Every magnet has a north pole and a south pole, and the obvious guess about what happens if you saw one in half is that you'd separate the two — one piece all north, the other all south. That isn't what happens. Cut a bar magnet down the middle and each half comes out as a complete, ordinary magnet, with its own north pole and its own south pole. Cut either of those halves again and the same thing happens again, all the way down to pieces small enough that the effect gets hard to measure. Nobody, in the entire history of experimental physics, has ever produced a lone north pole with no south pole attached, or a lone south with no north. The two always come as a pair.
The pairing goes all the way down
A bar magnet's overall north-south structure isn't sitting at the two ends waiting to be separated — it's built out of an enormous number of much smaller magnetic dipoles, each one already possessing its own north and south, contributed by the aligned spins and orbital motion of electrons throughout the material. In a magnetised piece of iron, billions of these tiny atomic-scale dipoles are lined up in the same direction, and the bar's north and south poles are simply where that alignment reads out at the two ends of the whole stack. Cutting the bar anywhere doesn't strip a pole away from the rest — it just draws a new boundary through a lattice of dipoles that were each already a complete north-south pair on their own. Every fragment you produce, no matter how you cut it, is made of the same self-contained dipoles, so every fragment keeps both poles.
The equation that quietly assumes this
One of Maxwell's four equations of electromagnetism, in its standard form, states that the magnetic field has no sources or sinks — mathematically, its divergence is zero everywhere. Electric charge, by contrast, does have sources and sinks: a lone positive charge is a perfectly ordinary, isolatable thing, which is part of why electric field lines can start and end at a single point charge while magnetic field lines, in every material ever observed, only ever form closed loops with no starting or ending point. That structural difference between electricity and magnetism is baked directly into Maxwell's equations as written, and it's the same fact showing up again: an isolated magnetic pole — a magnetic monopole — has a very specific mathematical meaning, and it's never once been detected.
What we're still unsure about
"Never detected" isn't the same claim as "impossible," and it's worth being precise about which one this post is making. Some theories that extend beyond the current standard model of particle physics — certain grand unified theories, and some models in string theory — predict that magnetic monopoles could exist as extremely rare, extremely massive exotic particles, likely produced only in the earliest, hottest moments of the universe. Physicists have run dedicated searches for them for decades, from cosmic-ray detectors to superconducting loop experiments, and none has ever produced a confirmed monopole. That leaves this as a genuinely open experimental question rather than a settled impossibility — Maxwell's equations describe every magnet anyone has ever built or measured, but they don't by themselves prove a monopole could never exist anywhere in the universe.
This sits inside Magnetic Fields & the Lorentz Force, one of eight topics in Electromagnetism, one of five domains in Physics, one of seventeen subjects the app can quiz you on.