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No, magnetic "charges" do not exist -- magnetic POLES exist, and they exist always as a North-South pair, never separate from each other. If you break a magnet into pieces, each piece will itself be a magnet with N and S sides. The origins of this polarity is found at the atomic level and have to do with spin and orbital electron motions inside atoms. So an electron moving in its atom has both N and S poles. Which is the main difference when comparing to ELECTRIC charges: the positive and negative electric charges are carried by two different particles (the proton and the electron) and can be separated because the proton and the electron exist separate from each other. The magnetic POLES are both carried by the same particle, the electron, and thus do not exist on their own. (You cannot hold a N-pole in one hand and a S-pole in the other.)

A lot of researchers have devoted loads of time trying to isolate a magnetic pole. (Looking for a "monopole.") Nobody has succeeded.

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