* You need to test Faraday's law You have a 12-turn rectangular coil that measures
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- Eddy current are induced currents set up in a piece of metal when it moves through a nonuniform magnetic field. For example, consider the flat metal plate swinging at the end of a bar as a pendulum, as shown in Figure CQ20.9. (a) At position 1, the pendulum is moving from a region where there is no magnetic field into a region where the field B is directed into the paper. Show that at position 1 the direction of the eddy current is counterclockwise. (b) At position 2, the pendulum is moving out of the field into a region of zero field. Show that the direction of the eddy current is clockwise in this case. (c) Use right-hand rule number 2 to show that these eddy currents lead to a magnetic force on the plate directed at shown in the figure. Because the induced eddy current always produces a retarding force when the plate enters or leaves the field, the swinging plate quickly comes to rest. Figure CQ20.9arrow_forwardMagnetic field values are often determined by using a device known as a search coil. This technique depends on the measurement of the total charge passing through a coil in a time interval during which the magnetic flux linking the windings changes either because of the coils motion or because of a change in the value of B. (a) Show that as the flux through the coil changes from 1 to 2, the charge transferred through the coil is given by Q = N(2 1)/R, where R is the resistance of the coil and N is the number of turns. (b) As a specific example, calculate B when a total charge of 5.00 104 C passes through a 100-turn coil of resistance 200 and cross-sectional area 40.0 cm2 as it is rotated in a uniform field from a position where the plane of the coil is perpendicular to the field to a position where it is parallel to the field.arrow_forwardTranscranial magnetic stimulation (TMS) is a noninvasive technique used to stimulate tedious of the human brain (Figure P31.3). In TMS, a small coil is placed on the scalp and a brief burst of current in the coil produces a rapidly changing magnetic field inside the brain. The induced emf can stimulate neuronal activity. (a) One such device generates an upward magnetic Held within the brain that rises from zero to 1.50 T in 120 ms. Determine the induced emf around a horizontal circle of tissue of radius 1.60 mm. (b) What If? The field next changes to 0.500 T downward in 80.0 ms. How does the emf induced in this process compare with that in part (a)? Figure P31.3 Problems 3 and 51. The magnetic coil of a Neurostar TMS apparatus is held near the head of a patient.arrow_forward
- An astronaut is connected to her spacecraft by a 25-m-long tether cord as she and the spacecraft orbit Earth in a circular path at a speed of 3.0 105 m/s. At one instant, the voltage measured between the ends of a wire embedded in the cord is measured to be 0.45 V. Assume the long dimension of the cord is perpendicular to the vertical component of Earths magnetic field at that instant. (a) What is the magnitude of the vertical component of Earths field at this location? (b) Does the measured voltage change as the system moves from one location to another? Explain.arrow_forwardAn astronaut is connected to her spacecraft by a 25-m-long tether cord as she and the spacecraft orbit Earth in a circular path at a speed of 3.0 105 m/s. At one instant, the voltage measured between the ends of a wire embedded in the cord is measured to be 0.45 V. Assume the long dimension of the cord is perpendicular to the vertical component of Earths magnetic field at that instant. (a) What is the magnitude of the vertical component of Earths field at this location? (b) Does the measured voltage change as the system moves from one location to another? Explain.arrow_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_forward
- (a) A dc power line for a light-rail system caries 1000 A at an angle of 30.0 to Earth's 5.0105 T field, What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.arrow_forwardWhen a magnet is thrust into a coil as in Figure 23.4(a), what is the direction of the louse exerted by the coil on the magnet? Draw a diagram showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the force depend on the resistance of the galvanometer?arrow_forwardMeasurements affect the system being measured, such as the current loop in Figure 22.56. (a) Estimate file field the loop creates by calculating the field at the center of a circular loop 20.0 cm in diameter carrying 5.00 A. (b) What is the smallest field strength this loop can be used to measure, if its field must alter the measured field by less than 0.0100%?arrow_forward
- Unreasonable Results A surveyor 100 m from a long straight 200-kV DC power line suspects that its magnetic field may equal that of the Earth and affect compass readings. (a) Calculate the current in the wire needed to create a 5.00105T field at this distance. (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?arrow_forwardA cyclometer is a device mounted on a bicycle that records and displays trip information such as elapsed time, distance traveled, and average speed. Modern versions employ small magnets attached to a spoke on either the front or rear wheel and a sensor located on the front fork or rear frame. As the magnet is carried past the detector once each wheel revolution, it produces an electrical pulse that is recorded and logged by an integrated circuit in the device. The distance traveled equals the total number of revolutions multiplied by the circumference of the wheel. (a) A typical mountain bike has a wheel diameter of 26 in. How far will a cyclist have traveled in both miles and kilometers if her cyclometer indicates that her front wheel has made 25,000 revolutions during her trip? (b) If the cyclometer clock shows that the elapsed time for the trip was 2 hours and 40 minutes, what was the rider’s average speed during this period?arrow_forwardConstruct Your Own Problem Consider using the torque on a current-carrying coil in a magnetic field to detect relatively small magnetic fields (less than the field of the Earth, for example). Construct a problem in which you calculate the maximum torque on a current- carrying loop in a magnetic field. Among the things to be considered are the size of the coil, the number of loops it has, the current you pass through the coil, and the size of the field you wish to detect. Discuss whether the torque produced is large enough to be effectively measured. Your instructor may also wish for you to consider the effects, if any, of the field produced by the coil on the surroundings that could affect detection of the small field.arrow_forward
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