It's a common question that sounds like a paradox: if you take a bar magnet and snap it in two, do you end up with a separate North pole piece and a South pole piece? The intuitive answer might be yes, but the reality reveals one of the most fundamental laws of magnetism.
The simple answer is that when you break a magnet in half, you don't get two isolated poles; instead, you get two smaller, complete magnets, each with its own North and South poles.

The Fundamental Rule: No Magnetic Monopoles
The reason this happens relates to the core nature of magnetism. A fundamental law of physics states that magnetic monopoles do not exist (or at least, they haven't been conclusively observed). This means you cannot have an isolated North pole or an isolated South pole.
Every magnet—no matter its size or shape—is a magnetic dipole, meaning it must have both a North pole and a South pole.
The Microscopic Source of Magnetism
To understand why breaking a magnet creates two new ones, we have to look at its internal structure. A permanent magnet isn't polarized just at its ends; its entire body is polarized at a microscopic level.
Magnetic Domains: A strong magnet is composed of countless tiny regions called magnetic domains. Within each domain, the magnetic fields of all the atoms are perfectly aligned, effectively acting like a microscopic magnet.
Alignment: When the material is magnetized, all these domains are aligned in the same direction, running continuously from one end (the North pole) to the other (the South pole).
What Happens When the Magnet Breaks?
When you apply enough force to break a bar magnet in half, you are simply creating a new physical break in the middle of this long chain of aligned domains.
New Surface Exposure: At the exact point of the break, the internal, aligned domains are suddenly exposed.
Instantaneous Pole Creation: Since the field lines must always exit a North pole and enter a South pole, a new South pole immediately forms on the severed end of the original North piece, and a new North pole forms on the severed end of the original South piece.
Two Complete Magnets: You now have two smaller pieces, but each piece has maintained the continuity of the magnetic field alignment, resulting in two separate, but complete, magnets.
If you were to break those two pieces again, the process would repeat. You would simply end up with four smaller magnets, each with a North and South pole. You could theoretically continue this process until you reached a single magnetic domain—the smallest possible magnet.

The Practical Implication
While the magnetic field strength of the individual pieces is weaker than the original whole magnet (since the volume of magnetic material has been reduced), the pieces still function as complete magnets. This demonstrates the powerful, unbreakable connection between North and South poles in any permanent magnet.
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