Playing around with a disc magnet, I notice that if I set it on edge (so it looks kind of like a car tire or something) and roll it <180 degrees, it rolls back, as if it were on a wound-up spring.
So far, I’ve tried it on a toenail clipper, a small metal ruler, and a cheapo pair of scissors. The magnet itself is one I got from a shipping box, where I suspect it was placed as an antitheft tag (sets off sensors you see around doors of large stores).
So, what’s going on with this thing?
Magnets seek the lowest-energy state with their environment, or at least a local minima. Typically, this means they feel a force towards the position where the strongest parts of the field intersect as much of a magnetic object as possible. For flat, smallish objects (like your toenail clippers), this is frequently the point where the magnet is centered along one or both axes, and for a disk or sphere magnet, it will roll to that point.
Magnetic fields can be imagined as field lines, which are emitted from one pole and converge on the other pole. The lines have tension on them (like rubber bands, say), but they also don’t want to be too close to each other, and they settle on some balance between the two. For a disk magnet, they are generally emitted from one face and converge on the other, and spread out symmetrically in a kind of donut shape. The field lines are hence fairly dense right at the edge of a magnet, and it will pull as much material into its influence there as possible.
The magnet doesn’t “care” which of its field lines intersect an object, so (when possible) it will happily roll in a way such that some field lines exit the object’s influence as long as a greater quantity enter its influence.
So you’re saying, if I set up a disk magnet on an arbitrarily-large flat ferrous plate, it will stay wherever I put it, but if I set it up on a relatively small plate, it will tend to roll toward the center of the plate?
You got it. As you guessed, with a large plate there will be no net force, because only the weak faraway portions will be different. Locally, the field intersects a symmetrical amount of material. But for a small plate, a symmetrical position ensures that the most material is within the strong parts of the field (i.e., as close to the edge as possible).
Of course it’s all much more complex than this. For one, a disk on its edge is likely only a local minima–it would be happier if it could snap one face flat on the plate. But the square edge keeps it upright, since the side forces aren’t too high.
Also, when you apply a magnet to a ferrous object, the object itself becomes magnetized, which distorts the field lines. They don’t just pass through objects indiscriminately.
Furthermore, when field lines are dragged through a conductive object, they set up currents. Ohm’s law ensures that these currents dissipate power (into heat), and this results in a drag force on the object. It’s proportional to the speed of the object, so the static forces are the same, but it means that if you have stuff rolling around, it will eventually come to a stop (even ignoring friction).
There are lots of fun videos on YouTube of people playing with magnets near copper objects. The copper obviously doesn’t attract the magnet, but it does induce the drag effect (rather well since copper is so conductive). Any magnet moving nearby feels like it’s being dragged through honey.
I did a little test and realized I was wrong about spherical magnets. They don’t behave like disk magnets.
Like all magnets, they have two poles, and for a sphere it’s rather like the poles of the Earth (appropriately enough). The field is strongest at the poles, and so the lowest-energy state is when one of the poles touches the magnetic material. It can’t roll away from this position, because every nearby movement is higher energy.
One could, in principle, balance it on the “equator” and it would roll around like the disk. But this is an unstable equilibrium; the lightest perturbation to one side or the other means it will snap to a pole. If it could slide frictionlessly it would move to the rough middle of a ferrous object, but this doesn’t happen in practice.
The disk rolls because it can’t tip over easily–push it to one side and the field has just a tad less material in its influence, which is a higher energy state. So it gets pulled back unless the side forces are very high. Just like why a disk can roll upright in gravity, really.
Of course, it’s also possible that the magnet is a bit asymmetrical. If one side of it is a bit more strongly magnetized than the other, then that side will tend to stick to the surface. Heck, even a non-magnetic cylinder could be a bit asymmetrical and so prefer one side, just from weight balance.
A disk can roll upright in gravity due to gyroscopic effects, right? Is that analogous to the magnet rolling upright due to the magnetic forces as you describe?
What if the edge of the disk magnet was rounded instead of flat? Then would it tend to tip over? A wheel with a rounded edge (e.g., a bicycle wheel) can continue to roll upright.
If I’m understanding you correctly, magnetic force lines are kind of like spokes rather than the even sphere/circle of forces like light and gravity. Thus when I roll it a bit, I’m stretching the ‘spoke’ with the shortest path from the poles through the material.
IF that’s the case, is there a consistent pattern to how many ‘spokes’ a magnet will have, according to it’s size?
Well, this is where the field line visualization starts to break down. Magnetic field lines are in fact continuous like gravity. The absolute number of lines isn’t important; it’s the density of the lines that tells you where the field is stronger or weaker.
The other thing the field line visualization conveys is the idea that the lines always connect one pole to the other. In fact, they are always loops–the lines connect internally to the magnet.
So while they are a very useful visualization tool, don’t take the field lines thing too seriously. There’s nothing truly physical about them. It’s just a way of imagining a complex vector field.
The gyroscopic factors are a separate thing. I was referring only to the flat edge, like on a nickel. It’s stable, either when rolling or stationary, as long as it isn’t perturbed too much. That’s because to push it over, its center of mass has to rise just a little bit, and that takes energy.
A disk magnet with a rounded edge would definitely tip over when not moving quickly. I’m not sure what would happen if it were rolling fast enough for gyroscopic effects to be relevant.
I bought a bunch of disc magnets at Walmart from the craft section. They behaved as the OP described. We also couldn’t get them to work in the motors we were building in my Physical Science classes. So, we checked them using iron filings. They are polarized as follows-
Imagine two half moon-shaped magnets. One has the north pole on its flat edge and its south on the round edge. The other has its north on the round edge and its south on the flat edge. Stick the two together at their flat edges, and you have how these magnets are polarized. They’re really two magnets in one.
We rearranged the polarity of some using a strong rare earth magnetizer. They worked then.
Well, all magnets are really two magnets in one. Cut any magnet in half, and you’ll create new poles so you have two magnets.
And in a sense, magnetic field lines really are real things, in that there’s a fundamental quantum of magnetic flux. It’s small enough, though, that any drawing you ever see of a real magnet must necessarily show only a tiny fraction of the full number of field lines.
These had four poles, without being cut. Cheap flexible sheet magnets are polarized n-s-n-s-n-s-n-s-n-s-n-s… in narrow bands.
There are some interesting magnets now that control the polarity at a fine-grained level to achieve neat effects. For instance, say that you glue together 9 small rectangular magnets in an array:
NSNSNSNSN
And in a different array:
SNSNNNSNS
Each array has more north than south, so when far away and the fields average out, they will repel. However, if you get them close enough, the 8 N-S pairs overwhelm the single N-N pair and they latch closed.
There are lots of things you can do using this basic principle, such as sets that repel at close range and attract farther away, or sets that attract in one orientation but release with a small twist.
On that side, at least. The other side of that array would necessarily have more south than north.
Another trick you can pull with clever arrangement of magnets is an array which has almost all of its field on one side, and none on the other.
Yeah, this trick is only useful when the magnets are physically constrained in some way. For instance, you could use it on a soft-closing drawer. Wouldn’t work if the magnets can flip around or misalign.
Halbach arrays are definitely neat. And the case that california jobcase, with simple alternating polarity, gives a field which is zero at long distance but strong up close.