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You are working for a company that manufactures motors and generators. At the end of your first day of work, your supervisor explains to you that you will be assigned to a team that is designing a new homopolar generator. You have no idea what that is, but agree wholeheartedly to the assignment. At home that evening, you go online to learn about the homopolar generator and find the following. The homopolar generator, also called the Faraday disk, is a low-voltage, high-current electric generator. It consists of a rotating
Figure P30.17
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Chapter 30 Solutions
Physics for Scientists and Engineers
- Three long, current-carrying wires are parallel to one another and separated by a distance d. The magnitudes and directions of the currents are shown in Figure P30.91. Wires 1 and 3 are fixed, but wire 2 is free to move. Wire 2 is displaced to the right by a small distance x. Determine the net force (per unit length) acting on wire 2 and the angular frequency of the resulting oscillation. Assume the mass per unit length of wire 2 is and x d. FIGURE P30.91arrow_forwardYou are working for a company that manufactures motors and generators. At the end of your first day of work, your supervisor explains to you that you will be assigned to a team that is designing a new homopolar generator. You have no idea what that is, but agree wholeheartedly to the assignment. At home that evening, you go online to learn about the homopolar generator and find the following. The homopolar generator, also called the Faraday disk, is a low-voltage, high-current electric generator. It consists of a rotating conducting disk with one stationary brush (a sliding electrical contact) at its axle and another at a point on its circumference as shown in Figure P30.17. A uniform magnetic field is applied perpendicular to the plane of the disk. When superconducting coils are used to produce a large magnetic field, a homopolar generator can have a power output of several megawatts. Such a generator is useful, for example, in purifying metals by electrolysis. If a voltage is applied to the output terminals of the generator, it runs in reverse as a homopolar motor capable of providing great torque, useful in ship propulsion. At work the next morning, your supervisor tells you that the homopolar generator under consideration will have a magnetic field of magnitude B = 0.900 T and the radius of the disk is r = 0.400 m. The desired emf to be generated with the device is E=25.0V. Your supervisor asks you to determine the required angular speed of the disk to achieve this result. Figure P30.17arrow_forwardReview. After removing one string while restringing his acoustic guitar, a student is distracted by a video game. His experimentalist roommate notices his inattention and attaches one end of the string, of linear density = 3.00 103 kg/m, to a rigid support. The other end passes over a pulley, a distance, = 64.0 cm from the fixed end, and an object of mass m = 27.2 kg is attached to the hanging end of the string. The roommate places a magnet across the string as shown in Figure P23.19. The magnet does not touch the string, but produces a uniform field of 4.50 mT over a 2.00-cm length of the string and negligible field elsewhere. Strumming the string sets it vibrating vertically at its fundamental (lowest) frequency. The section of the string in the magnetic field moves perpendicular to the field with a uniform amplitude of 1.50 cm. Find (a) the frequency and (b) the amplitude of the emf induced between the ends of the string.arrow_forward
- What is the Earths magnetic flux through a. a basketball, b. a hula hoop standing up perpendicularly on its rim at the North Pole, and c. a hula hoop lying on the ground at the North Pole?arrow_forward(a) Use the result of the previous problem to calculate the magnetic field between, above, and below the pair of infinite sheets shown in the accompanying figure, (b) Repeat your calculations if the direction of the current in the lower sheet is reversed.arrow_forwardA metal rod of mass m slides without friction along two parallel horizontal rails, separated by a distance l and connected by a resistor R, as shown in Figure P23.15. A uniform vertical magnetic field of magnitude B is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give die rod a speed v. In terms of m, l, R, B, and v, find the distance the rod will then slide as it coasts to a stop.arrow_forward
- A very long coaxial cylindrical cable is composed of an inner solid cylinder of radius R1 and an outer hollow cylinder of radius R2,{The space between inner and outer cylinders is empty}. An electrical current I runs through the inner cylindrical wire and returns through the outer cylindrical wire. (a) Write down the magnetic energy density function for both the inner and outer regions of the cable. (b) What is the energy per unit length L, for all regions (Both for inner and outer regions)? I did ask the same question last time, but I think the tutor was confused since the radius of the inner cylinder is R1, outer is R2. It's not R1 = 1R, R2 = 2R. Thank youarrow_forwardConsider the same situation as in the previous problem. This time the magnet has mass 6.31 kg and the force pulling themagnet to the right has magnitude 157.8 N. What is the magnitude of the tension force in the cord?A) 219.7 NB) 155.7 NC) 300.3 ND) 169.5 Narrow_forwardThe figure below is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, an outer conductor, and another rubber layer. In a particular application, the current in the inner conductor is I1 = 1.06 A out of the page and the current in the outer conductor is I2 = 2.84 A into the page. Assuming the distance d = 1.00 mm, answer the following. a) Determine the magnitude and direction of the magnetic field at point a. b) Determine the magnitude and direction of the magnetic field at point b. Note: See image for the orignal question and figurearrow_forward
- The figure below is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, an outer conductor, and another rubber layer. In a particular application, the current in the inner conductor is I1 = 1.14 A out of the page and the current in the outer conductor is I2 = 2.90 A into the page. Assuming the distance d = 1.00 mm, answer the following.(a) Determine the magnitude and direction of the magnetic field at point a.find magnitude ut and direction(b) Determine the magnitude and direction of the magnetic field at point b.find magnitude ut and directionarrow_forwardA packed bundle of 100 long, straight, insulated wires forms a cylinder of radius R = 0.500 cm. If each wire carries 2.00 A, what are (a) the magnitude and (b) the direction of the magnetic force per unit length acting on a wire located 0.200 cm from the center of the bundle? (c) What If? Would a wire on the outer edge of the bundle experience a force greater or smaller than the value calculated in parts (a) and (b)? Give a qualitative argument for your answer.arrow_forwardA magnetic dipole moment of m = (7.50, -8.38, 4.59) Am² is inside a uniform magnetic field of B = (3.34, -6.77, 6.79) T. What is the potential energy of the dipole? (a) What is the angle between the magnetic dipole moment vector and the magnetic field vector? (b) What is the magnitude of the torque acting on the dipole?arrow_forward
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