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ory general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikimedia commons wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia ability of magnetization this article is about the magnetic constant for the analogous electric constant see permittivity electromagnetism electricity magnetism optics history computational textbooks phenomena electrostatics electric charge charge density coulomb s law electric field electric flux gauss s law electric potential potential energy conductor electret electric dipole electrostatic discharge electrostatic induction insulator permittivity polarization static electricity triboelectricity magnetostatics magnetic field ampère s law ampère s force law biot savart law gauss s law for magnetism magnetic dipole magnetic flux magnetic scalar potential magnetic vector potential magnetization permeability right hand rule electrodynamics maxwell s equations displacement current electromagnetic field lorentz force helmholtz theorem retarded potentials liénard wiechert potential jefimenko s equations radiation cyclotron radiation faraday s law eddy current induction lenz s law electromagnetic mass abraham lorentz force larmor formula poynting s theorem maxwell tensor electrical network alternating current capacitance current density direct current electric current electric power electrolysis electromotive force impedance inductance joule heating kirchhoff s laws network analysis ohm s law parallel circuit resistance resonant cavities series circuit voltage watt waveguides london equations magnetic circuit ac motor dc motor electric machine electric motor gyrator capacitor induction motor linear motor magnetomotive force permeance reluctance complex reluctance real rotor stator transformer covariant formulation electromagnetic tensor electromagnetism and special relativity four current four potential mathematical descriptions maxwell equations in curved spacetime relativistic electromagnetism stress energy tensor synchrotron radiation bremsstrahlung scientists ampère arago biot coulomb davy einstein faraday fitzgerald fizeau franklin galvani gauss gibbs gilbert green heaviside helmholtz henry hertz hopkinson joule kelvin kirchhoff larmor lenz liénard lorentz maxwell neumann ohm ørsted poisson poynting ritchie savart singer steinmetz tesla thomson volta weber wiechert v t e in electromagnetism permeability is the measure of magnetization produced in a material in response to an applied magnetic field permeability is typically represented by the italicized greek letter μ it is the ratio of the magnetic induction b displaystyle b to the magnetizing field h displaystyle h in a material the term was coined by lord kelvin in 1872 1 and is used alongside its electrostatic equivalent permittivity coined by oliver heaviside in 1885 the reciprocal of permeability is magnetic reluctivity citation needed in si units permeability is measured in henries per meter h m or equivalently in newtons per square ampere n a 2 the permeability constant μ 0 also known as the magnetic constant or the permeability of free space is the proportionality between magnetic induction and magnetizing force when forming a magnetic field in a classical vacuum a closely related property of materials is magnetic susceptibility which is a dimensionless proportionality factor that indicates the degree of magnetization of a material in response to an applied magnetic field explanation edit in the macroscopic formulation of electromagnetism there appear two different kinds of magnetic field the magnetizing field h which is generated around electric currents and displacement currents and also emanates from the poles of magnets the si units of h are amperes per meter the magnetic flux density b which acts back on the electrical domain by curving the motion of charges and causing electromagnetic induction the si units of b are volt seconds per square meter a ratio equivalent to one tesla the concept of permeability arises since in many materials and in vacuum there is a simple relationship between h and b at any location or time in that the two fields are precisely proportional to each other 2 b μ h displaystyle mathbf b mu mathbf h where the proportionality factor μ is the permeability which depends on the material the permeability of vacuum also known as permeability of free space is a physical constant denoted μ 0 the si units of μ are volt seconds per ampere meter equivalently henry per meter typically μ would be a scalar but for an anisotropic material μ could be a second rank tensor however inside strong magnetic materials such as iron or permanent magnets there is typically no simple relationship between h and b the concept of permeability is then nonsensical or at least only applicable to special cases such as unsaturated magnetic cores not only do these materials have nonlinear magnetic behaviour but often there is significant magnetic hysteresis so there is not even a single valued functional relationship between b and h however considering starting at a given value of b and h and slightly changing the fields it is still possible to define an incremental permeability as 2 δ b μ δ h displaystyle delta mathbf b mu delta mathbf h assuming b and h are parallel in the microscopic formulation of electromagnetism where there is no concept of an h field the vacuum permeability μ 0 appears directly in the si maxwell s equations as a factor that relates total electric currents and time varying electric fields to the b field they generate in order to represent the magnetic response of a linear material with permeability μ this instead appears as a magnetization m that arises in response to the b field m μ 0 1 μ 1 b displaystyle mathbf m left mu _ 0 1 mu 1 right mathbf b the magnetization in turn is a contribution to the total electric current the magnetization current relative permeability and magnetic susceptibility edit relative permeability denoted by the symbol μ r displaystyle mu _ mathrm r is the ratio of the permeability of a specific medium to the permeability of free space μ 0 μ r μ μ 0 displaystyle mu _ mathrm r frac mu mu _ 0 where μ 0 displaystyle mu _ 0 approx 4 π 10 7 h m is the magnetic permeability of free space 3 in terms of relative permeability the magnetic susceptibility is χ m μ r 1 displaystyle chi _ m mu _ r 1 the number χ m is a dimensionless quantity sometimes called volumetric or bulk susceptibility to distinguish it from χ p magnetic mass or specific susceptibility and χ m molar or molar mass susceptibility diamagnetism edit main article diamagnetism 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 atom s nuclei thus changing the magnetic dipole moment in the direction opposing the external field diamagnets are materials with a magnetic permeability less than μ 0 a relative permeability less than 1 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 superconductors exhibit a strong effect paramagnetism edit main article paramagnetism 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 one or equivalently a positive magnetic susceptibility the magnetic moment induced by the applied field is linear in the field strength and it is rather weak it typically requires a sensitive analytical balance to detect the effect unlike 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 gyromagnetism edit 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 4 b ω μ 1 i μ 2 0 i μ 2 μ 1 0 0 0 μ z h ω displaystyle begin aligned mathbf b omega begin vmatrix mu _ 1 i mu _ 2 0 i mu _ 2 mu _ 1 0 0 0 mu _ z end vmatrix mathbf h omega end aligned values for some common materials edit the following table should be used with caution as the permeability of ferromagnetic materials varies greatly with field strength and specific composition and fabrication for example 4 electrical steel has an initial relative permeability at or near 0 t of 2 000 and a maximum of 38 000 at t 1 5 6 and different range of values at different percent of si and manufacturing process and indeed the relative permeability of any material at a sufficiently high field strength trends toward 1 at magnetic saturation magnetic susceptibility and permeability data for selected materials medium susceptibility volumetric si χ m relative permeability max μ μ 0 permeability μ h m magnetic field frequency max vacuum 0 1 exactly 7 1 256 637 061 10 6 metglas 2714a annealed 1 000 000 8 1 26 10 0 at 0 5 t 100 khz iron 99 95 pure fe annealed in h 200 000 9 2 5 10 1 permalloy 100 000 10 1 25 10 1 at 0 002 t nanoperm 80 000 11 1 0 10 1 at 0 5 t 10 khz mu metal 50 000 12 6 3 10 2 mu metal 20 000 13 2 5 10 2 at 0 002 t cobalt iron high permeability strip material 18 000 14 2 3 10 2 iron 99 8 pure 5000 9 6 3 10 3 electrical steel 2000 38000 5 15 6 5 0 10 3 at 0 002 t 1 t ferritic stainless steel annealed 1000 1800 16 1 26 10 3 2 26 10 3 martensitic stainless steel annealed 750 950 16 9 42 10 4 1 19 10 3 ferrite manganese zinc 350 20 000 17 4 4 10 4 2 51 10 2 at 0 25 mt approx 100 hz 4 mhz ferrite nickel zinc 10 2300 18 1 26 10 5 2 89 10 3 at 0 25 mt approx 1 khz 400 mhz citation needed ferrite magnesium manganese zinc 350 500 19 4 4 10 4 6 28 10 4 at 0 25 mt ferrite cobalt nickel zinc 40 125 20 5 03 10 5 1 57 10 4 at 0 001 t approx 2 mhz 150 mhz mo fe ni powder compound molypermalloy powder mpp 14 550 21 1 76 10 5 6 91 10 4 approx 50 hz 3 mhz nickel iron powder compound 14 160 22 1 76 10 5 2 01 10 4 at 0 001 t approx 50 hz 2 mhz al si fe powder compound sendust 14 160 23 1 76 10 5 2 01 10 4 approx 50 hz 5 mhz 24 iron powder compound 14 100 25 1 76 10 5 1 26 10 4 at 0 001 t approx 50 hz 220 mhz silicon iron powder compound 19 90 26 27 2 39 10 5 1 13 10 4 approx 50 hz 40 mhz carbonyl iron powder compound 4 35 28 5 03 10 6 4 4 10 5 at 0 001 t approx 20 khz 500 mhz carbon steel 100 13 1 26 10 4 at 0 002 t nickel 100 13 600 1 26 10 4 7 54 10 4 at 0 002 t martensitic stainless steel hardened 40 95 16 5 0 10 5 1 2 10 4 austenitic stainless steel 1 003 1 05 16 29 a 1 260 10 6 8 8 10 6 neodymium magnet 1 05 30 1 32 10 6 platinum 1 000 265 1 256 970 10 6 aluminum 2 22 10 5 31 1 000 022 1 256 665 10 6 wood 1 000 000 43 31 1 256 637 60 10 6 air 1 000 000 37 32 1 256 637 53 10 6 concrete dry 1 33 hydrogen 2 2 10 9 31 1 000 0000 1 256 6371 10 6 teflon 1 0000 1 2567 10 6 13 sapphire 2 1 10 7 0 999 999 76 1 256 6368 10 6 copper 6 4 10 6 or 9 2 10 6 31 0 999 994 1 256 629 10 6 water 8 0 10 6 0 999 992 1 256 627 10 6 bismuth 1 66 10 4 0 999 834 1 256 43 10 6 pyrolytic carbon 0 9996 1 256 10 6 superconductors 1 0 0 cobalt 50 1500 34 magnetisation curve for ferromagnets and ferrimagnets and corresponding permeability a good magnetic core material must have high permeability 35 for passive magnetic levitation a relative permeability below 1 is needed corresponding to a negative susceptibility permeability varies with a 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 the frequency is considered the permeability can be complex corresponding to the in phase and out of phase response complex permeability edit 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 36 these fields can be written as phasors such that h h 0 e j ω t b b 0 e j ω t δ displaystyle h h_ 0 e j omega t qquad b b_ 0 e j left omega t delta right where δ displaystyle delta is the phase delay of b displaystyle b from h displaystyle h 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 μ b h b 0 e j ω t δ h 0 e j ω t b 0 h 0 e j δ displaystyle 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 so that the permeability becomes a complex number by euler s formula the complex permeability can be translated from polar to rectangular form μ b 0 h 0 cos δ j b 0 h 0 sin δ μ j μ displaystyle mu frac b_ 0 h_ 0 cos delta j frac b_ 0 h_ 0 sin delta mu j mu the ratio of the imaginary to the real part of the complex permeability is called the loss tangent tan δ μ μ displaystyle tan delta frac mu mu which provides a measure of how much power is lost in material versus how much is stored see also edit antiferromagnetism diamagnetism electromagnet ferromagnetism magnetic reluctance paramagnetism permittivity si electromagnetism units notes edit the permeability of austenitic stainless steel strongly depends on the history of mechanical strain applied to it e g by cold working references edit magnetic permeability and analogues in electro static induction conduction of heat and fluid motion march 1872 1 2 jackson john david 1998 classical electrodynamics 3nd ed new york wiley p 193 isbn 978 0 471 30932 1 the international system of units page 132 the ampere bipm kales m l 1953 modes in wave guides containing ferrites journal of applied physics 24 5 604 608 bibcode 1953jap 24 604k doi 10 1063 1 1721335 1 2 g w c kaye t h laby table of physical and chemical constants 14th ed longman si steel 1 2 magnetic properties of electrical steel power transformer core losses and core design concepts archived from the original on 2020 02 29 by defi...