Why can a magnetic monopole not exist, assuming Maxwell's Equations are currently correct and complete?

Because closed magnetic field loops have to be formed between both ends of the magnet, a magnet will always have two poles.

Explanation:

Magnetic Monopoles do not exist in nature because a magnetic field always forms a loop that runs from one end of the magnet to the other.

Since this loop of the magnetic field has an origination and termination point which are at the two ends of the magnet (North and South poles).  A magnet will always be bipolar which is in this case, North and South; even at an atomic level.

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