## Discussion of The Classic Magnetic Motor.

It's interesting how an idea evolves. The figure to the right shows Chris Cheng's drawing of his idea in a simple form. The N pole at the center was doing nothing useful. The cylindrical shield is attached to the S pole so that the S pole "sees" through a window in the shield, seeing N poles a bit "ahead" so the attractive force has a forward component on the rotor. Chris' diagram also showed N poles on the outside, without explicitly showing the S poles of those magnets. No one has ever made magnetic monopoles, so we must decide how to arrange the magnets so that those S poles don't degrade the engine's performance.

In order to make use of both poles of the magnet inside the shield, I introduced a shield with two windows (color picture). You can easily imagine other ways to accomplish this. This is the version posted as a puzzle on my web page.

Many PM inventors these days are tinkering with magnets on wheels. Why the fascination with magnetism? I think it's because most people, even those who have had physics and engineering courses, still are a bit mystified by how magnets work, so they are less likely to see flaws in a magnetic engine design. One such inventor tried to convince me that magnets have unlimited stored energy, or can tap unlimited energy from "somewhere". "Just look at those magnets on your refrigerator," he said. "They support themselves, doing work against the force of gravity forever, so they must have infinite energy capability." This is a simple misunderstanding of force and work. A force must move an object to do work on it. The refrigerator magnet's force doesn't move anything, and it does no work.

This particular magnetic engine puzzle has been attracting a lot of attention lately from people who say they had similar ideas. Some folks complain to me that no solution was posted for a long time. Others, mostly physicists and engineers, wax eloquently about field theory, and seem to me to be missing the point of the exercise.

Many PM proposals have multiple flaws. You might say that they can fail on many levels. They have multiple failure modes. Some defects can be corrected by better engineering. Just as we allow one to assume that friction is absent, in order to expose more fundamental flaws, we can also, one by one, correct minor flaws by better engineering until one serious and unsurmountable one remains.

In this engine, some correspondents have pointed out minor problems:

1. The field due to the symmetric array of outer magnets will be zero at the center of the array. However, the rotating magnet poles are not at the center. Besides, these poles are shielded from the effect of most of the outer magnets.
2. The rotating magnet can see both N and S poles of the outer array, through the shield windows. And due to the angles, it sees more of the S than the N poles, which might compensate for their greater distance. This presents an interesting math problem, but we leave it aside and correct this alleged problem in another way (see below).
3. The finite array of outer magnets produces a field which varies in strength with rotation angle. The rotating assembly might simply find a position of relative equilibrium and just sit there, like a wheel in a roadway rut. OK, so we put more magnets in the outer array to even out the field. Actually this isn't a problem, for if we give the rotor enough initial speed, it rides over the field irregularities.
4. The idea of magnetic shields acting like light shields (simply blocking the field lines) is too simplistic. That's true. See below.
To meet objection 2 we improve the design by repositioning the magnets, adding another rotating assembly on the same shaft, and shielding the magnets in each rotor from "seeing" any poles of the wrong polarity.

The second rotor must be oriented on the shaft so that the forces on it tend to rotate the shaft in the same direction as the first rotor rotates. (IF it rotates!) We can even position the second rotor on the shaft in such a way as to smooth out the "bumpy" effects of the fields. See what a bit of engineering redesign can do? [Constructing this diagram was difficult enough. Don't expect me to explicitly show the supporting frame, shaft support, and the means for transfering the shaft rotation to something else to do useful work.]

Objection 4 is a serious one, we admit. However, in our usual spirit of fairness to inventors, let's grant that somehow we invent a shield that does act in such a simple way, blocking the influence of any magnets that aren't in a line of sight through the shield windows. This task might be every bit as difficult as building a PM machine of any kind. But by granting this concession, and temporarily setting aside the problem of making such a shield, we may expose yet another problem with this design.

Without getting into field theory, (which I'm ill-equipped to do anyway), I think the deception is something like this. Field shields, if they work, are made of matter (isn't everything in a machine made of matter?). They work by electromagnetic interaction with the field, usually be redirecting the field lines, or creating new ones. However, I don't think we need to sweat the details of that. There's some dispute whether a gravitational field shield can even exist, magnetic shields are only partially effective, and we know we can make pretty good electric field shields if they totally enclose something (Faraday cage of metal).

I think it's easier to find the flaw in such machines by looking instead at a similar machine using electric fields and electric shielding. It would have one + and one - charged body inside a metal enclosure, surrounded by a stationary ring of charge outside.

We illustrate this with an even simpler one-dimensional experiment. A positive charge (A, red) and a negative charge (B, blue)are in fixed position. A positive charge (C, red) is halfway between them. Charges A and B are "nailed down", but C is free to move, but only along the line joining A and B. (It's a one-dimensional system. Think of C being movable along a constraining track if you like.) All charges have equal magnitude. We assume an inverse square law of interaction here, but we will see that we will find a result that is more general than that.

The top figure (I) shows the relative sizes of the forces on each charge. We take the force between adjacent charges as of size 1, for convenience. The forces that A and B exert on each other are 1/4, since they are twice as far apart as C is from either A or B. (We are assuming an inverse square law.) So the net force on C has size +2, in the direction of charge B.

Figure (II) shows the same situation with the shield S in place. If a shield is to do what any good shield should, it must shield A from any influence from B or C, shield C and B from any influence from A. That's all we ask of it, the practical details of how it does this don't matter here. So now C and B "don't know" A is there, and the forces on each are of size 1. The force on C is to the right, of size +1, only half what it was without the shield.

Figure (III) models what the shield must do to accomplish this. It must reduce the force on A from -3/4 to 0, must reduce the force on B from -5/4 to -1, and must reduce the force on C from +2 to +1. Now watch this carefully. We do not assume any particular position for the shield, so long as it shields the charges in the manner described in the last paragraph. Look at charge A. To change the force on A from -3/4 to zero, the shield must exert a force of + 3/4 on A. Therefore by Newton's third law, A exerts a force of -3/4 on the shield. To change the force on B from -5/4 to -1, the shield must exert a force of +1/4 on B, so B must exert a force of -1/4 on the shield. To reduce the force on C from +2 to +1, the sheild must exert a force of -1 on C, so C must exert a force of +1 on the shield.

Note the perhaps unexpected result that the net force on the shield is zero, due to all of the charges. So whether or not we fasten down the shield, it will stay put.

But now suppose we fasten the shield to charge C as a "system" so they must move together. Figure (IV) shows this. The internal forces of shield on C and C on the shield add to zero, as all internal forces must. The net force on this system is zero. It isn't going anywhere!

This profound result, which I call the "shield futility theorem" is but one example of "classical shield theory". Although we used an inverse square force law for this illustrative example, any force law may be used. Try it with an inverse first power law. The argument rests on two principles: (1) additivity of forces and (2) Newton's third law. It also assumed a shield that does what you expect of a shield, but doesn't prove that one could make a shield which does that. It does say that if you could make such an idealized shield it wouldn't help you make a perpetual motion machine.

This is the heart of the problem with Chris Cheng's magnet motor puzzle. You can't fix the problem by making the shield stationary, for then it won't "follow" the rotating magnet. And if the rotating magnet has to drag the shield along, it won't work as you desire. Another one of nature's "gotchas".

 Perpetual motion machines fail because the inventor used at least one magical principle in the design.

In short, the deception is this: Shields are also subject to the laws of physics. They aren't "magical" entities. They have mass and are made of matter that has atoms consisting of electric charges, which respond to electric and magnetic fields. Shields are affected by forces, and if they are to work for a particular field, they must interact with that field in a way satisfying Newton's laws. One tends to forget that fact when the inventor directs our attention to the charges within the shield, on a static diagram, where you are thinking "static" and concluding something about "dynamic" (motion). Also the diagram lets you forget that the shields must be attached to something, and must have force interactions with whatever they are attached to. In Cheng's machine, the shield rotates with the magnet within it, if the magnet were to rotate around the axle (but it doesn't). I don't know whether Chris was the "inventor" if this, or saw something similar, but in any case, knowingly or not, this is a darned sneaky puzzle, with clever misdirection.

Check the Annex gallery of the Museum for a non-shielded magnet motor with a different method of deception.

—Donald E. Simanek