In Figure P30.26, a semicircular conductor of radius R = 0.250 m is rotated about the axis AC at a constant rate of 120 rev/min. A uniform magnetic field of magnitude 1.30 T fills the entire region below the axis and is directed out of the page. (a) Calculate the maximum value of the emf induced between the ends of the conductor. (b) What is the value of the average induced emf for each complete rotation? (c) What If? How would your answers to parts (a) and (b) change if the magnetic field were allowed to extend a distance R above the axis of rotation? Sketch the emf versus time (d) when the field is as drawn in Figure P30.26 and (e) when the field is extended as described in part (c).
Figure P30.26
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Chapter 31 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- 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_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_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 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 rectangular loop of length L and width W is placed in a uniform magnetic field B with its plane perpendicular to the field (Fig. P32.7). Determine the time-averaged induced emf if the loop rotatas with constant angular velocity through an angle of 180 around an axis passing through the loops center a. perpendicular to the loop and b. parallel to its width.arrow_forwardA square coil with a side length of 12.0 cm and 34 turns is positioned in a region with a horizontally directed, spatially uniform magnetic field of 82.0 mT and set to rotate about a vertical axis with an angular speed of 1.20 102 rev/min. a. What is the maximum emf induced in the spinning coil by this field? b. What is the angle between the plane of the coil and the direction of the field when the maximum induced emf occurs?arrow_forward
- A thin copper rod of length L rotates with constant angular velocity about a point O, in a plane perpendicular to a uniform magnetic field B as shown in Figure P32.20. Determine the induced emf across its ends. Consider that the emf produced between the point O and a small segment of the rod, d, is given by d=Bvd.arrow_forwardA square conducting loop with side length a = 1.25 cm is placed at the center of a solenoid 40.0 cm long with a current of 4.30 A flowing through its 420 turns, and it is aligned so that the plane of the loop is perpendicular to the long axis of the solenoid. The radius of the solenoid is 5.00 cm. a. What is the magnetic flux through the loop? b. What is the magnitude of the average emf induced in the loop if the current in the solenoid is increased from 4.30 A to 10.0 A in 1.75 s?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_forward
- An aluminum ring of radius r1 = 5.00 cm and resistance 3.00 104 is placed around one end of a long air-core solenoid with 1 000 turns per meter and radius r2 = 3.00 cm as shown in Figure P30.5. Assume the axial component of the field produced by the solenoid is one-half as strong over the area of the end of the solenoid as at the center of the solenoid. Also assume the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of 270 A/s. (a) What is the induced current in the ring? At the center of the ring, what are (b) the magnitude and (c) the direction of the magnetic field produced by the induced current in the ring? Figure P30.5 Problems 5 and 6.arrow_forwardA coil 4.00 cm in radius, containing 500 turns, is placed in a uniform magnetic field that varies with time according to B = (0.0120 T/s)t + (3.00 * 10-5 T/s4)t4. The coil is connected to a 600 Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil. (a) Find the magnitude of the induced emf in the coil as a function of time. (b) What is the current in the resistor at time t = 5.00 s?arrow_forward
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