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In many magnetic resonance imaging (MRI) systems, the magnetic field is produced by a superconducting magnet that must be kept cooled below the superconducting transition temperature. If the cryogenic cooling system fails, the magnet coils may lose their superconductivity and the strength of the magnetic field will rapidly decrease, or quench. The dissipation of energy as heat in the now-nonsupcrconducting magnet coils can cause a rapid boil-off of the cryogenic liquid (usually liquid helium) that is used for cooling. Consider a superconducting MRI magnet for which the magnetic field decreases from 8.0 T to nearly 0 in 20 s. What is the average emf induced in a circular wedding ring of diameter 2.2 cm if the ring is at the center of the MRI magnet coils and the original magnetic field is perpendicular to the plane that is encircled by the ring?
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University Physics with Modern Physics (14th Edition)
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- Review. The use of superconductors has been proposed for power transmission lines. A single coaxial cable (Fig. P31.47) could carry a power of 1.00 103 MW (the output of a large power plant) at 200 kV, DC, over a distance of 1.00 103 km without loss. An inner wire of radius a = 2.00 cm, made from the superconductor Nb3Sn, carries the current I in one direction. A surrounding superconducting cylinder of radius b = 5.00 cm would carry the return current I. In such a system, what is the magnetic field (a) at the surface of the inner conductor and (b) at the inner surface of the outer conductor? (c) How much energy would he stored in the magnetic field in the space between the conductors in a 1.00 103 km superconducting line? (d) What is the pressure exerted on the outer conductor due to the current in the inner conductor? Figure P31.47arrow_forwardThe density of charge carriers far copper is 8.471028 electrons per cubic meter. What will be the Hall voltage reading from a probe made up of 3cm2cm1cm ( (LWT) ) copper plate when a current of 1.5 A is passed through it in a magnetic field of 2.5 T perpendicular to the 3cm2cm .arrow_forwardThe Hall effect is to be used to find the density of charge carriers in an unknown material. A Hall voltage 40 V for 3-A current is observed in a 3-T magnetic field far a rectangular sample with length 2 cm, width 1.5 cm, and height 0.4 cm, Determine the density of the charge carriers.arrow_forward
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- An electron of kinetic energy 2000 eV passes between parallel plates that are 1.0 an apart and kept at a potential difference of 300 V. What is the strength of the uniform magnetic field B that will allow the electron to travel undeflected through the plates? Assume E and B are perpendicular.arrow_forwardReview. A fundamental property of a type 1 superconducting material is perfect diamagnetism, or demonstration of the Meissner effect, illustrated in Figure 29.27 in Section 29.6 and described as follows. If a sample of superconducting material is placed into an externally produced magnetic field or is cooled to become superconducting while it is in a magnetic field, electric currents appear on the surface of the sample. The currents have precisely the strength and orientation required to make the total magnetic field be zero throughout the interior of the sample. This problem will help you understand the magnetic force that can then act on the sample. Compare this problem with Problem 39 in Chapter 25, pertaining to the force attracting a perfect dielectric into a strong electric field. A vertical solenoid with a length of 120 cm and a diameter of 2.50 cm consists of 1 400 turns of copper wire carrying a counterclockwise current (when viewed from above) of 2.00 A as shown in Figure P31.48a. (a) Find the magnetic field in the vacuum inside the solenoid. (b) Find the energy density of the magnetic field. Now a superconducting bar 2.20 cm in diameter is inserted partway into the solenoid. Its upper end is far outside the solenoid, where the magnetic field is negligible. The lower end of the bar is deep inside the solenoid. (c) Explain how you identify the direction required for the current on the curved surface of the bar so that the total magnetic field is zero within the bar. The field created by the supercurrents is sketched in Figure P31.48b, and the total field is sketched in Figure P31.48c. (d) The field of the solenoid exerts a force on the current in the superconductor. Explain how you determine the direction of the force on the bar. (e) Noting that the units J/m3 of energy density are the as the units N/m2 of pressure, calculate the magnitude of the force by multiplying the energy density of the solenoid field times the area of the bottom end of the superconducting bar. Figure P31.48arrow_forwardChapter 23: Question 7: Suppose a conducting rod is 58.5 cm long and slides on a pair of rails at 2.5 m/s. Randomized Variables v = 2.5 m/s l = 58.5 cm a) What is the strength of the magnetic field in T if a 9 V emf is induced?arrow_forward
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