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Chapter 29: Q. 4 (page 829)
What is the current direction in the wire of FIGURE Q29.4? Explain.
Current is flowing toward out of the paper.
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A Hall-effect probe to measure magnetic field strengths needs to be calibrated in a known magnetic field. Although it is not easy to do, magnetic fields can be precisely measured by measuring the cyclotron frequency of protons. A testing laboratory adjusts a magnetic field until the proton's cyclotron frequency is . At this field strength, the Hall voltage on the probe iswhen the current through the probe is. Later, when an unknown magnetic field is measured, the Hall voltage at the same current is. What is the strength of this magnetic field?
shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio . The sample is ionized, the positive ions are accelerated (starting from rest) through a potential differencelocalid="1648976601527" , and they then enter a region of uniform magnetic field. The field bends the ions into circular trajectories, but after just half a circle they either strike the wall or pass through a small opening to a detector. As the accelerating voltage is slowly increased, different ions reach the detector and are measured. Consider a mass spectrometer with localid="1648976606181" a magnetic field and an localid="1648976610307" spacing between the entrance and exit holes. To five significant figures, what accelerating potential differences localid="1648978768434" are required to detect the ions localid="1648978902862" and localid="1648978898077" ? See Exercise localid="1648978753549" for atomic masses; the mass of the missing electron is less than localid="1648978758219" and is not relevant at this level of precision. Although localid="1648978910549" and localid="1648978778238" both have a nominal molecular mass of localid="1648978782098" , they are easily distinguished by virtue of their slightly different accelerating voltages. Use the following constants:
The earth’s magnetic field, with a magnetic dipole moment of , is generated by currents within the molten iron of the earth’s outer core. Suppose we model the core current as a -diameter current loop made from a 1000-km-diameter “wire.” The loop diameter is measured from the centers of this very fat wire.
a. What is the current in the current loop?
b. What is the current density in the current loop?
c. To decide whether this is a large or a small current density, compare it to the current density of a current in a -diameter wire.
The element niobium, which is a metal, is a superconductor (i.e., no electrical resistance) at temperatures below . How-ever, the superconductivity is destroyed if the magnetic field at the surface of the metal reaches or exceeds . What is the maximum current in a straight, --diameter superconducting niobium wire?
At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your answer as a multiple of R.
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