J Rosen (1980). "Redundancy and superfluity for electromagnetic fields and potentials". American Journal of Physics. 48 (12): 1071. Bibcode:1980AmJPh..48.1071R. doi:10.1119/1.12289.
J Rosen (1980). "Redundancy and superfluity for electromagnetic fields and potentials". American Journal of Physics. 48 (12): 1071. Bibcode:1980AmJPh..48.1071R. doi:10.1119/1.12289.
See magnetic monopole for a discussion of monopole searches. Recently, scientists have discovered that some types of condensed matter, including spin ice and topological insulators, display emergent behavior resembling magnetic monopoles. (See sciencemag.org and nature.com.) Although these were described in the popular press as the long-awaited discovery of magnetic monopoles, they are only superficially related. A "true" magnetic monopole is something where ∇ ⋅ B ≠ 0, whereas in these condensed-matter systems, ∇ ⋅ B = 0 while only ∇ ⋅ H ≠ 0.
See magnetic monopole for a discussion of monopole searches. Recently, scientists have discovered that some types of condensed matter, including spin ice and topological insulators, display emergent behavior resembling magnetic monopoles. (See sciencemag.org and nature.com.) Although these were described in the popular press as the long-awaited discovery of magnetic monopoles, they are only superficially related. A "true" magnetic monopole is something where ∇ ⋅ B ≠ 0, whereas in these condensed-matter systems, ∇ ⋅ B = 0 while only ∇ ⋅ H ≠ 0.
web.archive.org
Jackson, John. "Maxwell's equations". Science Video Glossary. Berkeley Lab. Archived from the original on 2019-01-29. Retrieved 2016-06-04.
The absence of sinks/sources of the field does not imply that the field lines must be closed or escape to infinity. They can also wrap around indefinitely, without self-intersections. Moreover, around points where the field is zero (that cannot be intersected by field lines, because their direction would not be defined), there can be the simultaneous begin of some lines and end of other lines. This happens, for instance, in the middle between two identical cylindrical magnets, whose north poles face each other. In the middle between those magnets, the field is zero and the axial field lines coming from the magnets end. At the same time, an infinite number of divergent lines emanate radially from this point. The simultaneous presence of lines which end and begin around the point preserves the divergence-free character of the field. For a detailed discussion of non-closed field lines, see L. Zilberti "The Misconception of Closed Magnetic Flux Lines", IEEE Magnetics Letters, vol. 8, art. 1306005, 2017.
