Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
9th Edition
ISBN: 9781305266292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 31, Problem 68AP
A
In this case, note that the emf decreases with increasing r as you might expect.
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29.57 The long, straight wire shown in Fig. P29.57a carries constant current I. A metal bar with length L is moving at constant velocity v, as shown in the figure. Point a is a distance d from the wire.
(a) Calculate the emf induced in the bar.
(b) Which point, a or b, is at higher potential?
(c) If the bar is replaced by a rectangular wire loop of resistance R (Fig. P29.57b), what is the magnitude of the current induced in the loop?
Hint: (b) and (c) are conceptual questions.
30. A short wire runs along an x axis from x = a to x = -a
(Figure P30.30). At t = 0, there is a small sphere carry-
ing charge +9o at x = a and a small sphere carrying charge
-9o at x = -a. As the spheres discharge and a current is
established in the wire, show that, for t>0, the generalized
form of Ampère's law (Eq. 30.13) and the Biot-Savart law
(Eq. 28.12) give the same result for the magnitude of the mag-
netic field a distance b up the y axis. (Hint: Obtain the elec-
tric flux through a circular disk in the yz plane, centered at
the origin. Because the electric field is not constant over the
surface of the disk, you must divide the disk into a nested set
of rings of various radii and integrate. A representative ring
should have radius r and radial extent dr.) •..
Figure P30.30
b
-90
A conducting rod of length ℓ moves on two horizontal, frictionless rails as shown inFigure P31.26. If a constant force of 1.00 N moves the bar at 2.00 m/s through amagnetic field B that is directed into the page (a) what is the current through the 8.00-Ω resistor R? (b) What is the rate at which energy is delivered to the resistor? (c) Whatis the mechanical power delivered by the force Fapp?
Chapter 31 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
Ch. 31.1 - A circular loop of wire is held in a uniform...Ch. 31.2 - QUICK QUIZ 30.2 In Figure 30.8a, a given applied...Ch. 31.3 - Figure 30.12 (Quick Quiz 30.3) QUICK QUIZ 30.3...Ch. 31.5 - Prob. 31.4QQCh. 31.6 - Prob. 31.5QQCh. 31 - Prob. 1OQCh. 31 - Prob. 2OQCh. 31 - Prob. 3OQCh. 31 - Prob. 4OQCh. 31 - Prob. 5OQ
Ch. 31 - Prob. 6OQCh. 31 - Prob. 7OQCh. 31 - Prob. 8OQCh. 31 - Prob. 9OQCh. 31 - Prob. 10OQCh. 31 - Prob. 11OQCh. 31 - Prob. 1CQCh. 31 - Prob. 2CQCh. 31 - Prob. 3CQCh. 31 - Prob. 4CQCh. 31 - Prob. 5CQCh. 31 - Prob. 6CQCh. 31 - Prob. 7CQCh. 31 - Prob. 8CQCh. 31 - Prob. 9CQCh. 31 - Prob. 10CQCh. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - Prob. 3PCh. 31 - Prob. 4PCh. 31 - Prob. 5PCh. 31 - Prob. 6PCh. 31 - Prob. 7PCh. 31 - Prob. 8PCh. 31 - Prob. 9PCh. 31 - Scientific work is currently under way to...Ch. 31 - Prob. 11PCh. 31 - Prob. 12PCh. 31 - Prob. 13PCh. 31 - Prob. 14PCh. 31 - Prob. 15PCh. 31 - Prob. 16PCh. 31 - A coil formed by wrapping 50 turns of wire in the...Ch. 31 - Prob. 18PCh. 31 - Prob. 19PCh. 31 - Prob. 20PCh. 31 - Prob. 21PCh. 31 - Prob. 22PCh. 31 - Prob. 23PCh. 31 - A small airplane with a wingspan of 14.0 m is...Ch. 31 - A 2.00-m length of wire is held in an eastwest...Ch. 31 - Prob. 26PCh. 31 - Prob. 27PCh. 31 - Prob. 28PCh. 31 - Prob. 29PCh. 31 - Prob. 30PCh. 31 - Prob. 31PCh. 31 - Prob. 32PCh. 31 - Prob. 33PCh. 31 - Prob. 34PCh. 31 - Prob. 35PCh. 31 - Prob. 36PCh. 31 - Prob. 37PCh. 31 - Prob. 38PCh. 31 - Prob. 39PCh. 31 - Prob. 40PCh. 31 - Prob. 41PCh. 31 - Prob. 42PCh. 31 - Prob. 43PCh. 31 - Prob. 44PCh. 31 - Prob. 45PCh. 31 - Prob. 46PCh. 31 - Prob. 47PCh. 31 - Prob. 48PCh. 31 - The rotating loop in an AC generator is a square...Ch. 31 - Prob. 50PCh. 31 - Prob. 51APCh. 31 - Prob. 52APCh. 31 - Prob. 53APCh. 31 - Prob. 54APCh. 31 - Prob. 55APCh. 31 - Prob. 56APCh. 31 - Prob. 57APCh. 31 - Prob. 58APCh. 31 - Prob. 59APCh. 31 - Prob. 60APCh. 31 - Prob. 61APCh. 31 - Prob. 62APCh. 31 - Prob. 63APCh. 31 - Prob. 64APCh. 31 - Prob. 65APCh. 31 - Prob. 66APCh. 31 - Prob. 67APCh. 31 - A conducting rod moves with a constant velocity in...Ch. 31 - Prob. 69APCh. 31 - Prob. 70APCh. 31 - Prob. 71APCh. 31 - Prob. 72APCh. 31 - Prob. 73APCh. 31 - Prob. 74APCh. 31 - Prob. 75APCh. 31 - Prob. 76APCh. 31 - Prob. 77APCh. 31 - Prob. 78APCh. 31 - Prob. 79CPCh. 31 - Prob. 80CPCh. 31 - Prob. 81CPCh. 31 - Prob. 82CPCh. 31 - Prob. 83CP
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- A conducting rod of length moves with velocity v parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with the near end a distance r away (Fig. P30.44). Show that the magnitude of the emf induced in the rod is E=0Iv2ln(1+lr) Figure P30.44arrow_forwardFigure P30.39 shows a stationary conductor whose shape is similar to the letter e. The radius of its circular portion is a = 50.0 cm. It is placed in a constant magnetic field of 0.500 T directed out of the page. A straight conducting rod, 50.0 cm long, is pivoted about point O and rotates with a constant angular speed of 2.00 rad/s. (a) Determine the induced emf in the loop POQ. Note that the area of the loop is a2/2. (b) If all the conducting material has a resistance per length of 5.00 /m, what is the induced current in the loop POQ at the instant 0.250 s after point P passes point Q? Figure P30.39arrow_forwardFigure P23.58 is a graph of the induced emf versus time for a coil of N turns rotating with angular speed ω in a uniform magnetic field directed perpendicular to the coil’s axis of rotation. What If? Copy this sketch (on a larger scale) and on the same set of axes show the graph of emf versus t (a) if the number of turns in the coil is doubled, (b) if instead the angular speed is doubled, and (c) if the angular speed is doubled while the number of turns in the coil is halved. Figure P23.58arrow_forward
- Show that Equation 32.28 in the text Ls Kirchhoffs loop rule as applied to the circuit in Figure P32.56 with the switch thrown to position b.arrow_forwardA coil with a self-inductance of 3.0 H and a resistance of 100 2 carries a steady current of 2.0 A. (a) What is the energy stored in the magnetic field of the coil? (b) What is the energy per second dissipated in the resistance of the coil?arrow_forwardA piece of insulated wire is shaped into a figure eight as shown in Figure P23.12. For simplicity, model the two halves of the figure eight as circles. The radius of the upper circle is 5.00 cm and that of the lower circle is 9.00 cm. The wire has a uniform resistance per unit length of 3.00 Ω/m. A uniform magnetic field is applied perpendicular to the plane of the two circles, in the direction shown. The magnetic field is increasing at a constant rate of 2.00 T/s. Find (a) the magnitude and (b) the direction of the induced current in the wire. Figure P23.12arrow_forward
- Review. Figure P31.31 shows a bar of mass m = 0.200 kg that can slide without friction on a pair of rails separated by a distance = 1.20 m and located on an inclined plane that makes an angle = 25.0 with respect to the ground. The resistance of the resistor is R = 1.00 and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails?arrow_forwardA Figure P32.74 shows an N-turn rectangular coil of length a and width b entering a region of uniform magnetic field of magnitude Bout directed out of the page. The velocity of the coil is constant and is upward in the figure. The total resistance of the coil is R. What are the magnitude and direction of the magnetic force on the coil a. when only a portion of the coil has entered the region with the field, b. when the coil is completely embedded in the field, and c. as the coil begins to exit the region with the field?arrow_forwardA 2.00×10-2 Ω square wire loop 40.0 cm on a side has its plane normal to a uniform magnetic field of magnitude B = 3.0 T. If you pull two opposite sides of the loop away from each other, the other two sides automatically draw toward each other, reducing the area enclosed by the loop.If the area is reduced to zero in a time of 0.30 s what is the average emf during this time interval? What is the average current during this time interval?arrow_forward
- An 820-turn wire coil of resistance 24.0 V is placed on top of a 12 500-turn, 7.00-cm-long solenoid, as in Figure P20.57. Both coil and solenoid have crosssectional areas of 1.00 × 10-4 m2 . (a) How long does it take the solenoid current to reach 0.632 times its maximum value? (b) Determine the average back emf caused by the self-inductance of the solenoid during this interval. The magnetic field produced by the solenoid at the location of the coil is one-half as strong as the field at the center of the solenoid. (c) Determine the average rate of change in magnetic flux through each turn of the coil during the stated interval. (d) Find the magnitude of the average induced current in the coil.arrow_forwardAn N - turn circular wire coil of radius r lies in thexy - plane (the plane of the page), as in Figure P20.10. A uniformmagnetic field is turned on, increasing steadily from 0to B0 in the positive z - direction in t seconds. (a) Find a symbolicexpression for the emf, ε, induced in the coil in termsof the variables given. (b) Looking down on at the xy -planefrom the positive z - axis, is the direction of the induced currentclockwise or counterclockwise? (c) If each loop hasresistance R, find an expression for the magnitude of theinduced current, I.arrow_forwardA conducting rod moves with a constant velocity in a direction perpendicular to a long, straight wire carrying a current I as shown in Figure. Find the magnitude of the emf generated between the ends of the rod.arrow_forward
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What is Electromagnetic Induction? | Faraday's Laws and Lenz Law | iKen | iKen Edu | iKen App; Author: Iken Edu;https://www.youtube.com/watch?v=3HyORmBip-w;License: Standard YouTube License, CC-BY