Permeability (electromagnetism)
754487
225490821
2008-07-13T23:44:03Z
Jimmy Lavoie
1805366
Reverted edits by [[Special:Contributions/125.236.175.241|125.236.175.241]] to last version by Sceptre (using [[WP:HG|Huggle]])
In [[electromagnetism]], '''permeability''' is the degree of [[magnetization]] of a material that responds linearly to an applied [[magnetic field]]. Magnetic permeability is typically represented by the Greek letter [[Mu (letter)|μ]]. The term was coined in September, [[1885]] by [[Oliver Heaviside]].
In [[SI]] units, permeability is measured in [[henry (unit)|henries]] per [[metre]] (H/m), or [[newton]]s per [[ampere]] squared (N/A<sup>2</sup>). The constant value <math> \mu_0 </math> is known as the [[magnetic constant]] or the permeability of free space, and has the exact (defined)<ref>[http://physics.nist.gov/cuu/Units/ampere.html The NIST reference on fundamental physical constants]</ref> value <math> \mu_0 </math> = 4π×10<sup>−7</sup> N·A<sup>−2</sup>.
== Explanation ==
In [[electromagnetism]], the [[Magnetic_field#The_H_Field|auxiliary magnetic field]] '''H''' represents how a magnetic field '''B''' influences the organization of magnetic dipoles in a given medium, including dipole migration and magnetic [[dipole]] reorientation. Its relation to permeability is
:<math>\mathbf{B}=\mu \mathbf{H}</math>
where the '''permeability μ''' is a [[scalar (physics)|scalar]] if the medium is [[isotropic]] or a second rank [[tensor |tensor]] for an anisotropic linear medium.
In general, permeability isn't a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In a [[nonlinear optics|nonlinear medium]], the permeability can depend on the strength of the magnetic field. Permeability as a function of frequency can take on real or complex values. In [[Ferromagnetism|ferromagnetic]] materials, the relationship between '''B''' and '''H''' exhibits both [[nonlinear optics|non-linearity]] and [[hysteresis]]: '''B''' is not a single-valued function of '''H'''<ref>Jackson (1975), p. 190</ref>, but depends also on the history of the material.
Permeability has dimensions [[inductance]] per unit length. In [[SI]] units, permeability is measured in [[henry (unit)|henries]] per [[metre]] (H/m). The [[Magnetic_field#The_H_Field|auxiliary magnetic field]] '''H''' has dimensions [[Electric current|current]] per unit length and is measured in units of [[ampere]]s per [[metre]] (A/m). The product '''μH''' thus has dimensions inductance times current per unit area. But inductance is [[magnetic flux]] per unit current, so the product has dimensions [[magnetic flux]] per unit area. This is just the magnetic field '''B''', which is measured in [[weber (unit)|webers]] ([[volt]]-[[second]]s) per square-[[metre]] (V•s/m<sup>2</sup>), or [[tesla (unit)|teslas]] (T).
'''B''' is related to the [[Lorentz force]] on a moving charge ''q'':
:<math>\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B})</math>.
The charge ''q'' is given in [[coulombs]] (C), the velocity ''v'' in m/s, so that the force ''F'' is in [[newtons]] (N):
:<math>q \mathbf{v} \times \mathbf{B}
= \mbox{C} \cdot \dfrac{\mbox{m}}{\mbox{s}} \cdot \dfrac{\mbox{V} \cdot \mbox{s}}{\mbox{m}^2}
= \dfrac{\mbox{C} \cdot (\mbox{J / C})}{\mbox{m}}
= \dfrac{\mbox{J}}{\mbox{m}} = \mbox{N}</math>
'''H''' is related to the [[Dipole#Field from a magnetic dipole|magnetic dipole]] density. A magnetic dipole is a closed circulation of electric current. The dipole moment has dimensions current times area, units ampere square-metres (A•m<sup>2</sup>), and magnitude equal to the current around the loop times the area of the loop.<ref>{{cite book | author=Jackson, John David | title=Classical Electrodynamics | edition=2nd ed. | location=New York | publisher=Wiley | year=[[1975]] | id=ISBN 0-471-43132-X}} p. 182 eqn. (5.57)</ref> The '''H''' field at a distance from a dipole has magnitude proportional to the dipole moment divided by distance cubed<ref>Jackson (1975) p. 182 eqn. (5.56)</ref>, which has dimensions current per unit length.
==Relative permeability==
Relative permeability, sometimes denoted by the symbol ''μ<sub>r</sub>'', is the ratio of the permeability of a specific medium to the permeability of free space given by the [[magnetic constant]] μ<sub>0</sub>:
:<math>\mu_{r} = \frac{\mu}{\mu_{0}}. </math>
In terms of relative permeability, the [[magnetic susceptibility]] is:
:<math>\chi_m = \mu_r - 1 \,</math>
χ<sub>m</sub>, a dimensionless quantity, is sometimes called ''volumetric'' or ''bulk'' susceptibility, to distinguish it from χ<sub>p</sub> (''magnetic mass'' or ''specific'' susceptibility) and χ<sub>M</sub> (''molar'' or ''molar mass'' susceptibility).
== Values for some common materials ==
{| class="wikitable"
|+Magnetic susceptibility and permeability data for selected materials
|-
! Medium
! Susceptibility (χ<sub>m</sub>)
! Permeability (μ) x10<sup>-6</sup>
! Magnetic field
|-
|[[Mu-metal]]
| 20,000<ref name="hyper">[http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html "Relative Permeability", ''Hyperphysics'']</ref>
| 25,000 N/A<sup>2</sup>
| at 0.002 T
|-
|[[Permalloy]]
| 8000<ref name="hyper"/>
| 10,000 N/A<sup>2</sup>
| at 0.002 T
|-
|[[Electrical steel]] with ρ=0.01 µΩ·m
| 4000<ref name="hyper"/>
| 5000 N/A<sup>2</sup>
| at 0.002 T
|-
|[[ferrite]] (nickel zinc)
|
| 20-800 N/A<sup>2</sup>
|
|-
|[[ferrite]] (manganese zinc)
|
| >800 N/A<sup>2</sup>
|
|-
|[[Steel]]
| 700<ref name="hyper" />
| 875 N/A<sup>2</sup>
| at 0.002 T
|-
|[[Nickel]]
| 100<ref name="hyper" />
| 125 N/A<sup>2</sup>
| at 0.002 T
|-
|[[Platinum]]
|2.65 × 10<sup>−4</sup>
| 1.2569701 N/A<sup>2</sup>
|-
|[[Aluminum]]
|2.22 × 10<sup>−5</sup><ref name="clarke">[http://www.ee.surrey.ac.uk/Workshop/advice/coils/mu/ Clarke, R. ''Magnetic properties of materials'', surrey.ac.uk]</ref>
| 1.2566650 N/A<sup>2</sup>
|-
|[[Hydrogen]]
|8 × 10<sup>−9</sup><br>or 2.2 × 10<sup>−9</sup><ref name="clarke" />
| 1.2566371 N/A<sup>2</sup>
|-
|[[Vacuum]]
|0
| 1.2566371 N/A<sup>2</sup> (μ<sub>0</sub>)
|-
|[[Sapphire]]
|−2.1 × 10<sup>−7</sup>
| 1.2566368 N/A<sup>2</sup>
|-
|[[Copper]]
|−6.4 × 10<sup>−6</sup><br>or −9.2 × 10<sup>−6</sup><ref name="clarke" />
| 1.2566290 N/A<sup>2</sup>
|-
|[[Water]]
|−8.0 × 10<sup>−6</sup>
| 1.2566270 N/A<sup>2</sup>
|-
|}
A good [[Magnetic_core#Common_magnetic_core_materials | magnetic core material]] must have high permeability.
Permeability varies with magnetic field. Values shown above are approximate and valid only at the magnetic fields shown. Moreover, they are given for a zero frequency; in practice, the permeability is generally a function of the frequency. When frequency is considered the permeability can be [[Complex number|complex]], corresponding to the in phase and out of phase response.
Note that the [[magnetic constant]] <math> \mu_0 </math> has an exact value in [[SI]] units (that is, there is no uncertainty in its value),
because the [[ampere#Definition|definition of ampere]] fixes its value to 4π × 10<sup>−7</sup> H/m exactly.
'''Ultra high permeability materials'''
The material with the highest magnetic permeability is Metglas Magnetic Alloy 2714A (Cobalt-based) <ref>http://www.lessemf.com/278.html</ref> with a high frequency annealed
permeability of 1,000,000 (Maximum DC Permeability (µ)). Hydrogen annealed (pure iron - N5 grade) can have a permeability of 160,000 (µ) but is very expensive.
== References ==
<references />
== External links ==
*[http://www.lightandmatter.com/html_books/0sn/ch11/ch11.html Electromagnetism] - a chapter from an online textbook
*[http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html Relative Permeability]
*[http://www.ee.surrey.ac.uk/Workshop/advice/coils/mu/ Magnetic Properties of Materials]
==See also==
*[[SI electromagnetism units]]
*[[ferromagnetism]]
*[[antiferromagnetism]]
*[[diamagnetism]]
*[[paramagnetism]]
*[[electromagnet]]
*[[permittivity]]
*[[figure of merit]]
[[Category:Electric and magnetic fields in matter]]
[[Category:Fundamental physics concepts]]
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