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GR9277 #92 |
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Problem
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\prob{92}
A flat coil of wire is rotated at a frequency of 10 hertz in the magnetic field produced by three pairs of magnets as shown above. The axis of rotation of the coil lies in the plane of the coil and is perpendicular to the field lines. What is the frequency of the alternating voltage in the coil?
- 10/6 Hz
- 10/3 Hz
- 10 Hz
- 30 Hz
- 60 Hz
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Electromagnetism }Frequency
A three-pole magnet should produce three voltage peaks, and thus the frequency is 30 Hz. (Solution due to David Latchman.)
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Alternate Solutions |
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Comments |
tmansuripur
2008-10-17 22:20:50 | This problem is best solved by symmetry, without even thinking about the B-field lines. In fact, I think the problem is poorly described, and I don't exactly see where the magnetic flux is going through. Anyways, if you rotate the coil 120 degrees, then you're in exactly the same place (relative to the field lines) that you started at , so the voltagemust be the same as where you started at. Thus each full rotation of the rod corresponds to 3 cycles in the emf, so the voltage frequency is 3 times as large as the rotational frequency--->30Hz. |  | thebigshow500
2008-09-13 21:10:49 | If you draw the magnetic field lines in the diagrams, you will see the field flowing from magnet's N pole to its own S pole. But I don't see how the voltage (or should we say current?) gets altered back and forth in the wire. Is the Lorentz force the one make the wire rotate?
Poop Loops
2008-10-25 20:16:00 |
*You* are rotating the wire at 10Hz and seeing what happens.
The voltage gets altered back and forth due to changing magnetic flux through the loop.
The picture is sort of misleading, but imagine that it isn't neat like that, but the magnets are smaller, so that magnetic field lines flow primarily from a magnet's own N to S (or whatever).
When the loop gets between the N and S poles, it has the greatest amount of flux going through it. So, as the loop approaches that point, flux goes up, creating a voltage, and then goes back down and negative as it starts going away.
Since there are 3 identical magnets spaced equally apart, this happens 3 times per rotation, so your frequency of whatever voltage waveform comes out gets tripled.
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