Editing Magnetic field (section)

===Magnetic pole model===
{{See also|Magnetic monopole}}
[[Image:VFPt dipole electric.svg|thumb|200px|upright|The magnetic pole model: two opposing poles, North (+) and South (−), separated by a distance d produce a {{math|'''H'''}}-field (lines).]]

Historically, early physics textbooks would model the force and torques between two magnets as due to magnetic poles repelling or attracting each other in the same manner as the [[Coulomb force]] between electric charges. At the microscopic level, this model contradicts the experimental evidence, and the pole model of magnetism is no longer the typical way to introduce the concept.<ref name="Griffiths3ed"/>{{rp|p=258}} However, it is still sometimes used as a macroscopic model for ferromagnetism due to its mathematical simplicity.<ref>{{cite book|title=Magnetostatic Principles in Ferromagnetism|first=William Fuller|last=Brown | year=1962 |publisher=North Holland publishing company|asin=B0006AY7F8|page=12}}</ref>

In this model, a magnetic {{math|'''H'''}}-field is produced by fictitious ''magnetic charges'' that are spread over the surface of each pole. These ''magnetic charges'' are in fact related to the magnetization field {{math|'''M'''}}. The {{math|'''H'''}}-field, therefore, is analogous to the [[electric field]] {{math|'''E'''}}, which starts at a positive [[electric charge]] and ends at a negative electric charge. Near the north pole, therefore, all {{math|'''H'''}}-field lines point away from the north pole (whether inside the magnet or out) while near the south pole all {{math|'''H'''}}-field lines point toward the south pole (whether inside the magnet or out). Too, a north pole feels a force in the direction of the {{math|'''H'''}}-field while the force on the south pole is opposite to the {{math|'''H'''}}-field.

In the magnetic pole model, the elementary magnetic dipole {{math|'''m'''}} is formed by two opposite magnetic poles of pole strength {{math|''q''{{sub|m}}}} separated by a small distance vector {{math|'''d'''}}, such that {{math|1='''m''' = ''q''{{sub|m}}&thinsp;'''d'''}}. The magnetic pole model predicts correctly the field {{math|'''H'''}} both inside and outside magnetic materials, in particular the fact that {{math|'''H'''}} is opposite to the magnetization field {{math|'''M'''}} inside a permanent magnet.

Since it is based on the fictitious idea of a ''magnetic charge density'', the pole model has limitations. Magnetic poles cannot exist apart from each other as electric charges can, but always come in north–south pairs. If a magnetized object is divided in half, a new pole appears on the surface of each piece, so each has a pair of complementary poles. The magnetic pole model does not account for magnetism that is produced by electric currents, nor the inherent connection between [[angular momentum]] and magnetism.

The pole model usually treats magnetic charge as a mathematical abstraction, rather than a physical property of particles. However, a [[magnetic monopole]] is a hypothetical particle (or class of particles) that physically has only one magnetic pole (either a north pole or a south pole). In other words, it would possess a "magnetic charge" analogous to an electric charge. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end. Some theories (such as [[Grand Unified Theory|Grand Unified Theories]]) have predicted the existence of magnetic monopoles, but so far, none have been observed.