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Chapter 30 Solutions
Physics for Scientists and Engineers
- 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 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 2arrow_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_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_forward
- 49. 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_forwardA metal rod PQ moves with a velocity v parallal to a very long straight wire CD carrying a current I as shown in Fig. 25.15. The ends P and Q of the rod are at distances a and b from the wire as shown. Obtain the expression for the emf induced between the ends of the rod. b a D I Fig. 25.15arrow_forwardAn L=57.0 cm wire is moving to the right at a speed of v=7.50 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=0.930 T and is directed into the screen. What is the emf E induced in the wire? If the moving wire and the rails have a combined total resistance of 1.75 Ω, what applied force F 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_forward
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