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 on anything. 
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:
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 other fundamental problems with this design.
The short answer.First, lets look at the field produced by a circular ring of magnet poles of the same polarity lying in a plane. Due to symmetry and the vector nature of force, their combined field at the center of the circle is zero. But what of their combined field elsewhere in the plane? The surprising result is that the combined field is very nearly zero anywhere in the plane, within the circle.  In fact, if the ring were a continous distribution of poles, the field would be exactly zero anywhere within the circle and in the plane of the circle. That continuous distribution is a useful model for further analysis.
The original form of the motor had magnets lying in a plane. This is equivalent to one circle of N poles and a larger circle of S poles. Each circle contributes nearly zero field anywhere within the smaller circle, so the net field from all magnets is nearly zero anywhere within the smaller circle, and in that same plane. 
So the rotating magnet and shield are "seeing" nearly zero field from the outer magnets. Therefore those magnets exert no force on the rotor. There's nothing to make the rotor move, whether or not it has shields attached. 
Broader implications.The behavior of magnets is often fascinating to observe, as they exert force on each other, and on metallic objects. One is tempted to think that their movement is due to their "stored" magnetic energy, and if you could design a device to turn that stored energy into useful work, you'd have achieved, if not perpetual motion, at least something very useful. Such is the allure of magnets to perpetual motion seekers. Even if they understand that magnet internal energy is not being extracted, they suppose that the magnets are somehow a conduit of energy stored in the vacuum, or somewhere else.
The magnetic energy stored in a magnet is a paltry amount. It may easily be "extracted" by sharp blows to the magnet, or by heating the magnet. Such actions compromise the alignment of magnetic domains within the magnet. After you do this, the magnet isn't magnetized anymore. In the absence of such processes, the motion of magnets in a motor or generator device is not due to their stored magnetic energy. Such motions are entirely the result of the initial mechanical energy you give to the magnets when you place them in position relative to each other. (There can be a very slight demagnetization due to thermal and other stresses when the magnet is part of a motor or generator.)
You have seen those toys with magnet pendulums moving eratically in the field of stationary magnets placed underneath. The pendulum has very little friction, so the device moves for quite a long time before it comes to rest. But that motion hasn't used any of the energy stored in the magnetsnot one bit. You can pull the pendulum aside (giving it initial energy) and start it up again and it will run as long as before. You can repeat this time after time, day after day, and never extract any energy stored in the magnets. The only energy it needs is that you gave it when you initially pulled the magnet aside, and when that is used up, it stops.
These devices haven't extracted energy from unknown sources either. If you carefully measure and account for the mechanical energy you put into the system, and the mechanical energy that is dissipated into thermal energy, you find that all energy is fully accounted for. Magnet machines don't extract energy from the vacuum, the ether, the fourth dimension, or any other magical realm.
 If the "nearly" zero bothers you, you may argue that the field, though small, actually has a periodic variation in strength with angle, having M periods in 360° if there are M magnets. This does not help the cause of perpetual motion. If you gave the rotor a spin, pushing strongly enough, it would move with a varying speed with that same periodic variation, until frictional forces brought it to rest at one of the M positions of force equilibrium. This is the behavior one observes when attempting to make a magnet motor perpetual motion machine. Perpetual motion believers call these "sticking points", and imagine that if sticky points could be eliminated by redesign, they'd achieve perpetual motion or even over-unity performance.
 Using different language, the potential energy of the rotor with respect to the stator magnets has periodic variation around the circle. The rotor will come to rest at a position of relative minimum potential energy. To move it out of such a "potential well" requires exerting a force sufficient to give it additional energy equal to that of the nearby potential peak. But this is just good old energy conservation at work.
The magnetic shield turns out to be a distractor, of no importance in this device. Most respondents have gone to great lengths to argue that the perfect magnetic shield is itself an impossible device, or to postulate how a shield distorts magnetic fields, without realizing that the shield is completely irrelevant to this version of the device. 
Check the Annex gallery of the Museum for a non-shielded magnet motor with a different method of deception.
 Apparently this misconception is more pervasive than I thought. I seldom read internet forums and discussion groups because too many people there waste everyone's time with unfounded opinions, or by pontificating nonsense about physics as if they really understood it. A correspondent pointed me to one such instance where someone confidently declared that my comment about the refrigerator magnet was wrong:
There is [sic] a few things wrong here. One is something that was said by the person who created the site.In physics, the definition of work is this: "Work done by a force acting on a body is the product of the size of that force multiplied by the distance the body moves, multiplied by the cosine of the angle between the force and the distance." [Both force and distance are vectors.] Or, W = F x cos θ. (x is the distance the body moves. θ is the angle between the vectos F and x.) So, no motion, no distance moved, zero work. The clueless soul, who is so certain that I am wrong, cites the example of a person hanging from a bar, supporting his own weight. This person is certainly expending energy in this process, since muscular effort involves muscle fibres contracting and relaxing, doing microscopic scale work within the body. This work is dissipated as heat. But he does no macroscopic work on the bar or anything else outside of his body. If he were condemned to be hung by a noose until dead, his lifeless body would hang there just as well, doing no work at all.
Our refrigerator magnet is likewise doing no work, niether external nor internal, as it remains at rest firmly in place and unmoving, on the refrigerator wall, supporting its own weight.
This is just another example, of many, that shows that misunderstanding of basic, elementary, physics is the fuel that motivates perpetual motionists. Most of these folks are unable to do force and torque analysis of systems using free-body diagrams, skills that are supposed to be learned in the first half of the first semester of an elementary physics course.
The clinker is that field shields are never "magical" in their operation. They still must obey Newton's third law, which ensures that when a shield is acted upon by forces due other parts of the system, then the shield in turn exerts equal size and oppositely directed forces on those parts of the system. Perpetual motion machine designers seldom even consider Newton's third law, yet it is the law of nature that dooms their efforts.
[Jan 2009] I like to leave some unanswered questions to frustrate readers. One reader informs me that the answer above isn't crystal clear. So here's more.
Note that Jacob does not include the times when the stationary magnet's S pole is "seen" through one of the shield windows, and in those cases the forces retard the supposed motion of the wheel. Granted, due to the additional distance, these are somewhat weaker than the ones that flash on the screen in blue. Also, no forces are indicated during the majority of time when the windows are not aimed at a stationary pole. But there are still forces of attraction and repulsion during that time, mostly repulsion. Magnetic shields don't "beam" fields like the beam of a flashlight. The fields spread out. In fact there's strong field lines all the time from N to S pole of the rotating magnet. And, it turns out, the forces due to the fringing field are mostly such as to retard any motion of the rotor. Of course, this description assumes that there is rotational motion. There may be, for short duration, but the rotor will quickly find a position of stable equilibrium and stop there.
And, finally. If the shield is effective in modifying the field of the rotating magnet, it does so by creating a field of its own in response to the field from the small magnet (Newton's third law), and this field of the shield is opposite in size and direction (mostly) in those regions where it is effective in "canceling" the magnet's field. Now if it does that, than it must also be doing the same sort of thing for the fixed (larger) magnet at lower right. (Shields don't discriminate.) And here Lenz's law comes into play (a magnetic result of Newton's third), such that the motion of the magnetic shield is opposed by the larger magnet. On my physics demo page I have a Lenz law demo that involves dropping a strong magnet down an aluminum tube. When this is done, the moving field of the magnet induces current in the aluminum which has fields which oppose the change in motion of the magnet. So this decreases the magnet's downward acceleration, and it quickly reaches a slow terminal velocity and arrives at the bottom of the tube much later than if it were in free fall the same distance.
I was hoping some computer whiz with access to software that models magnetic fields dynamically might run this through the computer and see what results. Quite a few perpetual motion enthusiasts have done this for their own inventions, and report that their idea "shows promise". But none took the bait and modeled this one. The software that I've seen which does such simulations usually has propagating computational errors that can fool you into thinking there's a "slight tendency to sustain rotational motion". Very slight. Besides, this software is not designed to calculate forces on a magnetic shield.
That's when the software is set up properly. But usually these people don't set it up right, and omit some "little detail" that they didn't think important.
Here we need to remind ourselves, yet again, that there is no known perfect magnetic shield for static or quasi-static magnetic fields. But even if we allow such a perfect shield for the sake of analysis (just as we allow frictionless bearings), these magnetic motors using shields would not have over-unity performance.