Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 30, Problem 44AP
A
Figure P30.44
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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 moves with a constant velocity in a direction perpendicular to a long, straight wire carrying a current I as shown in Figure P30.40. Show that the magnitude of the emf generated between the ends of the rod isChapter 30, Problem 40AP, A conducting rod moves with a constant velocity in a direction perpendicular to a long, straight , example 1In this case, note that the emf decreases with increasing r as you might expect.Figure P30.40Chapter 30, Problem 40AP, A conducting rod moves with a constant velocity in a perpendicular to a long, straight , example 2
Chapter 30 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 30.1 - A circular loop of wire is held in a uniform...Ch. 30.2 - QUICK QUIZ 30.2 In Figure 30.8a, a given applied...Ch. 30.3 - Figure 30.12 (Quick Quiz 30.3) QUICK QUIZ 30.3...Ch. 30.5 - Prob. 30.4QQCh. 30 - A circular loop of wire of radius 12.0 cm is...Ch. 30 - An instrument based on induced emf has been used...Ch. 30 - Scientific work is currently under way to...Ch. 30 - A long solenoid has n = 400 turns per meter and...Ch. 30 - An aluminum ring of radius r1 = 5.00 cm and...Ch. 30 - Prob. 6P
Ch. 30 - A coil formed by wrapping 50 turns of wire in the...Ch. 30 - Prob. 8PCh. 30 - A toroid having a rectangular cross section (a =...Ch. 30 - A small airplane with a wingspan of 14.0 m is...Ch. 30 - A helicopter (Fig. P30.11) has blades of length...Ch. 30 - A 2.00-m length of wire is held in an eastwest...Ch. 30 - A metal rod of mass m slides without friction...Ch. 30 - Prob. 14PCh. 30 - Prob. 15PCh. 30 - Prob. 16PCh. 30 - You are working for a company that manufactures...Ch. 30 - You are working in a laboratory that uses motional...Ch. 30 - You are working in a factory that produces long...Ch. 30 - Prob. 20PCh. 30 - Within the green dashed circle show in Figure...Ch. 30 - Prob. 22PCh. 30 - Prob. 23PCh. 30 - Figure P30.24 (page 820) is a graph of the induced...Ch. 30 - The rotating loop in an AC generator is a square...Ch. 30 - In Figure P30.26, a semicircular conductor of...Ch. 30 - Prob. 27PCh. 30 - Prob. 28APCh. 30 - Prob. 29APCh. 30 - Prob. 30APCh. 30 - A circular coil enclosing an area of 100 cm2 is...Ch. 30 - Prob. 32APCh. 30 - A guitars steel string vibrates (see Fig. 30.5)....Ch. 30 - Prob. 34APCh. 30 - A conducting rod of length = 35.0 cm is free to...Ch. 30 - Prob. 36APCh. 30 - Prob. 37APCh. 30 - In Figure P30.38, the rolling axle, 1.50 m long,...Ch. 30 - Figure P30.39 shows a stationary conductor whose...Ch. 30 - Prob. 40APCh. 30 - Figure P30.41 shows a compact, circular coil with...Ch. 30 - Review. In Figure P30.42, a uniform magnetic field...Ch. 30 - An N-turn square coil with side and resistance R...Ch. 30 - A conducting rod of length moves with velocity v...Ch. 30 - A long, straight wire carries a current given by I...Ch. 30 - A rectangular loop of dimensions and w moves with...Ch. 30 - A thin wire = 30.0 cm long is held parallel to...Ch. 30 - Prob. 48CPCh. 30 - Prob. 49CPCh. 30 - Prob. 50CPCh. 30 - Review. The bar of mass m in Figure P30.51 is...
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- A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in Figure P23.7. (a) Determine the magnetic flux through the loop due to the current I. (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the emf that is induced in the loop if b = 10.0 A/s, h = 1.00 cm, w = 10.0 cm, and L = 1.00 m. (c) What is the direction of the induced current in the rectangle? Figure P23.7arrow_forwardA thin wire = 30.0 cm long is held parallel to and d = 80.0 cm above a long, thin wire carrying I = 200 A and fixed in position (Fig. P30.47). The 30.0-cm wire is released at the instant t = 0 and falls, remaining parallel to the current-carrying wire as it falls. Assume the falling wire accelerates at 9.80 m/s2. (a) Derive an equation for the emf induced in it as a function of time. (b) What is the minimum value of the emf? (c) What is the maximum value? (d) What is the induced emf 0.300 s after the wire is released? Figure P30.47arrow_forwardIn Figure P30.38, the rolling axle, 1.50 m long, is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resistor R = 0.400 is connected to the rails at points a and b, directly opposite each other. The wheels make good electrical contact with the rails, so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R. A uniform magnetic field B = 0.080 0 T is vertically downward. (a) Find the induced current I in the resistor. (b) What horizontal force F is required to keep the axle rolling at constant speed? (c) Which end of the resistor, a or b, is at the higher electric potential? (d) What If? After the axle rolls past the resistor, does the current in R reverse direction? Explain your answer. Figure P30.38arrow_forward
- The magnetic field through a square loop of wire with sides of length 3.00 cm changes with time as shown in Figure P32.8, where the sign indicates the direction of the field relative to the axis of the loop. Plot the emf induced in the loop versus time. FIGURE P32.8arrow_forwardIn Figure P20.65 the rolling axle of length 1.50 m is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resist or R = 0.400 is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) A uniform magnetic field B = 0.800 T is directed vertically downward. (a) Find the induced current I in the resistor. (b) What horizontal force F is required to keep the axle rolling at constant speed? (c) Which end of the resistor, a or b. is at the higher electric potential? (d) Alter the axle rolls past the resistor, does the current in R reverse direction? Explain your answer. Figure P20.65arrow_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_forward
- 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?arrow_forwardAn L = 47.0 ncm wire is moving to the right at a speed of v = 6.50 m/s across two parallel wire rails that are connected on the left side, as shown in the figure. The whole apparatus is immersed in a uniform magnetic field that has a magnitude of B = 0.910 T and is directed into the screen. What is the emf induced in the wire? If the moving wire and the rails have a combined total resistance of 1.15 Ohms, what applied force would be required to keep the wire moving at the given velocity? Assume that there is no friction between the moving wire and the rails.arrow_forward49. A bar of mass m and resistance R slides without friction in a horizontal plane, moving on parallel rails as shown in Figure P30.49. The rails are separated by a distance d. A battery that maintains a constant emf ɛ is connected between the rails, and a constant magnetic field B is directed perpendicularly out of the page. Assuming the bar starts from rest at time t = 0, show that at time t it moves with a speed - B²d²t/mR U = Bd 1-e 'out Figure P30.49arrow_forward
- ☺☺ 000000000 What is the length of the rod? m ·V 000 500 50000 A rod is moving from left to right toward a resistor along two parallel conducting rails. The entire loop is inside a magnetic field oriented out of the page. The rod is moving at 54, the magnetic field has a magnitude of 4.3 T, and the induced emf in the loop is 12.5 V. The resistor has a resistance of 61 Q. What is the current through the rod? I = A R What is the magnitude of the Lorentz Force on the rod? F = Narrow_forwardA single loop of copper wire, lying flat in a plane, has an area of 7.60 cm² and a resistance of 2.40 Q. A uniform magnetic field points perpendicular to the plane of the loop. The field initially has a magnitude of 0.500 T, and the magnitude increases linearly to 1.50 T in a time of 1.08 s. What is the induced current (in mA) in the loop of wire over this time? How does Faraday's law relate the change in flux per unit time to the emf? What are the initial and final flux values through the loop? How is the induced emf related to the resistance and induced current? Be careful of units-note the final answer should be expressed in mA. mAarrow_forwardA circular loop of wire with a radius of 0.2 m is placed in a uniform magnetic field of 0.3 T. The loop is oriented so that its plane is perpendicular to the magnetic field. At time t=0, the magnetic field begins to decrease at rate of 0.1 T/s. What is the magnitude of the EMF induced in the loop at t=0.5 seconds? A rectangular loop of wire with dimensions 0.2 m x 0.3 m is placed in a magnetic field that is changing at a rate of 0.1 T/s. The loop is oriented so that its long side is parallel to the magnetic field. At time t=0, the magnetic field begins to decrease at a rate of 0.1 T/s. What is the magnitude of the EMF induced in the loop at t=0.5 seconds?arrow_forward
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