It might seem common sense that when we split a magnet we get 2 magnets with their own N-S poles. But somehow, I find it hard to accept this fact. (Which I now know is stated by the magnetic Gauss's Law $\vec{\nabla}\cdot \vec{B} =0.$)
I have had this doubt ever since reading about the quantum-field-theory and I know I might sound crazy but is it really impossible to separate the poles of a magnet?
Is there some proof/explanation for an independently existing magnetic monopole?
Answer
Well, in order for this splitting to be possible, the magnet would have to be made of two magnetic monopoles (like charged particles, but with "magnetic charge" instead of electric charge) bound together. No known magnet is actually constructed this way; all real magnets that have been studied are made of either little current loops, or particles that have a spin magnetic moment (and these basically act like little current loops).
It's still an open question whether or not magnetic monopoles exist. Some theories predict that they should, but most have nothing to say about it either way. I am not aware of any theories that prohibit the existence of these monopoles. Quantum field theory in general falls in the second category; that is, there is nothing inherent in QFT that requires magnetic monopoles to exist or not exist.
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