Naked Science Forum
Non Life Sciences => Technology => Topic started by: Atomic-S on 30/07/2016 07:18:47
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Consider a magnetic toroid composed of four permanent magnets as follows: There is an upper and lower bowl section (figures 1 and 2), and an upper and lower funnel section (figures 3 and 4). Each section is magnetized in such a way that the field always lies in a plane that includes the central axis, and otherwise follows the lay of the material (see blue arrows). These four magnets are then assembled by bringing the bowls together and placing the funnels inside them as shown in Figure 5, so that the entire assembly constitutes a toroid in which the magnetic field circulates in planes that include the central axis, except that there is left small gaps between the various pieces (See Figure 5, and for a cross section, see Figure 6). These gaps are small, so that the flux straying due to them is presumably negligible. The four magnets are held in this relative position, keeping the gaps small but greater than zero, by an external mechanical apparatus (not shown). A conducting circuit is added to the assembly, consisting of a rectangular loop that lies in a plane containing the central axis (the orange rectangle in Figures 5 and 6). It passes through the magnetic assembly in the upper and lower gaps that exist between the upper bowl and funnel, and between the lower bowl and funnel, as shown. There are four switches placed in the circuit, A, B, C, and D, located just outside and inside the toroid near the upper and lower gaps.
Now, the external mechanical apparatus is activated in such a way that the upper bowl and the upper funnel spin about the central axis with the same angular speed ω that is different than 0, but the lower bowl and funnel are held stopped.
With all the switches open:
What is the potential difference between the ends of the conductor from Switch A to Switch B, passing through the upper gap?
What is the potential difference between the ends of the conductor from Switch C to Switch D, passing through the lower gap?
What is the potential difference between the ends of the conductor inside the toroid from Switch B to Switch C?
What is the potential difference from Switch A to Switch D measured along the external circuit?
If all switches are closed, will a current flow?
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An ant sitting on the upper bowl, which is spinning along with the upper funnel, near the upper gap, will observe the conductor pass him moving at right angles to both its length and the field, imlying that there is a potential difference between the end connected to Switch A and the end connected to Switch B. An ant sitting on the lower bowl, which is stationary along with the lower funnel, will observe the conductor at rest within the field that passes through it, concluding therefore that there is no potential difference along that conductor between where it connects to Switch C and Switch D. This constitutes an imbalance of potential. However, we must still look at the sections of conductor from Switch B to Switch C, and then the outside path from Switch D back to Switch A. Because the magnetic field is (presumably) confined within the material of the toroidal structure except at the gaps, from which it cannot stray appreciably, the magnetic field intersecting these other portions of the circuit is zero, suggesting that there can be no induced voltages in them. If that is so, the sum of voltage changes around the complete circuit is simply that which is from Switch A to Switch B, which is nonzero. If this calculation is correct, when the switches are all closed, a current flows, and we have here a remarkable machine that can generate a smooth direct current without the use of power-wasting, maintenance-requiring brushes, or complicated rectifier circuitry.