A magnetic monopole carries an isolated magnetic charge, producing nonzero net magnetic flux through a closed enclosing surface. In the usual macroscopic Maxwell equations without magnetic charges, Gauss's law for magnetism instead gives . Cutting a conventional bar magnet produces smaller magnetic dipoles, rather than separating its north and south poles into isolated charges.
A model radial field away from the origin has flux through every enclosing sphere. It can be described locally by a magnetic vector potential, but not by one potential smooth over the whole enclosing sphere: the Stokes theorem would otherwise force its total flux to vanish. The two-patch vector potential for a radial monopole makes that obstruction explicit. A classical monopole model, a monopole solution in a field theory, and a monopole-like excitation in a material require their own physical interpretation and evidence.
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