On Over Unity Machines
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Fig. 1 depicts a Faraday disc that is solidly attached to a disc-shaped ceramic magnet. The geometric center of the disc/magnet remains at rest in the lab (inertial) frame. By means of sliding contacts, a closing wire with load establishes electrical contact between the disc periphery and a conducting drive shaft.w is the angular velocity of the disc/magnet.
Faraday Disc/Magnet Assembly
Whenw=0 there is no current through the load. But as previously discussed, Faraday found that current flows when w>0. His explanation was that the magnetís field lines do not rotate with the magnet. Thus when w>0 the discís conduction electrons cut across the fixed magnetic lines of force and experience magnetic forces toward the discís center.
As also previously discussed, Faraday (and more recently, others) does not seem to have considered the possibility that a rotating, uncharged, disc-shaped (or cylindrical) permanent magnet has a spin-induced electric field with radial components. This E field can be attributed to the translation-induced electric dipole moments in the microscopic, uncharged current loops that hypothetically and collectively engender the magnetís B field. In Fig. 1 the radial components of this field would point toward the drive shaft.
The direction of this spin-induced radial E field is such that the electric forces experienced by disc conduction electrons point opposite to the magnetic forces. Indications are that the net radial electromagnetic force components are practically zero. This being the case, the emf in the disc, from drive shaft to periphery, would be zero.
Now the magnetís spin-induced E field is presumably conservative, and ordinarily would engender no net emf around a closed circuit. For example, in Fig. 2 the closing wire/drive shaft constitute a closed circuit in which no current flows, even whenw>0.
Conservative E Causes No Current
But in the configuration depicted in Fig. 1, the conducting disc comprises one leg of the circuit, and the emf in the closing wire/load/drive shaft part is unopposed in the disc. Consequently there is hypothetically a net emf around the circuit and current flows.
What Faraday (and more recently, others) seems not to have realized is that the closing wire is the active part of the circuit. The magnetic forces on the discís conduction electrons are canceled by electric forces and hence contribute nothing to the power engendered by the remainder of the circuit.
If we disallow the spinning discís electric field, then the magnetic forces in the disc do indeed constitute an unbalanced emf. We might call this the "Faraday emf." This point of view raises interesting issues. For theoretically no power is required to move a charge through a magnetic field, since the magnetic force always acts perpendicular to the chargeís velocity. Thus the only power required from the drive shaft would be that needed to account for the heat generated in the sliding contacts.
The only other obvious power source would seem to be the magnet itself. That is, oneís initial impression might be that the magnet must exert the emf-inducing radial forces on the disc conduction electrons via the B field intermediary. (It is noteworthy that although the myriad magnetic forces sum to zero, each acts on a conduction electron in the direction of that electronís radial drift. Hence there is a net power gain.)
It is at this point that a rather celebrated conundrum is encountered. According to Newtonís third law and/or momentum conservation, each conduction electron must react to its experienced magnetic force with an equal and oppositely directed reaction force. But on what would such a reaction force act? It isnít clear how the radially drifting conduction electrons would exert a force on the disc-shaped magnet!
Historically some very distinguished heads have grappled with this apparent violation of momentum conservation. A recent conjecture is that the conduction electrons in the disc interact (again via the magnetic field intermediary) with a hither-to-unknown universal reservoir of energy. If this is so, then the exciting prospect is suggested that unlimited energy could be extracted from this mysterious pool, and used to do work on familiar loads.
The hypothetical machines, designed to exploit this hypothetical phenomenon, have been called "Over Unity" machines because of their hypothetical net power gain. As mentioned above, part of the power would have to be used to provide necessary (but slight) torque to the drive shaft. But the idea is that, with careful engineering, this power could be minimized, leaving power to spare. And this surplus power could be used for other purposes. In view of mankindís quest for a clean and unlimited source of energy, such a possibility has seized the imaginations of more than a few.
At this juncture it is perhaps instructive to emphasize that the drift speed of conduction electrons, throughout the circuit depicted in Fig. 1, is essentially constant. In the disc, the magnetic forces on such charges cannot accelerate them along the circuit. But such forces nonetheless act in the direction of individual electron velocities along the circuit, and hence sum to net power.
Of course all of the above "Faraday emf" paradigms must be reassessed when the spinning magnetís hypothetical radial electric field is taken into account. In this case it is presumably the electric forces, acting on conduction charges in the closing wire/load/conducting shaft that do the work. The Newton/conservation of momentum question now becomes: What is the mechanism whereby that part of the circuit's conduction electrons exert reaction forces back on the magnet and, ultimately, on its hypothetical microscopic current loops?
To the extent the charge density around the circuit is constant, we are inclined to look for a magnetic feedback mechanism. And the "top" and "bottom" legs of a microscopic current loop might suggest an answer. For when current flows, the circuit has its own magnetic field, and this field exerts a magnetic force on the circulating (presumed positive) charge in a given microscopic current loop. The key idea here would be that the circuitís magnetic field is slightly stronger at one tiny current loop leg than it is at the opposite leg. Fit. 3 illustrates. The horizontal line is the projection of the circuitís plane onto the disc. (The circuit would be above the plane of the diagram.)
Net Magnetic Forces on Microscopic Current Loops
It is clear in Fig. 3 that each microscopic current loop experiences a net magnetic force, and that this force tends to angularly decelerate the parent magnet. The net force on any particular current loop would of course be small. But there are, hypothetically, enormous numbers of such tiny loops. Assuming the loops are held in place in the magnetís lattice, there is an overall torque on the parent magnet. This torque tends to lessenw, and must be counteracted by the drive shaft if w is to remain constant. It is ultimately the drive shaft, acting through the fields, that does positive work on the load. And it is ultimately the conduction electrons that react with negative power on the hypothetical microscopic current loops, and hence collectively on the magnet.
Of course this requirement, that the drive shaft exert a constant torque on the magnet/disc, casts doubt upon the whole idea of a hidden, inexhaustible pool of energy. The author has not had access to Faradayís diaries where the original experimental results were recorded. And it isnít clear whether or not Faraday measured the torque (if any) that had to be applied to the drive shaft when his homopolar generatorís magnet and disc were spun in tandem. (More recent investigators seem to have paid scant attention to this torque, perhaps assuming a priori that it is negligible.)
What is known at present is that all attempts to tap into the conjectured hidden energy pool have evidently been unsuccessful. In brief, all actually constructed "Over Unity" prototypes have turned out to be Under Unity devices.
To be sure, variations of the Faraday Disc may become more widely used to generate DC power. But this will almost certainly be accomplished only through the expenditure of even greater mechanical power. The time-tested adage seems once again to be appropriate. There is no free lunch!