Electromagnetic Attraction

William Sturgeon's original horseshoe electromagnet, from https://en.wikipedia.org/wiki/William_Sturgeon#/media/File:Sturgeon_electromagnet.png

Energy is conserved

Electrical engineers are routinely taught, correctly, that energy is conserved in electromagnets as far as forces of magnetic attraction are concerned.

Fig 3.23 — Magnetic pull between two iron surfaces.
(Figure from Electrical Technology, Edward Hughes, Longmans, Second Edition, 1966, p92)

The usual textbook approach is generally as shown in Figure 3.23 above, where conservation is assumed between electromagnetic and mechanical energy, in order to derive a formula for the attractive force between two magnetised ferromagnetic surfaces. Since experimental results for the force agree with this theoretical approach, the assumption is validated.

Force formula derivation

The formula for attractive force between the two adjacent surfaces in the above figure is derived like this:—

D and E are end portions of a one-piece laminated flexible ferromagnetic core, of cross-sectional area A, wound with coil C, carrying current I, which produces flux density B in the airgap of width g.  Then:

        Energy stored per cubic meter of airgap = B²/2μ₀ joules.

Force P balances the magnetic force of attraction between the surfaces of D and E. Suppose E is moved a small distance dg away from D, and also that I is increased simultaneously to keep B unaltered. Then from Faraday's Law and Lenz's Law, no e.m.f. will have been induced in C, and no energy will have been exchanged between the electric circuit and the magnetic circuit. Hence, all energy stored in the additional volume of airgap A × dg must have been derived from the work done when a force of magnitude P acted through a distance dg, i.e:

        P × dg = (B²/2μ₀)× A × dg

  So  P = B²A/2μ₀ newtons.

I'll just state, without proving it here, that energy is also always conserved regarding the energy taken from the electrical source to produce the magnetic field in the varying-volume airgap.

So there seems to be no possibility of over-unity performance from electromagnetic attraction alone.

What if a permanent magnet is added?

However, I will also raise, but not answer the question of whether energy is still conserved overall if a permanent magnet is added into the attracting magnetic circuit discussed above — especially if the (ferro)magnetic circuit is still not quite driven into magnetic saturation by the energised coil and the permanent magnet combined.

I'll look further at that question in future. In particular, in a future post I'll look at what seems likely to have been an over-unity device invented by the very orthodox and prestigious EPRI (Electric Power Research Institute), that exploited this idea as part of its operating principle.

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A cut-away view of an industrial switched-reluctance motor. The operating principle of all such motors relies on electromagnetic attraction. Analysis of switched-reluctance motor operation assumes (correctly) that energy is conserved overall.
Image from Electronic Control of Switched Reluctance Motors, Edited by TJE Miller, Newnes, 2001.

Another Interlude and Final Change in Direction

So far I have been looking at magnet motors incorporating only permanent magnets. The difficulty apparent with such magnets is that they cannot be switched.

It would seem that better-performing devices could be made having at least some magnets that could be switched on or off as required. There is one obvious candidate for this: the electromagnet.

A large scrapyard electromagnet, shown in the "switched-on" state.
Image from https://www.sinfo-t.jp/eng/lifmag/scrap.html

In following posts I'll look first at the issue of electromagnetic attraction (briefly), then at electromagnetic repulsion (in more detail). I'll also take an extended look at a problem I've been investigating for a long time, that can be summarised with the image below:—

A disc rotor carries an arc-shaped permanent magnet which is initially attracted,
and is then repelled by a toroidal electromagnet.
(Bearings, framework, electromagnet inner coil layers etc not shown)

Is energy conserved overall when the permanent magnet in the rotor is attracted-in to the unenergized electromagnet's core, and is then immediately repelled-out by supplying a short pulse of electricity to the electromagnet's coil? In a repulsion case like this, a large portion of the electrical pulse's energy can be ultimately returned to its source. The question is — how much of that electrical pulse energy is lost compared with the total mechanical energy gained?

The Howard Johnson Magnet Motor

Primary references:—

 Science & Mechanics magazine, Spring 1980, p45, and US Patents 4,151,431 and 4,877,983.

On April 2, 1979, Howard Johnson obtained US Patent 4,151,431 for a permanent magnet motor. Further details of Johnson's inventions were reported in the Spring 1980 issue of the now defunct Science & Mechanics magazine. From my old, faded copy of it, here is a scan of its cover:—

Science & Mechanics magazine, Spring 1980

A discrepancy

Right at the outset, there is an obvious discrepancy on the cover page. A fifteen horsepower output converts to 11,185.5 watts. With say a 95% efficient belt drive, a 15-HP motor should still easily be able to drive a generator rated at 10,000 watts, i.e. twice the 5000 watts stated.

The Science & Mechanics report showed some of the devices that Johnson had built:—

Some of Johnson's experimental devices

The device shown at top right is apparently the one that convinced the US Patent Office to grant the first patent. However other experimenters (including myself) soon found that it is not too difficult to obtain continuous rotor movement in a device like this provided that the central magnet is hand held, as shown above. The manual effort required to hold the magnet more or less in the correct position means that the person holding it is unavoidably exerting energy, which is transmitted by magnetic forces to the rotor, causing it to turn. As soon as the central magnet is mounted — even spring-mounted — on some kind of stator, the device no longer works (in my experiments, at least).

Modelling

Nevertheless, more recently I decided to analyse a few examples of Johnson motors. I started with one based fairly closely on Figures 9 and 10 from the patent:—

Example 1

I also looked at a couple of variations:—

Example 2

Example 3

At first, I had difficulty obtaining clear-cut results from my analyses of these models. Generally, there were unbalanced forces and torques for all of them; but I was very skeptical about these — one reason being that they failed to meet some simple Newton's Third Law checks.

Ultimately I added a small ring around the three outer magnets as shown in this example. For whatever reason, in his patent Johnson preferred the outer magnets to be the rotor (which he called the armature). They are circumferentially magnetised, and the inner magnets are radially magnetised.  

This added ring meant the outer magnets could be modelled as a single object, with full symmetry about the z-axis (red). The small ring would make only a very minor difference to the device's performance. Now, to find any net energy output, it was only necessary to find whether this outer object had any net integral of torque through angle, over an operating cycle.

This approach gave consistent and credible results. With this approach I didn't find any net energy output in either of the Examples 1 or 3 above.

Conclusion

It is not worthwhile for me to spend further time on Johnson's work, at least for his US Patent 4,151,431 motor.

Showing magnetic flux lines for a 2D model of a Johnson motor
with a single armature magnet