Poles and Magnetism in Ordinary Matter
All matter ever isolated to date—including every atom on the periodic table and every particle in the standard model—has no magnetic monopole charge. Therefore, the ordinary phenomena of magnetism and magnets have nothing to do with magnetic monopoles.
Instead, magnetism in ordinary matter comes from two sources. First, electric currents create magnetic fields according to Ampère's law. Second, many elementary particles have an "intrinsic" magnetic moment, the most important of which is the electron magnetic dipole moment. (This magnetism is related to quantum-mechanical "spin".)
Mathematically, the magnetic field of an object is often described in terms of a multipole expansion. This is an expression of the field as a superposition (sum) of component fields with specific mathematical forms. The first term in the expansion is called the "monopole" term, the second is called "dipole", then "quadrupole", then "octupole", and so on. Any of these terms can be present in the multipole expansion of an electric field, for example. However, in the multipole expansion of a magnetic field, the "monopole" term is always exactly zero (for ordinary matter). A magnetic monopole, if it exists, would have the defining property of producing a magnetic field whose "monopole" term is nonzero.
A magnetic dipole is something whose magnetic field is predominantly or exactly described by the magnetic dipole term of the multipole expansion. The term "dipole" means "two poles", corresponding to the fact that a dipole magnet typically contains a "north pole" on one side and a "south pole" on the other side. This is analogous to an electric dipole, which has positive charge on one side and negative charge on the other. However, an electric dipole and magnetic dipole are fundamentally quite different. In an electric dipole made of ordinary matter, the positive charge is made of protons and the negative charge is made of electrons, but a magnetic dipole does not have different types of matter creating the north pole and south pole. Instead, the two magnetic poles arise simultaneously from the aggregate effect of all the currents and intrinsic moments throughout the magnet. Because of this, the two poles of a magnetic dipole must always have equal and opposite strength, and the two poles cannot be separated from each other.
Read more about this topic: Magnetic Monopole
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