The Unipolar Dynamotor: A Genuine Relational Engine
| Scientific Paper | |
|---|---|
| Title | The Unipolar Dynamotor: A Genuine Relational Engine |
| Read in full | Link to paper |
| Author(s) | Jorge A Guala-Valverde, Pedro Mazzoni |
| Keywords | relational physics, unipolar devices, Weber' statements |
| Published | 2001 |
| Journal | Apeiron |
| Volume | 8 |
| Number | 4 |
| No. of pages | 12 |
| Pages | 41-52 |
Read the full paper here
Abstract
We describe two quasi trivial, old fashioned, but cleverly conceived, undisputable, experiments which disprove Kennard-type absolutistic interpretations of unipolar machines. Our findings are in agreement with Weber's statements concerning the role of relative motion in electrodynamics, as advanced by himself towards the middle of the 19th century. And also we agree with Mach's views concerning motion at the most general level. This work settles our earlier contributions devoted to unipolar induction. For nearly a century after its discovery by Faraday in 1832 the unipolar generator was a conundrum for the theory of electromagnetism D. F. Bartlett et al. Phys. Rev D 16 (12), 3459 (1977). We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. - Isaac Newton
Overview
The unipolar or homopolar machine — Faraday's disc of 1832 — has been an irritant to electromagnetic theory for the reason the authors quote from Bartlett: it produces a steady emf with no time-varying flux anywhere, so the flux rule that carries most of induction has nothing to say about it. The classic question is where the seat of the emf actually sits, and in particular whether a rotating magnet carries its field around with it. Jorge Guala-Valverde and Pedro Mazzoni set up the dispute as a contest between two named positions: A, the absolutist, after E. H. Kennard, for whom the field belongs to laboratory space and only absolute rotation of the conductor can polarise it; and R, the relativist in the sense of Weber and Mach, for whom only the relative motion of magnet and conductor can matter.
The paper reports two bench experiments, a generator and a motor, built around an annular ceramic magnet with a small sector cut out of it. The claim is that in each case A predicts one outcome and R another, and that the measurement goes R's way — decisively enough that the authors call the results "undisputable" and say the work "settles" their earlier contributions on unipolar induction in the American Journal of Physics. They are explicit that this is not an argument about special or general relativity: "the matter developed in this paper has nothing to do with Special Relativity, nor with the General Theory". The relativity at issue is Weber's and Mach's — the older doctrine that only relative positions and motions of bodies are physically real.
The argument
The two positions
The authors first rehearse the standard cases as a two-body problem. Spin the disc D over a magnet M at rest: both A and R expect current, since disc rotation is simultaneously absolute motion and relative motion. Spin M with D at rest: no current is observed. A explains this trivially — a rotating magnet cannot induce anything. R explains it differently and more interestingly: the rotation of M does polarise D, but it polarises the closing-circuit (CC) wire in exactly the same way, so the loop contains two equal and opposite emf sources and no current can flow. Finally, when D and M co-rotate soldered together, A locates the emf in D; R must locate it in the stationary CC wire, since D and M are at relative rest. The two accounts are then distinguishable only by measuring where the potential drop appears, not merely whether current flows — which is what the apparatus is designed to do.
Experiment 1: the generator
The rotor R comprises an axially magnetized ceramic annulus (25 mm inner, 75 mm outer radius) with about 1/30 of the annulus cut away, embedded in a 100 mm teflon disc and dynamically balanced. Radial copper branches ap and qr are soldered to the magnet, their inner ends joined by a copper ring c, their outer ends taken to two copper rings Ca and Cb. Because of the cut sector, the branch ap lies in the region where B reverses sense. Carbon electrodes on micrometric screws close the circuit against the rings.
- Conductor rotating, rotor at rest. A brass disc spun clockwise at ω ≈ 150 rad/s beside the stationary rotor gives Vap = +2.0 ± 0.1 mV, Vqr = +20.0 ± 0.1 mV, Var = +22.0 ± 0.1 mV = Vap + Vqr. The small value on ap is attributed to eddy (Foucault) currents where B reverses; radial cuts in the disc raise it. The point established is that the two branches behave as two independently polarised emf sources in series, understood by the Lorentz force q[(ω×r)×B] acting on the moving conductor. Replacing the disc with a spun hollow brass cylinder gives Vrb = 0.0 ± 0.1 mV, so Vab ≈ Var ≥ 22 mV.
- Rotor rotating, circuit at rest. Now the rotor is spun clockwise and the potentials are read through sliding contacts. The result is Vap′ = −20.0 ± 0.1 mV, Vqb′ ≈ Vqr′ = +20.0 mV, and Vab′ = 0.0 ± 0.1 mV.
The authors take care to exclude a time-varying-flux artefact: the topology admits none, and a 600-turn coil enclosing the rotor showed an alternating signal at the rotation frequency of under 0.01 mV per turn. Sliding-contact noise was filtered with a 200 µF capacitor, readings taken on a 1 MΩ voltmeter.
The analysis is the crux. On A's account the branches ap and qr are the seat of induction, so he must expect Vab′ ≈ Var > 20 mV with Vap′ positive — two sources in series — whereas the measured Vap′ is −20 mV and the sum is zero. On R's account the rotating branches are at rest relative to the magnet and can generate nothing; the emf arises entirely in the stationary CC wire from its relative motion with respect to M, and since the CC wire "essentially sees, over time, the same B field distribution", the cut sector is a local perturbation only. A second magnet with the cut reduced to 1/150 of the annulus gave the same reversal, supporting that reading.
Experiment 2: the motor
The same rotor is rebuilt with the magnet in a wooden cylinder on a conducting axle X, pivoted on polished glass so that it turns nearly frictionlessly; the outer ends a and b of the radial branches dip into two semicircular mercury channels. All the wires lie over the magnet's north pole.
- Current in at a1, out at X. The whole assembly turns counter-clockwise once the current reaches about 2 A. A attributes this to the Laplace force dF = I(dl×B) on branch aX "dragging" M around. R denies that aX can torque M at all — by Newton's third law the reaction on M is opposite, and aX is soldered to M, so the pair cannot torque itself; the only surviving interaction is between M and the CC wire.
- Current in at X, out at b1. The rotor now turns clockwise. A's dragging account gives counter-clockwise again and fails.
- The decisive null test: current in at a1, out at b1. Both branches now carry current and A predicts counter-clockwise rotation from two additive torques. R predicts nothing at all, because the only external closing conductors left are portions of the mercury channels and the leads, none of which can deliver a torque about the symmetry axis. No rotation whatever was detected as the current was raised from 1 A to 100 A.
A supporting observation: with the branches made flexible enough, they visibly bent counter-clockwise while the magnet turned clockwise in the first configuration and stayed put in the third — which the authors regard as sufficient on its own "to reject the dragging effect claimed by A". They note that with div B = 0 and elementary topology the argument generalises to a closing circuit of arbitrary shape.
Assessment
The experimental design is the strong part of this paper, and it is genuinely well made. The authors do not rest on a single measurement of ambiguous sign: they arrange a case where the two interpretations predict opposite signs (Vap′), a case where they predict rotation in opposite senses, and — best of all — a case where one predicts rotation and the other predicts a null, then push the current a hundredfold past the threshold to show the null holds. Null tests of that kind are much harder to explain away than agreements. The auxiliary controls are also conscientious for a bench experiment: the coil test bounding stray time-varying flux below 0.01 mV/turn, the capacitor against sliding-contact noise, and the second magnet with a 1/150 cut to check that the reversal is not an artefact of the gap. The internal arithmetic is consistent (+2.0 + 20.0 = +22.0 mV; −20.0 + 20.0 = 0.0 mV), and the magnitudes are physically sensible: for a branch spanning 25 to 75 mm at 150 rad/s, the elementary unipolar emf ½ωB(r22 − r12) reproduces 20 mV for B ≈ 0.05 T, which is the right order for a ceramic ferrite a few millimetres away. One transcription slip should be noted for readers: Vqb′ is printed as "+20.0 ± 0.1 V", which the surrounding arithmetic shows must be mV.
The difficulty is with the inference, not the data. What the experiments establish very cleanly is that the emf and the torque are located in the stationary part of the circuit rather than in the co-rotating branches, and that a co-rotating branch cannot torque the magnet it is soldered to. Both of these are consequences of ordinary Maxwell-Lorentz electrodynamics correctly applied, once one recognises that the field of an axially symmetric magnet spinning about its symmetry axis is static in the laboratory — the field does not rotate with the magnet, and the emf is then computed by integrating v×B around the actual circuit, which gives exactly the reported results including the null. The authors' "absolutist A" is not the standard theory but a specific and long-refuted position — Kennard's, from 1912 and 1917 — that the field co-rotates. Disproving A therefore does not select Weber's relational electrodynamics over Maxwell's; it selects the correct application of either over a mistaken one. The paper does not present the Maxwellian calculation of its own configurations, so the reader cannot see the two theories' predictions differ, which is what a decisive test between them would require.
Two smaller points reinforce this. First, the third-law argument in the motor section is deployed as though it were peculiar to relational physics, but it is simply Newton's third law applied to a rigid assembly, available to any theory; the flexible-branch observation, where the branches bend one way while the magnet turns the other, is a nice demonstration of exactly that and is not evidence about the form of the force law. Second, Weber's force law and the Lorentz force differ in genuinely testable ways — Weber's force is longitudinal and velocity- and acceleration-dependent, and the classic discriminating tests are Ampère longitudinal-tension and exploding-wire experiments of the kind cited in the authors' own reference list (Graneau, Assis). None of the three configurations here reaches that difference. The word "undisputable" in the abstract is therefore doing more work than the experiments can carry: the measurements are convincing, the identification of the seat of the emf with the stationary circuit is well supported, and the Machian moral drawn at the end is an interpretive preference rather than a result the apparatus can distinguish.
Taken for what it is — a careful, low-cost, sign-and-null experimental settlement of where the emf and the torque live in a unipolar machine — the paper is sound and useful. Taken as a disproof of field-theoretic electrodynamics in favour of Weber's relational alternative, it overreaches.