Iron filings can be used to illustrate the direction of a magnetic field, say due to a bar magnet. This works because when exposed to a magnetic field, the filings are themselves temporarily magnetized along their long axis. Now being magnets, they tend to align in the bar magnet's field. But why is each filing magnetized along its longest axis rather than along some other axis? It must be because that is the lowest-energy configuration, but why?
[Physics] Why do iron filings become magnetized along their long axis instead of in a random direction
electromagnetism
Related Solutions
It's a fair question. A particle in a magnetic field becomes magnetized, and experiences two forces: a torque due to the face that its (induced) dipole moment is not aligned with the magnetic field, and a force due to the gradient of the magnetic field.
Now on a macroscopic level, the gradient is strongest near the poles of the magnet, and you will see a considerable quantity of filings pile up there; but as you get further from the poles, the gradient becomes very weak (roughly as the fourth power of the distance).
The induced dipole itself is proportional to the strength of the field, and the force is the product of dipole and gradient. This means that the gradient effect becomes much weaker with distance: for a bar magnet, field falls roughly with distance cubed (at sufficiently large distance), so gradient falls with fourth power and the attractive force with the seventh power of distance. By contrast, the torque that aligns the particles goes as the sixth power. That sounds really bad as well, until you realize that a metal filing will act as a local "field amplifier": it "pulls the field lines towards it", leading to a concentration of field lines at the tip - and a strong (but very localized) gradient. This gradient means that nearby filing particles will strongly attract each other, and align into the characteristic pattern you are familiar with. But there is no such amplification at a distance - so the particles won't move on a large scale, as there are no large scale gradients to push them.
Electromagnetism – If Magnetic Field Lines Don’t Exist, What Do Iron Filings Around a Magnet Show?
Here's a map of the barometric pressure in the United States.
The map contains isobars, which are lines of constant pressure. These are constructed by starting from an arbitrary point, and following the direction where the pressure doesn't change.
Isobars don't "exist", in the sense that there isn't literally a big white line in the sky hovering over New York City at this moment. Isobars aren't made of anything, and whether or not an isobar goes through a point on a map is decided entirely by how the map maker decided to draw them. But they help you visualize pressure, which is very real.
When people say that magnetic field lines don't "exist", they mean they're like isobars: a completely arbitrary visualization tool that doesn't exist outside of diagrams. But like pressure, the magnetic field itself is as real as it gets. Iron filings follow its direction.
Best Answer
My suggestion is that at the atomic level, each dipole is in a low-energy relationship (or "state") with any dipoles that are end-to-end with it, but at a higher-energy state with any dipoles that are side-by-side with it. Aligning the dipoles the long way results in a greater number of lower-energy states than aligning the short way. For example, consider a tiny iron filing consisting of only 6 dipoles arranged in a 2x3 grid. If the grid is aligned the "long" way, it looks like
where
^indicates a dipole oriented up,|is a low-energy state (north pole of one dipole meets south pole of another), and-is a high-energy state (north meets north). But if aligned the "short" way (the grid is rotated 90 degrees while keeping the dipoles oriented upward), the 2x3 grid looks likeIn the "long" configuration, there are 3 high-energy states between pairs of neighboring dipoles, and 4 low-energy states. But in the "short" configuration, there are 4 high-energy states and 3 low-energy states. Hence the "long" configuration has the lowest overall energy. You could scale this up to any size grid; the long way is always favored.