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| '''Magnetic pressure''' is an [[energy density]] associated with a [[magnetic field]]. Any magnetic field has an associated magnetic pressure contained by the boundary conditions on the field. It is identical to any other physical [[pressure]] except that it is carried by the magnetic field rather than (in the case of a [[gas]]) by the [[kinetic energy]] of gas molecules. A gradient in field strength causes a force due to the magnetic [[pressure gradient]] called the '''magnetic pressure force'''.
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| The magnetic pressure force is readily observed in an unsupported loop of [[wire]]. If an [[electric current]] passes through the loop, the wire serves as an [[electromagnet]], such that the magnetic field strength inside the loop is much greater than the field strength just outside the loop. This gradient in field strength gives rise to a magnetic pressure force that tends to stretch the wire uniformly outward. If enough current travels through the wire, the loop of wire will form a [[circle]]. At even higher currents, the magnetic pressure can create [[tensile stress]] that exceeds the [[tensile strength]] of the wire, causing it to fracture, or even explosively fragment. Thus, management of magnetic pressure is a significant challenge in the design of ultrastrong electromagnets.
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| The force (in [[Centimeter gram second system of units|cgs]]) {{math|'''F'''}} exerted on a coil by its own current is<ref>{{harvnb|Garren|1994|p=3425}}</ref>
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| :<math>
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| \mathbf{F} =\dfrac{I^2}{c^2R} [\ln(\dfrac{8R}{a}) - 1 + Y] | |
| </math>
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| Where ''Y'' is the internal inductance of the coil, defined by the distribution of current. ''Y'' is 0 for high frequency currents carried mostly by the outer surface of the conductor, and 0.25 for DC currents distributed evenly throughout the conductor. See [[inductance]] for more information.
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| Interplay between magnetic pressure and ordinary gas pressure is important to [[magnetohydrodynamics]] and [[plasma physics]]. Magnetic pressure can also be used to propel [[projectiles]]; this is the operating principle of a [[railgun]].
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| If any currents present are parallel to a magnetic field, the field lines follow shapes in which the magnetic pressure gradient is balanced by the [[magnetic tension force]]. Such a field configuration is called [[force-free magnetic field|force-free]] because there is no [[Lorentz force]] (<math>j\times B=0</math>). The familiar [[potential magnetic field]] is a special case of a force-free field: potential field configurations occupy space that contains no electric current at all.
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| The magnetic pressure <math>P_B</math> is given in [[International System of Units|SI]] units (''P'' in [[Pascal (unit)|Pa]], ''B'' in [[Tesla (unit)|T]], [[Permeability constant|μ<sub>0</sub>]] in [[Henry (unit)|H]]/m) by
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| :<math>P_B = \frac{B^2}{2\mu_0}</math> | |
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| and in [[Centimeter gram second system of units|cgs]] units (''P'' in [[Barye|dyn/cm²]], ''B'' in [[Gauss (unit)|G]]) by
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| :<math>P_B = \frac{B^2}{8\pi}</math>.
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| ==See also==
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| * [[Magnetic tension force]]
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| * [[Maxwell stress tensor]]
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| == Notes ==
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| {{Reflist|3}}
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| == References ==
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| *{{cite journal
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| | author = Garren & Chen
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| | title = Lorentz Self Forces on Curved Current Loops
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| | year = 1994
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| | journal = [[Physics of Plasmas]]
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| | volume = 1
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| | issue = 10
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| | pages = 3425–3436
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| | doi = 10.1063/1.870491|bibcode = 1994PhPl....1.3425G }}
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| <references />
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| {{DEFAULTSORT:Magnetic Pressure}}
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| [[Category:Plasma physics]]
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| {{Physics-stub}}
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