to a circular wire loop 12.0 cm in diameter is changed from +0.52 T to –0.45 T in 180 ms, where + means the field points away from an observer and – toward the observer, (a) Calculate the induced emf. (b) In what direction does the induced current flow?

Problem 1P The magnetic flux through a coil of wire containing two loops changes from -50 Wb to +38 Wb in 0.42 s. What is the emf induced in the coil?

Problem 11Q Will an eddy current brake (Fig. 21–20) work on a copper or aluminum wheel, or must the wheel be ferromagnetic? Explain.

Problem 12P (II) The moving rod in Fig. 21–11 is 12.0 cm long and is pulled at a speed of 18.0 cm/s. If the magnetic field is 0.800 T, calculate (a) the emf developed, and (b) the electric field felt by electrons in the rod.

Problem 1Q What would be the advantage, in Faraday’s experiments (Fig. 21–1), of using coils with many turns?

(I) The rectangular loop in Fig. 21–46 is being pushed to the right, where the magnetic field points inward. In what direction is the induced current?

Problem 2Q What is the difference between magnetic flux and magnetic field?

Problem 12Q It has been proposed that eddy currents be used to help sort solid waste for recycling. The waste is first ground into tiny pieces and iron removed with a magnet. The waste then is allowed to slide down an incline over permanent magnets. How will this aid in the separation of nonferrous metals (Al, Cu, Pb, brass) from nonmetallic materials?

Problem 13P A circular loop in the plane of the paper lies in a 0.75-T magnetic field pointing into the paper. If the loop’s diameter changes from 20.0 cm to 6.0 cm in 0.50 s, (a) what is the direction of the induced current, (b) what is the magnitude of the average induced emf, and (c) if the coil resistance is 2.5 ?, what is the average induced current?

(I) The north pole of the magnet in Fig. 21–47 is being inserted into the coil. In which direction is the induced current flowing through resistor R?

Problem 3Q Suppose you are holding a circular ring of wire in front of you and (a) suddenly thrust a magnet, south pole first, away from you toward the center of the circle. Is a current induced in the wire? (b) Is a current induced when the magnet is held steady within the ring? (c) Is a current induced when you withdraw the magnet? For each yes answer, specify the direction. Explain your answers.

Problem 4P A 9.6-cm-diameter circular loop of wire is in a 1.10-T magnetic field. The loop is removed from the field in 0.15 s. What is the average induced emf?

Problem 4Q Two loops of wire are moving in the vicinity of a very long straight wire carrying a steady current as shown in Fig. 21–43 Find the direction of the induced current in each loop. Figure 21–43

Problem 5P A 12.0-cm-diameter loop of wire is initially oriented perpendicular to a 1.5-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.20 s. What is the average induced emf in the loop?

Problem 5Q Suppose you are looking along a line through the centers of two circular (but separate) wire loops, one behind the other. A battery is suddenly connected to the front loop, establishing a clockwise current. (a) Will a current be induced in the second loop? (b) If so, when does this current start? (c) When does it stop? (d) In what direction is this current? (e) Is there a force between the two loops? (f ) If so, in what direction?

Problem 6P A 10.2-cm-diameter wire coil is initially oriented so that its plane is perpendicular to a magnetic field of 0.63 T pointing up. During the course of 0.15 s, the field is changed to one of 0.25 T pointing down. What is the average induced emf in the coil?

In Fig. 21–44, determine the direction of the induced current in resistor RA when (a) when coil B is moved toward coil A, (b) when coil B is moved away from A, (c) when the resistance RB is increased.

Problem 7P A 15-cm-diameter circular loop of wire is placed in a 0.50-T magnetic field, (a) When the plane of the loop is perpendicular to the field lines, what is the magnetic flux through the loop? (b) The plane of the loop is rotated until it makes a 35° angle with the field lines. What is the angle ? in Eq. 21–1 for this situation?(c) What is the magnetic flux through the loop at this angle? Equation 21–1 ?B = B? A = BA cos ?

Problem 7Q In situations where a small signal must travel over a distance, a shielded cable is used in which the signal wire is surrounded by an insulator and then enclosed by a cylindrical conductor (shield) carrying the return current. Why is a “shield” necessary?

Problem 8Q What is the advantage of placing the two insulated electric wires carrying ac close together or even twisted about each other?

(II) If the resistance of the resistor in Fig. is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop? (b) What would it be if the small loop were placed outside the larger one, to the left?

(II) What is the direction of the induced current in the circular loop due to the current shown in each part of Fig.

Problem 9Q Explain why, exactly, the lights may dim briefly when a refrigerator motor starts up. When an electric heater is turned on, the lights may stay dimmed as long as the heater is on. Explain the difference.

(II) If the solenoid in Fig. is being pulled away from the loop shown, in what direction is the induced current in the loop?