Electromagnetic Propulsion using the Concepts of a Homopolar Motor
| Scientific Paper | |
|---|---|
| Title | Electromagnetic Propulsion using the Concepts of a Homopolar Motor |
| Read in full | Link to paper |
| Author(s) | John R Warfield |
| Keywords | Electromagnetic Propulsion, Newton's Third Law |
| Published | 2010 |
| No. of pages | 10 |
Read the full paper here
Abstract
The intention of this article is to describe an electromagnetic propulsion demonstration proof of concept model, which will propel itself without a propellant, furthermore in apparent violation of Newton's third Law.
Overview
Warfield's aim is a device that accelerates itself using only a battery, a magnet and a wire — no exhaust, no reaction mass. His route to it is the homopolar motor, chosen deliberately for its cheapness: the third of his papers on electromagnetic propulsion, this one is meant to describe something "perhaps costing only a few hundred dollars or less" rather than the elaborate apparatus of the earlier two. The paper is entirely a design study; no device is built and no measurement is reported.
The physical claim is a comparison of two forces. In a homopolar motor the current crosses the magnet's field at right angles and inside the magnet, where the field is strongest, so the Lorentz force on it is at a maximum. The return current in the closing wire also sits in the magnet's field, but out where the field is weak and, for much of its path, running parallel to the field lines, where it feels nothing at all. If the closing wire is routed so as to follow the curving field lines for as long as possible before turning back to the battery, the opposing force on it can be made much smaller than the driving force on the disc. What is left over, Warfield argues, is an uncompensated force on the apparatus as a whole — "a violation of Newton's Third Law". A mirror-symmetric arrangement of two magnets and two closing wires on a fixed platform is then offered to cancel the rotations and lateral components and leave pure translation.
The argument
Preliminaries: rules and field lines
Sections 2.1–2.2 set out Fleming's left- and right-hand rules and the right-hand rule for F = IL × B, together with a list of the conventional properties of magnetic lines of force. Warfield notes at the outset that current is really a flow of electrons, but adopts the positive-current convention "for the sake simplicity", switching to electrons only where the electromotive force on them has to be traced.
The homopolar generator and Faraday's paradox
A conducting disc, a coaxial permanent disc magnet, and a stationary closing wire from the disc's centre to a peripheral brush. Warfield states the three classic results: rotating the disc produces a current; rotating the magnet alone produces none; and rotating disc and magnet together produces a current exactly as if the magnet were still. He calls the second and third "a violation of Einstein's relative motion concept" and of "Faraday's induction theory".
His own resolution is that lines of force do not exist. The iron-filing picture, he argues, is an artefact: the filings magnetise, align end to end, and the resulting chains repel one another, so that finer filings give finer and more numerous "lines" — which shows the lines are a property of the filings, not of the field. "Basically a magnetic field possesses a magnitude and direction for a given point in space. Therefore, as in our example, if a uniform disk like magnetic field is rotated, then with respect to any given point in space, there is no change in the magnitude and direction of this field." He nonetheless adds that a current appearing under co-rotation, when there is none at rest, "necessitates a third frame, perhaps a preferred frame or in other words the old discarded term; the Ether."
Where the reaction is supposed to go
Sections 2.5–2.6 and 3.5–3.11 work through the co-rotating screw-and-magnet motor (battery, magnetised screw, disc magnet, copper brush wire), labelling the current path a–f. Sections a and f run parallel to the field: no force. Section b, inside the magnet, crosses the field at right angles at full strength: force out of the page. Sections c, d and e in the closing wire feel forces into the page. Warfield's design move is to make c forceless as well, by routing the wire along the curving field lines, so that only the short segments d and e — far from the magnet, where "the strength of the magnetic field created by a magnet does not obey the inverse square law" and falls off faster — oppose the motion. He also insists that in the motor there is no back Lorentz force at all, only a back electromotive force: as the disc turns, charges are driven radially and build a voltage opposing the battery, and the current falls until equilibrium.
The self-propulsion device
Section 4 first distinguishes a force from a torque: "A force is oriented in only one direction. A torque is two forces oriented in opposite directions, resulting in rotation." A single Lorentz force applied at the rim of a wheel floating in space produces rotation and forward translation; a couple produces rotation only. The device (Figs. 21, 22, 24) mounts two bar magnets, magnetised across their width, and two mirror-image closing wires on a vertical wooden platform, everything fixed. Segment by segment: a and g parallel to the field (no force, though the antiparallel currents repel — cancelled by symmetry); b and f at right angles in the full field, force out of the page; c and e parallel, nothing; d in the weak far field at oblique angles, force into the page. Mirror symmetry kills every lateral and rotational component, leaving out-of-page against into-of-page — and since b and f sit in the strong field at right angles while d sits in the weak field at oblique angles, "the overall Lorentz force driving the platform into the page is significantly less compared to the overall Lorentz force driving the platform out of the page. If so, there exists translational electromagnetic propulsion without a propellant."
Assessment
The paper is careful where most treatments are careless, and one of its complaints is well taken. Warfield is right that discussions of the homopolar motor routinely ignore the closing wire, and right that the closing wire carries current through the same field and therefore experiences forces of its own. His force-by-force labelling of the current path is done consistently and, as far as the printed descriptions allow it to be checked, correctly: the segments parallel to B contribute nothing, the segment crossing B inside the magnet contributes the most, and the return path contributes an opposing force whose size depends on where it is routed. His account of the iron filings is also right, and the conclusion he draws from it — that the field is a magnitude and direction at each point, not a set of physical threads — is the modern field concept, not a departure from it. So is his explanation of why rotating an axially symmetric magnet about its own axis induces nothing: the field distribution is unchanged at every point in space, so there is nothing for the conductor to respond to. That is the standard resolution of Faraday's paradox, arrived at independently.
The trouble is that the reaction force he is looking for is not in the closing wire, and the whole construction depends on assuming that it is.
The force on the current in the disc is the force exerted by the magnet on that current. Its Newton's-third-law partner is the force exerted by that current back on the magnet — on the Ampèrian magnetisation currents that are the source of B. In the screw-and-magnet motor the magnet and the conductor are, as Warfield himself emphasises, one and the same object; in the Section 4 platform the magnets are bolted to the same board as the wires. The reaction is therefore not located out in the weak field where the closing wire turns; it acts on the magnet, at the very place where the field is at its maximum, and it is exactly equal and opposite by construction. The closing wire is a third party, not the partner. Once the reaction is put where it belongs, the entire asymmetry argument — strong field here, weak field there — has nothing to work on.
This is not a matter of bookkeeping preference. The net force that a closed steady current distribution exerts on itself, through its own magnetic field, is identically zero: the Biot–Savart double line integral over a closed loop acting on itself vanishes, and for two closed loops the forces are equal and opposite even though the element-by-element Grassmann forces are not. The magnet is a collection of closed Ampèrian loops and falls under the same theorem. More generally, conservation of momentum for charges plus fields follows from Maxwell's equations and the Lorentz force together with the field momentum ε0∫E×B dV; in a magnetostatic device with steady currents and no radiation there is no field momentum being carried off, so the mechanical momentum of the isolated apparatus cannot change. A device of the kind described would have to violate that, and it is not an independent postulate that could simply be wrong — it is a consequence of the same equations Warfield uses to compute every force in the paper. Using F = IL × B on the current while declining to apply it to the source of B is what produces the imbalance.
The free-floating wheel analogy (Figs. 11 and 20) does not help, because it assumes what is in dispute. It is perfectly true that a single off-centre force on a free body produces both linear acceleration F/M and angular acceleration FR/I — that is ordinary Newtonian mechanics and nobody disputes it. The question is whether there is any such single unbalanced force, and the analogy simply stipulates one. The definition offered alongside it is also not right: a torque is not "two forces oriented in opposite directions" — that is a couple. A single force off the axis produces a torque and a net force at once, which is why the distinction the section is built on does not do the work asked of it.
Two smaller inconsistencies. First, the appeal to a preferred frame contradicts the explanation Warfield has just given. If, as he correctly argues, rotating an axisymmetric magnet changes the field nowhere, then no third frame is required to explain why nothing happens: the asymmetry is between a conductor whose charges physically move through B and a source whose rotation alters B nowhere. His own paragraph removes the need for the ether he then invokes two paragraphs later. It should also be said that special relativity's postulate concerns inertial frames, and a spinning disc is not one, so no violation of "Einstein's relative motion concept" arises in the first place; and Faraday's flux rule, applied with the standard convention that the lines of an axisymmetric magnet do not co-rotate with it, gives the observed answer. Second, the paper's list of properties of lines of force in Section 2.2 — that they all have the same strength, seek paths of least resistance, and flow south to north within a material — is used as physics in the early sections and then declared not to exist in Section 3.2.
Finally, the abstract describes "a demonstration proof of concept model", but nothing was assembled and no observation is offered. That matters more than usual here, because the claim is one that a scale is enough to test. A closed self-contained apparatus of the kind drawn in Fig. 24, hung from a torsion fibre or floated on a low-friction bearing and switched on, would show a deflection if the net force were real; that experiment costs less than the few hundred dollars the introduction budgets and would settle the question directly. Its absence leaves the paper as a careful qualitative catalogue of Lorentz forces on one half of each interacting pair.