# Magnetic fields inside hollow magnets, are the poles reversed?

In a hollow magnet, a cube for example, are the magnetic poles reversed or is that a myth? In other words, if you consider the magnet in the image is hollow, and you place a smaller cube magnet inside it, would the magnets prefer to orient themselves like in example 1 in the image at the bottom? Or, are the poles inside the hollow cube somehow reversed, such that the magnets prefer a reverse orientation, example 2?

Note, this question is slightly similar to a previously asked question, it is not intended as spam but as genuine interest.

• Hint: the cube magnet already has a smaller magnetized cube of metal inside it. Is it desperately trying to turn around? – eyeballfrog May 8 at 23:07
• You mean the magnetic poles are "reverse" on the inside, like in example 2? – user612 May 8 at 23:21
• re: your analogy, two bar magnets placed side by side with poles in same direction will desperately try to turn around, yet a single bar magnet the size of two magnets with poles in same direction will not. – user612 May 8 at 23:23
• It will depend on the exact geometry of the surrounding magnet. In other words, whether or not the magnet is long and thin, or wide and flat. I would suggest writing a small program to calculate the field for various magnet shapes if you have that skill, or maybe finding a program online that does this. I don't know what the answer is for the particular case of a cube though. – Ricky Tensor May 9 at 0:11
• exact geometry is a cube, c^3 – user612 May 9 at 0:44

If we are truly considering a hollow magnet, then example 2 is the preferred view. This is because magnets are made up of dipoles: you cannot have just a south pole, there must be a north. So, if you have a south pole that you've hollowed out, then the inside of said south pole must be north, because you cannot break apart a magnet to only have a south pole. By hollowing out the magnet, you have created a northern surface on the interior of the south pole, and a southern surface on the interior of the north pole. Theoretically, both configurations will sometimes work based on symmetry, but the first example is an example of an unstable configuration, while the second is an example of a stable configuration. What this means is that if there is any slight perturbation on either the hollow magnet or the interior magnet, then both configurations will tend towards the second example. You'd have to place a magnet perfectly in the first example to get it to work.

For any example that you wish to examine, you can apply the fundamental rule that magnets exist only as dipoles. If you'd like

$$\nabla\cdot\vec{B}=0$$

is the second Maxwell's equation and is taken as the mathematical explanation for why there are no such thing as magnetic monopoles. Thus you cannot have a magnetic north pole without an attached magnetic south pole. If you cut a magnet directly across the N-S line, you will just be left with 2 smaller bar magnets with a north and a south pole.

If you have a bar magnet that I will write simply as S-N, then what you actually have is a whole collection of tiny dipoles aligned S-N S-N S-N S-N S-N. You can see if you wish to hollow out the intertior, you need to remove a S-N pair, you cannot just remove an S or an N (in particular, you must remove a connected pair).

• That makes sense. I have gotten contradictory answers so far, which is why I have tried to narrow down what I was asking (so a few seemingly similar questions if you look at this profile history. ) Roughly 50-50 actually on both examples, but I think most people are not that experienced with the subject. – user612 May 9 at 1:48
• What about horseshoe magnets? They are "hollowed out" sort of between the U shaped magnet, yet seem to not follow what you said, since they have a north pole on the "interior" surface as well as exterior. – user612 May 9 at 1:49
• @user612 That is not the interior surface, that is the exterior. The actual northern and southern surfaces are the tips of the U. Why does this make sense? Because again, there are only magnetic dipoles. The actual sides of the U will have a magnetic field around them coming from the tips of the U, but the dipoles are parallel to the side and so those sides do not really contribute to the magnetic field. The interior in that case would be INSIDE the tips, not in between them. – Kraig May 9 at 2:17
• What about this diametrically magnetized cylinder magnet, it shows magnetic flux lines from north pole to south pole on a dipole, imgur.com/a/Mogup8o The image is from this paper espace.curtin.edu.au/bitstream/handle/20.500.11937/63348/… – user612 May 9 at 2:19
• @user If you take a look at my final paragraph, you can imagine bending that configuration (keep in mind that there are much more than trillions of these tiny magnetic poles aligned, so any slight curvature is negligible to any tiny dipole, but globablly you can achieve that bent shape). That is exactly what your images are there. The hollow region would still be physically inside the N or S poles, not in between them. – Kraig May 9 at 2:26