Editing Magnetic field (section)

===Amperian loop model===
{{Main|Magnetic dipole}}
{{see also|Spin magnetic moment|Micromagnetism}}

{{Multiple image|header=The Amperian loop model
| align = right | total_width = 320
|image1=VFPt dipole magnetic3.svg | alt1 = |caption1=
|image2=VFPt dipole animation magnetic.gif| alt2 = |caption2=
|footer=A current loop (ring) that goes into the page at the x and comes out at the dot produces a {{math|'''B'''}}-field (lines). As the radius of the current loop shrinks, the fields produced become identical to an abstract "magnetostatic dipole" (represented by an arrow pointing to the right).}}

In the model developed by [[André-Marie Ampère|Ampere]], the elementary magnetic dipole that makes up all magnets is a sufficiently small Amperian loop with current {{math|''I''}} and loop area {{math|''A''}}. The dipole moment of this loop is {{math|1=''m'' = ''IA''}}.

These magnetic dipoles produce a magnetic {{math|'''B'''}}-field.

The magnetic field of a magnetic dipole is depicted in the figure. From outside, the ideal magnetic dipole is identical to that of an ideal electric dipole of the same strength. Unlike the electric dipole, a magnetic dipole is properly modeled as a current loop having a current {{math|''I''}} and an area {{math|''a''}}. Such a current loop has a magnetic moment of
<math display="block">m = Ia ,</math>
where the direction of {{math|'''m'''}} is perpendicular to the area of the loop and depends on the direction of the current using the right-hand rule. An ideal magnetic dipole is modeled as a real magnetic dipole whose area {{math|''a''}} has been reduced to zero and its current {{math|''I''}} increased to infinity such that the product {{math|1=''m'' = ''Ia''}} is finite. This model clarifies the connection between angular momentum and magnetic moment, which is the basis of the [[Einstein–de Haas effect]] ''rotation by magnetization'' and its inverse, the [[Barnett effect]] or ''magnetization by rotation''.<ref name=Graham>See [[Magnetic moment#Magnetic dipoles|magnetic moment]]{{Broken anchor|date=2024-03-25|bot=User:Cewbot/log/20201008/configuration|target_link=Magnetic moment#Magnetic dipoles|reason= The anchor (Magnetic dipoles) [[Special:Diff/839030611|has been deleted]].}} and {{cite book |title=Introduction to Magnetic Materials |author1=B. D. Cullity |author2=C. D. Graham |url=https://books.google.com/books?id=ixAe4qIGEmwC&pg=PA103 |page=103 |isbn=978-0-471-47741-9 |year=2008 |publisher=Wiley-IEEE |edition=2}}</ref> Rotating the loop faster (in the same direction) increases the current and therefore the magnetic moment, for example.