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>&nbsp;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 &mu;''' 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 '''&mu;H''' 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&nbsp;×&nbsp;10<sup>−7</sup>&nbsp;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]] [[bg:Магнитна проницаемост]] [[ca:Permeabilitat]] [[cs:Permeabilita]] [[de:Permeabilität (Magnetismus)]] [[el:Μαγνητική διαπερατότητα]] [[es:Permeabilidad magnética]] [[eu:Permeabilitate magnetiko]] [[fr:Perméabilité magnétique]] [[is:Segulsvörunarstuðull]] [[it:Permeabilità magnetica]] [[he:מקדם מגנטיות]] [[lt:Magnetinė skvarba]] [[nl:Magnetische permeabiliteit]] [[ja:透磁率]] [[pl:Przenikalność magnetyczna]] [[pt:Permeabilidade (física)]] [[ru:Магнитная проницаемость]] [[sk:Permeabilita (magnetizmus)]] [[sl:Magnetna permeabilnost]] [[fi:Permeabiliteetti]] [[sv:Permeabilitet]] [[uk:Магнітна проникність]]