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Figure P30.44
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Chapter 31 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- 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_forwardA long, straight wire carries a current given by I = Imax sin (t + ). The wire lies in the plane of a rectangular coil of N turns of wire as shown in Figure P30.45. The quantities Imax, , and are all constants. Assume Imax = 50.0 A, = 200 s1, N = 100, h = = 5.00 cm, and L = 20.0 cm. Determine the emf induced in the coil by the magnetic field created by the current in the straight wire. Figure P30.45arrow_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
- A rectangular conducting loop with dimensions w = 32.0 cm and h = 78.0 cm is placed a distance a = 5.00 cm from a long, straight wire carrying current I = 7.00 A in the downward direction (Fig. P32.75). a. What is the magnitude of the magnetic flux through the loop? b. If the current in the wire is increased linearly from 7.00 A to 15.0 A in 0.230 s, what is the magnitude of the induced emf in the loop? c. What is the direction of the current that is induced in the loop during this time interval?arrow_forwardThe 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_forwardA toroid having a rectangular cross section (a = 2.00 cm by b = 3.00 cm) and inner radius R = 4.00 cm consists of N = 500 turns of wire that carry a sinusoidal current I = Imax sin t, with Imax = 50.0 A and a frequency f = /2 = 60.0 Hz. A coil that consists of N = 20 turns of wire is wrapped around one section of the toroid as shown in Figure P30.9. Determine the emf induced in the coil as a function of time. Figure P30.9arrow_forward
- Figure 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_forwardA square loop with side length L, mass M, and resistance R lies in the xy plane. A magnetic field B = B0(y/L) k is present in the region of the space near the loop. Determine the magnitude and direction of the induced current in the loop as the loop starts moving at velocity v = B0(y/L) j.arrow_forwardFigure P32.21 shows a circular conducting loop with a 5.00-cm radius and a total resistance of 1.30 placed within a uniform magnetic field pointing into the page. a. What is the rate at which the magnetic field is changing if a counterclockwise current I = 4.60 102 A is induced in the loop? b. Is the induced current caused by an increase or a decrease in the magnetic field with time?arrow_forward
- A helicopter (Fig. P30.11) has blades of length 3.00 m, extending out from a central hub and rotating at 2.00 rev/s. If the vertical component of the Earths magnetic field is 50.0 T, what is the emf induced between the blade tip and the center hub? Figure P30.11arrow_forwardA long solenoid, with its axis along the x axis, consists of 200 turns per meter of wire that carries a steady current of 15.0 A. A coil is formed by wrapping 30 turns of thin wire around a circular frame that has a radius of 8.00 cm. The coil is placed inside the solenoid and mounted on an axis that is a diameter of the coil and coincides with the y axis. The coil is then rotated with an angular speed of 4.00 rad/s. The plane of the coil is in the yz plane at t = 0. Determine the emf generated in the coil as a function of time.arrow_forwardA wire is bent in the form of a square loop with sides of length L (Fig. P30.24). If a steady current I flows in the loop, determine the magnitude of the magnetic field at point P in the center of the square. FIGURE P30.24arrow_forward
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