Magnetic Field Polarity of a Broken Magnet

Very simply put. Very nice. GA

GA - It cannot be anything else.

If one uses a band saw it divide a square magnet bar into two equal size wedges (small north big south & small south big north) one should at least expect to have an east and west pole as well

What about cutting a cubical magnet into two equal sized pyramids?

From the dreaded Wikipedia:

Magnets exert forces on one another, similar to the force associated with electric charges. Like poles will repel each other, and unlike poles will attract. When any magnet (an object conventionally described as having magnetic north and south poles) is cut in half across the axis joining those "poles", the resulting pieces are two normal (albeit smaller) magnets. Each has its own north pole and south pole.

Even atoms and subatomic particles have tiny magnetic fields. In the Bohr model of an atom, electrons orbit the nucleus. Their constant motion gives rise to a magnetic field. Permanent magnets have measurable magnetic fields because the atoms and molecules in them are arranged in such a way that their individual magnetic fields align, combining to form large aggregate fields. In this model, the lack of a single pole makes intuitive sense: cutting a bar magnet in half does nothing to the arrangement of the molecules within. The end result is two bar magnetics whose atoms have the same orientation as before, and therefore generate a magnetic field with the same orientation as the original larger magnet.

Not as wonderfully concise as Tornado's answer above, but hopefully also helpful.

What about a spherical magnet? Or an Escher magnet? Liquid magnet?

Just do the topology.

simple answer

Here's an example of an answer most of us can agree on:

but when it gets down to it, we don't really know..

Bohr's model of an atom makes a nice pik-a-ture for our minds to contemplate,

it has no relationship to whatever is behind the concept

of an electron in a valence shell

merrily circling a nucleus (or "nukulus" according to Dubya):

and magnetic monopoles? Keep lookin'.

meanwhile, the paradigm of "science" and "engineering"

allows us to make predictions:

which is good enuff, I guess:

if we could just grow some wisdom (or whatever)

so we didn't continuously screw things up..

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Look:

you take two flat flexible magnets,

and curve each of them into a ball, but contrary-wise:

one with all + on the outside,

the other with all -:

that would be just like two monoples, huh?

Couldn't keep them apart..

Tru love!

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Why would this not work?

Topologically speaking, I mean.