Editing Magnet (section)

== Physics ==

=== Magnetic field ===
[[File:Magnet0873.png|thumb|Iron filings that have oriented in the magnetic field produced by a bar magnet]]
[[File:Magnet bar.ogv|thumb|thumbtime=35|Detecting magnetic field with compass and with iron filings]]
{{Main|Magnetic field}}

The [[magnetic field|magnetic flux density]] (also called magnetic '''B''' field or just magnetic field, usually denoted  by '''B''') is a [[vector field]]. The magnetic '''B''' field [[Euclidean vector|vector]] at a given point in space is specified by two properties:

# Its ''direction'', which is along the orientation of a [[compass|compass needle]].
# Its ''magnitude'' (also called ''strength''), which is proportional to how strongly the compass needle orients along that direction.

In [[SI]] units, the strength of the magnetic '''B''' field is given in [[tesla (unit)|teslas]].<ref>{{cite book |last=Griffiths |first=David J. |title=Introduction to Electrodynamics |edition=3rd |publisher=[[Prentice Hall]] |pages=[https://archive.org/details/introductiontoel00grif_0/page/255 255–8] |year=1999 |isbn=0-13-805326-X |oclc=40251748 |url-access=registration |url=https://archive.org/details/introductiontoel00grif_0/page/255 }}
</ref>

=== Magnetic moment ===
{{Main|Magnetic moment}}

A magnet's magnetic moment (also called magnetic dipole moment and usually denoted '''μ''') is a [[vector (geometry)|vector]] that characterizes the magnet's overall magnetic properties. For a bar magnet, the direction of the magnetic moment points from the magnet's south pole to its north pole,<ref>Knight, Jones, & Field, "College Physics" (2007) p. 815.</ref> and the magnitude relates to how strong and how far apart these poles are. In [[SI]] units, the magnetic moment is specified in terms of A·m<sup>2</sup> (amperes times meters squared).

A magnet both produces its own magnetic field and responds to magnetic fields. The strength of the magnetic field it produces is at any given point proportional to the magnitude of its magnetic moment. In addition, when the magnet is put into an external magnetic field, produced by a different source, it is subject to a [[torque]] tending to orient the magnetic moment parallel to the field.<ref name=Graham>{{ cite book |title=Introduction to Magnetic Materials |author1=Cullity, B. D. |author2=Graham, C. D. |name-list-style=amp |url=https://books.google.com/books?id=ixAe4qIGEmwC&pg=PA103 |page=103 |isbn=978-0-471-47741-9 |year=2008 |publisher=[[Wiley-IEEE Press]]|edition=2}}</ref> The amount of this torque is proportional both to the magnetic moment and the external field. A magnet may also be subject to a force driving it in one direction or another, according to the positions and orientations of the magnet and source. If the field is uniform in space, the magnet is subject to no net force, although it is subject to a torque.<ref>{{cite journal | author = Boyer, Timothy H. | title = The Force on a Magnetic Dipole | year = 1988 | journal = [[American Journal of Physics]] | volume = 56 | issue = 8 | pages = 688–692 | doi = 10.1119/1.15501|bibcode = 1988AmJPh..56..688B }}</ref>

A wire in the shape of a circle with area ''A'' and carrying [[electric current|current]] ''I'' has a magnetic moment of magnitude equal to ''IA''.

=== Magnetization ===
{{Main|Magnetization}}

The magnetization of a magnetized material is the local value of its magnetic moment per unit volume, usually denoted '''M''', with units [[ampere|A]]/[[meter|m]].<ref>{{cite web|url=http://www.magneticmicrosphere.com/resources/Units_for_Magnetic_Properties.pdf|archive-url=https://web.archive.org/web/20110714020750/http://www.magneticmicrosphere.com/resources/Units_for_Magnetic_Properties.pdf|archive-date=2011-07-14|title=Units for Magnetic Properties|publisher=Lake Shore Cryotronics, Inc.|access-date=2012-11-05}}</ref> It is a [[vector field]], rather than just a vector (like the magnetic moment), because different areas in a magnet can be magnetized with different directions and strengths (for example, because of domains, see below). A good bar magnet may have a magnetic moment of magnitude 0.1&nbsp;A·m<sup>2</sup> and a volume of 1&nbsp;cm<sup>3</sup>, or 1×10<sup>−6</sup>&nbsp;m<sup>3</sup>, and therefore an average magnetization magnitude is 100,000&nbsp;A/m. Iron can have a magnetization of around a million amperes per meter. Such a large value explains why iron magnets are so effective at producing magnetic fields.

=== Modelling magnets ===
[[File:VFPt cylindrical magnet thumb.svg|thumb|Field of a cylindrical bar magnet computed accurately]]
{{See also|Magnetic moment#Models|label 1=Two definitions of moment}}

Two different models exist for magnets: magnetic poles and atomic currents.

Although for many purposes it is convenient to think of a magnet as having distinct north and south magnetic poles, the concept of poles should not be taken literally: it is merely a way of referring to the two different ends of a magnet. The magnet does not have distinct north or south particles on opposing sides. If a bar magnet is broken into two pieces, in an attempt to separate the north and south poles, the result will be two bar magnets, ''each'' of which has both a north and south pole. However, a version of the magnetic-pole approach is used by professional magneticians to design permanent magnets.{{Citation needed|date=December 2011}}

In this approach, the [[divergence]] of the magnetization ∇·'''M''' inside a magnet is treated as a distribution of [[magnetic monopole]]s. This is a mathematical convenience and does not imply that there are actually monopoles in the magnet. If the magnetic-pole distribution is known, then the pole model gives the [[magnetic field]] '''H'''. Outside the magnet, the field '''B''' is proportional to '''H''', while inside the magnetization must be added to '''H'''. An extension of this method that allows for internal magnetic charges is used in theories of ferromagnetism.

Another model is the [[André-Marie Ampère|Ampère]] model, where all magnetization is due to the effect of microscopic, or atomic, circular [[bound current]]s, also called Ampèrian currents, throughout the material. For a uniformly magnetized cylindrical bar magnet, the net effect of the microscopic bound currents is to make the magnet behave as if there is a macroscopic sheet of [[electric current]] flowing around the surface, with local flow direction normal to the cylinder axis.<ref>{{ cite book |  title = Philosophy of the Mechanics of Nature, and the Source and Modes of Action of Natural Motive-Power |  author = Allen, Zachariah |  publisher = D. Appleton and Company |  year = 1852 |  page = [https://archive.org/details/bub_gb_EpUIAAAAIAAJ/page/n260 252] |  url = https://archive.org/details/bub_gb_EpUIAAAAIAAJ }}</ref> Microscopic currents in atoms inside the material are generally canceled by currents in neighboring atoms, so only the surface makes a net contribution; shaving off the outer layer of a magnet will ''not'' destroy its magnetic field, but will leave a new surface of uncancelled currents from the circular currents throughout the material.<ref>{{ cite book |  title = Electricity, Magnetism, and Light |  edition = 3rd |  author = Saslow, Wayne M. |  publisher = Academic Press |  year = 2002 |  isbn = 978-0-12-619455-5 |  page = 426 |  url = https://books.google.com/books?id=4liwlxqt9NIC&pg=PA426 |  url-status = live |  archive-url = https://web.archive.org/web/20140627092809/http://books.google.com/books?id=4liwlxqt9NIC&pg=PA426 |  archive-date = 2014-06-27 }}</ref> The [[right-hand rule]] tells which direction positively-charged current flows. However, current due to negatively-charged electricity is far more prevalent in practice.{{Citation needed|date=January 2018}}<ref>{{Cite web |date=2024-08-01 |title=Right Hand Rule |work=PASCO scientific |url=https://www.pasco.com/resources/articles/right-hand-rule }}</ref>

=== Polarity ===

The north pole of a magnet is defined as the pole that, when the magnet is freely suspended, points towards the Earth's [[North Magnetic Pole]] in the Arctic (the magnetic and [[Geographical pole|geographic poles]] do not coincide, see [[magnetic declination]]). Since opposite poles (north and south) attract, the North Magnetic Pole is actually the ''south'' pole of the Earth's magnetic field.<ref>{{cite book | last = Serway | first = Raymond A. | author2 = Chris Vuille | title = Essentials of college physics | publisher = Cengage Learning | year = 2006 | location = USA | page = 493 | url = https://books.google.com/books?id=8n4NCyRgUMEC&pg=PA493 | isbn = 0-495-10619-4 | url-status = live | archive-url = https://web.archive.org/web/20130604005509/http://books.google.com/books?id=8n4NCyRgUMEC&pg=PA493 | archive-date = 2013-06-04 }}</ref><ref>{{cite book | last = Emiliani | first = Cesare | title = Planet Earth: Cosmology, Geology, and the Evolution of Life and Environment | publisher = Cambridge University Press | year = 1992 | location = UK | page = 228 | url = https://books.google.com/books?id=MfAGpVq8gpQC&pg=PA228 | isbn = 0-521-40949-7 | url-status = live | archive-url = https://web.archive.org/web/20161224181416/https://books.google.com/books?id=MfAGpVq8gpQC&pg=PA228 | archive-date = 2016-12-24 }}</ref><ref>{{cite book | last = Manners | first = Joy | title = Static Fields and Potentials | publisher = CRC Press | year = 2000 | location = USA | page = 148 | url = https://books.google.com/books?id=vJyqbRPsXYQC&pg=PA148 | isbn = 0-7503-0718-8 | url-status = live | archive-url = https://web.archive.org/web/20161224182401/https://books.google.com/books?id=vJyqbRPsXYQC&pg=PA148 | archive-date = 2016-12-24 }}</ref><ref name="Hyperphysics">{{cite web | last = Nave | first = Carl R. | title = Bar Magnet | work = Hyperphysics | publisher = Dept. of Physics and Astronomy, Georgia State Univ. | year = 2010 | url = http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html | access-date = 2011-04-10 | url-status = live | archive-url = https://web.archive.org/web/20110408200208/http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html | archive-date = 2011-04-08 }}</ref> As a practical matter, to tell which [[wikt:magnetic pole|pole]] of a magnet is north and which is south, it is not necessary to use the Earth's magnetic field at all. For example, one method would be to compare it to an [[electromagnet]], whose poles can be identified by the [[right-hand rule]]. The magnetic field lines of a magnet are considered by convention to emerge from the magnet's north pole and reenter at the south pole.<ref name="Hyperphysics" />

=== Magnetic materials ===
{{Main|Magnetism}}

The term ''magnet'' is typically reserved for objects that produce their own persistent magnetic field even in the absence of an applied magnetic field. Only certain classes of materials can do this. Most materials, however, produce a magnetic field in response to an applied magnetic field – a phenomenon known as magnetism. There are several types of magnetism, and all materials exhibit at least one of them.

The overall magnetic behavior of a material can vary widely, depending on the structure of the material, particularly on its [[electron configuration]]. Several forms of magnetic behavior have been observed in different materials, including:
* [[Ferromagnetic]] and [[ferrimagnetic]] materials are the ones normally thought of as magnetic; they are attracted to a magnet strongly enough that the attraction can be felt. These materials are the only ones that can retain magnetization and become magnets; a common example is a traditional [[refrigerator magnet]]. Ferrimagnetic materials, which include [[ferrite (magnet)|ferrites]] and the longest used and naturally occurring magnetic materials [[magnetite]] and [[lodestone]], are similar to but weaker than ferromagnetics. The difference between ferro- and ferrimagnetic materials is related to their microscopic structure, as explained in [[Magnetism]].
* [[Paramagnetic]] substances, such as [[platinum]], [[aluminum]], and [[oxygen]], are weakly attracted to either pole of a magnet. This attraction is hundreds of thousands of times weaker than that of ferromagnetic materials, so it can only be detected by using sensitive instruments or using extremely strong magnets. Magnetic [[ferrofluid]]s, although they are made of tiny ferromagnetic particles suspended in liquid, are sometimes considered paramagnetic since they cannot be magnetized.
* [[Diamagnetic]] means repelled by both poles. Compared to paramagnetic and ferromagnetic substances, diamagnetic substances, such as [[carbon]], [[copper]], [[water]], and [[plastic]], are even more weakly repelled by a magnet. The permeability of diamagnetic materials is less than the [[Vacuum permeability|permeability of a vacuum]]. All substances not possessing one of the other types of magnetism are diamagnetic; this includes most substances. Although force on a diamagnetic object from an ordinary magnet is far too weak to be felt, using extremely strong [[superconducting magnet]]s, diamagnetic objects such as pieces of [[lead]] and even mice<ref>[http://www.livescience.com/animals/090909-mouse-levitation.html Mice levitated in NASA lab] {{webarchive|url=https://web.archive.org/web/20110209062936/http://www.livescience.com/animals/090909-mouse-levitation.html |date=2011-02-09 }}. Livescience.com (2009-09-09). Retrieved on 2011-10-08.</ref> can be [[diamagnetic levitation|levitated]], so they float in mid-air. [[Superconductors]] repel magnetic fields from their interior and are strongly diamagnetic.

There are various other types of magnetism, such as [[spin glass]], [[superparamagnetism]], [[superdiamagnetism]], and [[metamagnetism]].

=== Shape ===
{{Main|Demagnetizing field}}
The shape of a permanent magnet has a large influence on its magnetic properties. When a magnet is [[Magnetization|magnetized]], a [[demagnetizing field]] will be created inside it. As the name suggests, the demagnetizing field will work to demagnetize the magnet, decreasing its magnetic properties. The strength of the demagnetizing field <math>H_d</math> is proportional to the magnet's magnetization <math>M</math> and shape, according to
:<math> H_d = -N_d M.</math>
Here, <math>N_d</math> is called the demagnetizing factor, and has a different value depending on the magnet's shape. For example, if the magnet is a [[sphere]], then <math>N_d = \frac{1}{3}</math>.

The value of the demagnetizing factor also depends on the direction of the magnetization in relation to the magnet's shape. Since a sphere is symmetrical from all angles, the demagnetizing factor only has one value. But a magnet that is shaped like a long [[cylinder]] will yield two different demagnetizing factors, depending on if it's magnetized [[Parallel (geometry)|parallel]] to or [[perpendicular]] to its length. <ref name="Graham" />