Editing Maxwell's equations (section)

== Variations ==
Popular variations on the Maxwell equations as a classical theory of electromagnetic fields are relatively scarce because the standard equations have stood the test of time remarkably well.

=== Magnetic monopoles ===
{{main|Magnetic monopole}}

Maxwell's equations posit that there is [[electric charge]], but no [[magnetic charge]] (also called [[magnetic monopole]]s), in the universe. Indeed, magnetic charge has never been observed, despite extensive searches,<ref group="note">See [[magnetic monopole]] for a discussion of monopole searches. Recently, scientists have discovered that some types of condensed matter, including [[spin ice]] and [[topological insulator]]s, display ''emergent'' behavior resembling magnetic monopoles. (See [http://www.sciencemag.org/cgi/content/abstract/1178868 sciencemag.org] and [http://www.nature.com/nature/journal/v461/n7266/full/nature08500.html 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 {{math|∇ ⋅ '''B''' ≠ 0}}, whereas in these condensed-matter systems, {{math|1=∇ ⋅ '''B''' = 0}} while only {{math|∇ ⋅ '''H''' ≠ 0}}.</ref> and may not exist. If they did exist, both Gauss's law for magnetism and Faraday's law would need to be modified, and the resulting four equations would be fully symmetric under the interchange of electric and magnetic fields.<ref name=Jackson/>{{rp|273–275}}