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| | Technical Director Walter Delrio from Saint-Malo, enjoys cycling, free coins fifa 14 hack and rock music. Intends to retire and take the family to most of the noteworthy heritage listed locales on earth like Early Christian Monuments of Ravenna.<br><br>my weblog ... [https://Youtube.com/watch?v=HSoNAvTIeEc fifa 14 hacks Ipad] |
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| [[File:Permeability by Zureks.svg|thumb|Simplified comparison of permeabilities for: [[ferromagnetism|ferromagnets]] (μ<sub>f</sub>), [[paramagnetism|paramagnets]](μ<sub>p</sub>), free space(μ<sub>0</sub>) and [[diamagnetism|diamagnets]] (μ<sub>d</sub>)]]
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| In [[electromagnetism]], '''permeability''' is the measure of the ability of a material to support the formation of a [[magnetic field]] within itself. In other words, it is the degree of [[magnetization]] that a material obtains in response 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]]. The reciprocal of magnetic permeability is '''magnetic reluctivity'''.
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| In [[SI]] units, permeability is measured in [[Henry (unit)|henries]] per meter (H·m<sup>−1</sup>), or [[newton (unit)|newtons]] per [[ampere]] squared (N·A<sup>−2</sup>). The permeability constant (μ<sub>0</sub>), also known as the [[magnetic constant]] or the permeability of free space, is a measure of the amount of resistance encountered when forming a magnetic field in a classical [[vacuum]]. The magnetic constant has the exact (defined)<ref>{{cite web|url=http://physics.nist.gov/cuu/Units/ampere.html |title=The NIST reference on fundamental physical constants |publisher=Physics.nist.gov |date= |accessdate=2011-11-08}}</ref> value µ<sub>0</sub> = 4π×10<sup>−7</sup> H·m<sup>−1</sup>≈ 1.2566370614…×10<sup>−6</sup> H·m<sup>−1</sup> or N·A<sup>−2</sup>).
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| A closely related property of materials is [[magnetic susceptibility]], which is a measure of the magnetization of a material in addition to the magnetization of the space occupied by the material.
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| ==Explanation==
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| 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
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| :<math>\mathbf{B}=\mu \mathbf{H},</math>
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| where the '''permeability''', μ, is a [[scalar (physics)|scalar]] if the medium is [[isotropic]] or a second rank [[tensor]] for an anisotropic medium.
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| In general, permeability is not 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. For these materials it is sometimes useful to consider the ''incremental permeability'' defined as
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| :<math>\Delta\mathbf{B}=\mu_{\Delta} \Delta\mathbf{H}.</math>
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| This definition is useful in local linearizations of non-linear material behavior, for example in a [[Newton–Raphson]] iterative solution scheme that computes the changing [[Saturation (magnetic)|saturation]] of a magnetic circuit.
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| Permeability is the [[inductance]] per unit length. In [[SI]] units, permeability is measured in [[henry (unit)|henries]] per metre (H·m<sup>−1</sup> = J/(A<sup>2</sup>·m) = N A<sup>−2</sup>). The auxiliary magnetic field '''H''' has dimensions [[Electric current|current]] per unit length and is measured in units of [[ampere]]s per metre (A m<sup>−1</sup>). The product μ'''H''' thus has dimensions inductance times current per unit area (H·A/m<sup>2</sup>). 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).
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| '''B''' is related to the [[Lorentz force]] on a moving charge ''q'':
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| :<math>\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}).</math>
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| The charge ''q'' is given in [[coulomb]]s (C), the velocity ''v'' in [[meter]]s per [[second]] (m/s), so that the force ''F'' is in [[newton (unit)|newtons]] (N):
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| :<math>q \mathbf{v} \times \mathbf{B}
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| = C \cdot \dfrac{m}{s} \cdot \dfrac{V \cdot s}{m^2}
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| = \dfrac{C \cdot (J / C)}{m}
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| = \dfrac{J}{m} = N</math>
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| '''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-metre (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 | 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.
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| == Relative permeability and magnetic susceptibility==
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| 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, μ<sub>0</sub>:
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| :<math>\mu_r = \frac{\mu}{\mu_0},</math>
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| where μ<sub>0</sub> = 4π × 10<sup>−7</sup> N A<sup>−2</sup>. In terms of relative permeability, the [[magnetic susceptibility]] is
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| :<math>\chi_m = \mu_r - 1.</math>
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| 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).
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| ==Diamagnetism==
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| {{main|Diamagnetism}}
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| '''Diamagnetism''' is the property of an object which causes it to create a magnetic field in opposition of an externally applied [[magnetic field]], thus causing a repulsive effect. Specifically, an external magnetic field alters the orbital velocity of electrons around their nuclei, thus changing the [[magnetic dipole moment]] in the direction opposing the external field. Diamagnets are materials with a [[magnetic permeability]] less than ''μ''<sub>0</sub> (a relative permeability less than 1).
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| Consequently, diamagnetism is a form of [[magnetism]] that a substance exhibits only in the presence of an externally applied magnetic field. It is generally a quite weak effect in most materials, although [[superconductor]]s exhibit a strong effect.
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| ==Paramagnetism==
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| {{main|Paramagnetism}}
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| '''Paramagnetism''' is a form of [[magnetism]] which occurs only in the presence of an externally applied magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than [[1 (number)|one]] (or, equivalently, a positive [[magnetic susceptibility]]).
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| The magnetic moment induced by the applied field is ''linear'' in the field strength and rather ''weak''. It typically requires a sensitive analytical balance to detect the effect. Unlike [[ferromagnetism|ferromagnets]], paramagnets do not retain any magnetization in the absence of an externally applied magnetic field, because [[thermal motion]] causes the spins to become ''randomly oriented'' without it. Thus the total magnetization will drop to zero when the applied field is removed. Even in the presence of the field there is only a small ''induced'' magnetization because only a small fraction of the spins will be oriented by the field. This fraction is proportional to the field strength and this explains the linear dependency. The attraction experienced by ferromagnets is non-linear and much stronger, so that it is easily observed, for instance, in magnets on one's refrigerator.
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| ==Gyromagnetism==
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| For gyromagnetic media (see [[Faraday rotation]]) the magnetic permeability response to an alternating electromagnetic field in the microwave frequency domain is treated as a non-diagonal tensor expressed by:<ref>{{cite doi|10.1063/1.1721335}}</ref>
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| :<math>\begin{align}
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| \mathbf{B}(\omega) & = \begin{vmatrix}
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| \mu_{1} & -i \mu_{2} & 0\\
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| i \mu_{2} & \mu_{1} & 0\\
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| 0 & 0 & \mu_{z}\\
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| \end{vmatrix} \mathbf{H}(\omega)\\
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| \end{align}</math>
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| ==Values for some common materials==
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| The following table should be used with caution as the permeability of ferromagnetic materials varies greatly with field strength. For example 4% Si steel has an initial relative permeability (at or near 0T) of 2,000 and a maximum of 35,000<ref>G.W.C. Kaye & T.H. Laby, Table of Physical and Chemical Constants, 14th ed, Longman</ref> and, indeed, the relative permeability of any material at a sufficiently high field strength tends to 1.
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| {| class="wikitable sortable"
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| |+Magnetic susceptibility and permeability data for selected materials
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| |-
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| ! Medium
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| ! class="unsortable"|Susceptibility χ<sub>m</sub><br>(volumetric SI)
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| ! class="unsortable"|Permeability μ [H/m]
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| ! data-sort-type="number" | Relative permeability μ/μ<sub>0</sub>
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| ! class="unsortable"|Magnetic field
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| ! class="unsortable"|Frequency max.
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| |-
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| |[[Metglas]]
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| | {{val|1.25}}
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| | {{val|1000000}}<ref name="Metglas">{{cite web|url=http://www.metglas.com/products/page5_1_2_6.htm |title="Metglas Magnetic Alloy 2714A", ''Metglas'' |publisher=Metglas.com |date= |accessdate=2011-11-08}}</ref>
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| | at 0.5 T
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| | 100 kHz
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| |-
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| |[[Iron]] (99.95% pure Fe annealed in H)
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| | {{val|200000}}<ref name="Iron">{{cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/tables/magprop.html#c2 |title="Magnetic Properties of Ferromagnetic Materials", ''Iron'' |publisher=C.R Nave Georgia State University |date= |accessdate=2013-12-01}}</ref>
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| |-
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| |Nanoperm
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| | {{val|10|e=-2}}
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| | {{val|80000}}<ref name="Nanoperm">{{cite web|url=http://www.magnetec.de/eng/pdf/werkstoffkennlinien_nano_e.pdf |title="Typical material properties of NANOPERM", ''Magnetec'' |format=PDF |date= |accessdate=2011-11-08}}</ref>
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| | at 0.5 T
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| | 10 kHz
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| |-
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| |[[Mu-metal]]
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| | {{val|2.5|e=-2}}
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| | {{val|20000}}<ref name="hyper">{{cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html |title="Relative Permeability", ''Hyperphysics'' |publisher=Hyperphysics.phy-astr.gsu.edu |date= |accessdate=2011-11-08}}</ref>
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| | at 0.002 T
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| |-
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| |[[Mu-metal]]
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| | {{val|50000}}<ref name="nickal">{{cite web|url=http://www.nickel-alloys.net/nickelalloys.html |title=Nickel Alloys-Stainless Steels, Nickel Copper Alloys, Nickel Chromium Alloys, Low Expansion Alloys |publisher=Nickel-alloys.net |date= |accessdate=2011-11-08}}</ref>
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| |-
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| |[[Cobalt-Iron (high permeability strip material)]]
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| | {{val|18000}}<ref name="vacuumschmeltze">{{cite web|url=http://www.vacuumschmelze.com/fileadmin/Medienbiliothek_2010/Downloads/HT/2013-03-27_Soft_Magnetic_Cobalt-_Iron_Alloys_final_version.pdf |title="Soft Magnetic Cobalt-Iron Alloys", ''Vacuumschmeltze'' |publisher=www.vacuumschmeltze.com |date= |accessdate=2013-08-03}}</ref>
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| |-
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| |[[Permalloy]]
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| | {{val|8000}}
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| | {{val|1.0|e=-2}}
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| | {{val|8000}}<ref name="hyper"/>
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| | at 0.002 T
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| |-
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| |[[Iron]] (99.8% pure)
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| | {{val|5000}}<ref name="Iron" />
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| |-
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| |[[Electrical steel]]
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| | {{val|5.0|e=-3}}
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| | {{val|4000}}<ref name="hyper"/>
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| | at 0.002 T
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| |-
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| |Ferritic stainless steel (annealed)
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| | 1000–1800<ref name="Carpenter">{{cite web|url=http://www.cartech.com/techarticles.aspx?id=1476|title=Magnetic Properties of Stainless Steels|author=Carpenter Technology Corporation|publisher=Carpenter Technology Corporation|year=2013}}</ref>
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| |-
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| |Martensitic stainless steel (annealed)
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| | 750–950<ref name="Carpenter" />
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| |-
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| |Ferrite (manganese zinc)
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| | >{{val|8.0|e=-4}}
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| | 640 (or more)
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| |100 kHz ~ 1 MHz
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| |-
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| |[[Ferrite (magnet)|Ferrite]] (nickel zinc)
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| | {{val|2.0|e=-5}} – {{val|8.0|e=-4}}
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| | 16–640
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| |100 kHz ~ 1 MHz{{Citation needed|date=February 2012}}
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| |-
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| |[[Steel|Carbon Steel]]
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| | {{val|8.75|e=-4}}
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| | 100<ref name="hyper" />
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| | at 0.002 T
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| |-
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| |[[Nickel]]
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| | {{val|1.25|e=-4}}
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| | 100<ref name="hyper" /> – 600
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| | at 0.002 T
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| |-
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| |Martensitic stainless steel (hardened)
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| | 40–95<ref name="Carpenter" />
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| |-
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| |Austenitic stainless steel
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| | 1.003–7 <ref name="Carpenter" /><ref name="SSAS">{{cite web|url=http://www.bssa.org.uk/cms/File/SSAS2.81-Magnetic%20Properties.pdf|title=Magnetic Properties of Stainless Steel|author=British Stainless Steel Association|publisher=Stainless Steel Advisory Service|year=2000}}</ref> <ref group="note">The permeability of Austenitic Stainless Steel strongly depends on the history of mechanical stress applied to it, such as [[Work hardening|cold working]]</ref>
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| |-
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| |-
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| |[[Neodymium magnet]]
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| | 1.05<ref>{{cite book|url=http://books.google.com/?id=_y3LSh1XTJYC&pg=PT232|page=232|title=Design of Rotating Electrical Machines|author=Juha Pyrhönen, Tapani Jokinen, Valéria Hrabovcová|publisher=John Wiley and Sons|year=2009|isbn=0-470-69516-1}}</ref>
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| |-
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| |[[Platinum]]
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| | {{val|1.2569701|e=-6}}
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| | {{val|1.000265}}
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| |-
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| |[[Aluminum]]
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| | {{val|2.22|e=-5}}<ref name="clarke">{{cite web|author=Richard A. Clarke |url=http://www.ee.surrey.ac.uk/Workshop/advice/coils/mu/ |title=Clarke, R. ''Magnetic properties of materials'', surrey.ac.uk |publisher=Ee.surrey.ac.uk |date= |accessdate=2011-11-08}}</ref>
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| | {{val|1.2566650|e=-6}}
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| | {{val|1.000022}}
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| |-
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| |[[Wood]]
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| | {{val|1.00000043}}<ref name="clarke"/>
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| |-
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| |[[Air]]
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| |{{val|1.2566375|e=-6}}
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| |{{val|1.00000037}} <ref name=Cullity2008>B. D. Cullity and C. D. Graham (2008), Introduction to Magnetic Materials, 2nd edition, 568 pp., p.16</ref>
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| |-
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| |[[Concrete]] (dry)
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| | 1<ref>{{cite web|author=NDT.net |url=http://www.ndt.net/article/ndtce03/papers/v078/v078.htm |title=Determination of dielectric properties of insitu concrete at radar frequencies |publisher=Ndt.net |date= |accessdate=2011-11-08}}</ref>
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| |[[Vacuum]]
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| | 0
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| | π{{val|4|e=-7}} (μ<sub>0</sub>)
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| | 1<ref>exactly, by definition</ref>
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| |-
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| |[[Hydrogen]]
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| | {{val|-2.2|e=-9}}<ref name="clarke" />
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| | {{val|1.2566371|e=-6}}
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| | {{val|1.0000000}}
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| |-
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| |[[Teflon]]
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| | {{val|1.2567|e=-6}}<ref name="hyper"/>
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| | {{val|1.0000}}
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| |-
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| |[[Sapphire]]
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| | {{val|-2.1|e=-7}}
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| | {{val|1.2566368|e=-6}}
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| | {{val|0.99999976}}
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| |
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| |
| |-
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| |[[Copper]]
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| | {{val|-6.4|e=-6}}<br>or {{val|-9.2|e=-6}}<ref name="clarke" />
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| | {{val|1.2566290|e=-6}}
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| | {{val|0.999994}}
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| |-
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| |[[Water]]
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| | {{val|-8.0|e=-6}}
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| | {{val|1.2566270|e=-6}}
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| | {{val|0.999992}}
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| |
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| |
| |-
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| |[[Bismuth]]
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| | {{val|-1.66|e=-4}}
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| | {{val|0.999834}}
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| |-
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| |[[Superconductor]]s
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| | −1
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| | 0
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| | 0
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| |}
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| [[File:Permeability of ferromagnet by Zureks.svg|thumb|Magnetisation curve for ferromagnets (and ferrimagnets) and corresponding permeability]]
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| A good [[Magnetic core#Common magnetic core materials|magnetic core material]] must have high permeability.<ref>{{cite web|
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| url=http://www.ti.com/lit/ml/slup124/slup124.pdf|
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| title=Magnetics Design 2 – Magnetic Core Characteristics|
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| author=Dixon, L H|
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| publisher=Texas Instruments|
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| year=2001}}</ref>
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| For '''passive''' [[magnetic levitation]] a relative permeability below 1 is needed (corresponding to a negative susceptibility).
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| Permeability varies with magnetic field. Values shown above are approximate and valid only at the magnetic fields shown. 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.
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| Note that the [[magnetic constant]] ''μ''<sub>0</sub> has an exact value in [[SI]] units (that is, there is no uncertainty in its value),
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| because the [[ampere#Definition|definition of the ampere]] fixes its value to 4π × 10<sup>−7</sup> H/m exactly.
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| ==Complex permeability==
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| A useful tool for dealing with high frequency magnetic effects is the complex permeability. While at low frequencies in a linear material the magnetic field and the auxiliary magnetic field are simply proportional to each other through some scalar permeability, at high frequencies these quantities will react to each other with some lag time.<ref name="getzlaff">M. Getzlaff, ''Fundamentals of magnetism'', Berlin: Springer-Verlag, 2008.</ref> These fields can be written as [[Phasor (electronics)|phasors]], such that
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| :<math>H=H_0 e^{j \omega t} \qquad B=B_0 e^{j\left(\omega t - \delta \right)}</math>
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| where <math>\delta</math> is the phase delay of <math>B</math> from <math>H</math>. Understanding permeability as the ratio of the magnetic flux density to the magnetic field, the ratio of the phasors can be written and simplified as
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| :<math>\mu = \frac{B}{H} = \frac{ B_0 e^{j\left(\omega t - \delta \right) }}{H_0 e^{j \omega t}} = \frac{B_0}{H_0}e^{-j\delta},</math>
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| so that the permeability becomes a complex number.
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| By [[Euler's formula]], the complex permeability can be translated from polar to rectangular form,
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| :<math>\mu = \frac{B_0}{H_0}\cos \delta - j \frac{B_0}{H_0}\sin\delta = \mu^\prime - j \mu ^{\prime\prime}.</math>
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| The ratio of the imaginary to the real part of the complex permeability is called the [[loss tangent]],
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| :<math>\tan\delta = \frac{\mu^{\prime\prime}}{\mu^\prime},</math>
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| which provides a measure of how much power is lost in a material versus how much is stored.
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| ==See also==
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| * [[Antiferromagnetism]]
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| * [[Diamagnetism]]
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| * [[Electromagnet]]
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| * [[Ferromagnetism]]
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| * [[Figure of merit]]
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| * [[Magnetic reluctance]]
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| * [[Paramagnetism]]
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| * [[Permittivity]]
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| * [[SI electromagnetism units]]
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| ==Notes==
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| <references group="note" />
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://www.lightandmatter.com/html_books/0sn/ch11/ch11.html Electromagnetism] - a chapter from an online textbook
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| * [http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html Relative Permeability]
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| * [http://www.denichsoiltest.com Soil Permeability Test]
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| * [http://www.ee.surrey.ac.uk/Workshop/advice/coils/mu/ Magnetic Properties of Materials]
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| {{DEFAULTSORT:Permeability (Electromagnetism)}}
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| [[Category:Electric and magnetic fields in matter]]
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| [[Category:Concepts in physics]]
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