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Maxwell's equations
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=== Gauss's law for magnetism === {{Main|Gauss's law for magnetism}} [[Image:VFPt dipole magnetic1.svg|right|thumb|[[Gauss's law for magnetism]]: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current.]] [[Gauss's law for magnetism]] states that electric charges have no magnetic analogues, called [[magnetic monopole]]s; no north or south magnetic poles exist in isolation.<ref name=VideoGlossary>{{cite web | url =http://videoglossary.lbl.gov/#n45 | title =Maxwell's equations | last =Jackson | first =John | website =Science Video Glossary | publisher =Berkeley Lab | access-date =2016-06-04 | archive-date =2019-01-29 | archive-url =https://web.archive.org/web/20190129113142/https://videoglossary.lbl.gov/#n45 | url-status =dead }}</ref> Instead, the magnetic field of a material is attributed to a [[dipole]], and the net outflow of the magnetic field through a closed surface is zero. Magnetic dipoles may be represented as loops of current or inseparable pairs of equal and opposite "magnetic charges". Precisely, the total [[magnetic flux]] through a Gaussian surface is zero, and the magnetic field is a [[solenoidal vector field]].<ref group="note">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 [https://zenodo.org/record/4518772#.YCJU_WhKjIU "The Misconception of Closed Magnetic Flux Lines"], IEEE Magnetics Letters, vol. 8, art. 1306005, 2017.</ref>
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