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Permeability (electromagnetism)
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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 µ. The term was coined in September, 1885 by Oliver Heaviside.
In SI units, permeability is measured in henries per metre (H/m), or newtons per ampere squared (N/A2). The constant value is known as the magnetic constant or the permeability of free space, and has the exact (defined) value = 4p×10-7 N·A-2.
a class="link1" onMouseover='showByLink("m2419126",this)' onMouseout='hide("m2419126")'href="http://www.absoluteastronomy.com/topics/Electromagnetism">electromagnetism, the 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.
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Encyclopedia
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 µ. The term was coined in September, 1885 by Oliver Heaviside.
In SI units, permeability is measured in henries per metre (H/m), or newtons per ampere squared (N/A2). The constant value is known as the magnetic constant or the permeability of free space, and has the exact (defined) value = 4p×10-7 N·A-2.
Explanation
In electromagnetism, the 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
where the permeability µ is a scalar if the medium is isotropic or a second rank 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 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 ferromagnetic materials, the relationship between B and H exhibits both non-linearity and hysteresis: B is not a single-valued function of H, but depends also on the history of the material.
Permeability is the inductance per unit length. In SI units, permeability is measured in henries per metre (H/m = J/(A2•m) = N/A2). The auxiliary magnetic field H has dimensions current per unit length and is measured in units of amperes per metre (A/m). The product µH thus has dimensions inductance times current per unit area (H•A/m2). 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 webers (volt-seconds) per square-metre (V•s/m2), or teslas (T).
B is related to the Lorentz force on a moving charge q:
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The charge q is given in coulombs (C), the velocity v in m/s, so that the force F is in newtons (N):
H is related to the 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•m2), and magnitude equal to the current around the loop times the area of the loop. The H field at a distance from a dipole has magnitude proportional to the dipole moment divided by distance cubed, which has dimensions current per unit length.
Relative permeability
Relative permeability, sometimes denoted by the symbol µr, is the ratio of the permeability of a specific medium to the permeability of free space given by the magnetic constant µ0:
In terms of relative permeability, the magnetic susceptibility is:
?m, a dimensionless quantity, is sometimes called volumetric or bulk susceptibility, to distinguish it from ?p (magnetic mass or specific susceptibility) and ?M (molar or molar mass susceptibility).
Values for some common materials
Magnetic susceptibility and permeability data for selected materials | Medium | Susceptibility (?m) | Permeability (µ) | Magnetic field | Frequency max. |
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| Mu-metal | 20,000 | 25,000 × 10-6 H/m | at 0.002 T | | Permalloy | 8000 | 10,000 × 10-6 H/m | at 0.002 T | | Electrical steel | 4000 | 5000 × 10-6 H/m | at 0.002 T | | ferrite (nickel zinc) | | 20-800 × 10-6 H/m | | 100kHz ~ 1 MHz | | ferrite (manganese zinc) | | >800 × 10-6 H/m | | 100kHz ~ 1 MHz | | Steel | 700 | 875 × 10-6 H/m | at 0.002 T | | Nickel | 100 | 125 × 10-6 H/m | at 0.002 T | | Platinum | 2.65 × 10-4 | 1.2569701 x10-6 H/m | | Aluminum | 2.22 × 10-5 | 1.2566650 × 10-6 H/m | | Hydrogen | 8 × 10-9
or 2.2 × 10-9 | 1.2566371 × 10-6 H/m | | Vacuum | 0 | 1.2566371 × 10-6 H/m (µ0) | | Sapphire | -2.1 × 10-7 | 1.2566368 × 10-6 H/m | | Copper | -6.4 × 10-6
or -9.2 × 10-6 | 1.2566290 × 10-6 H/m | | Water | -8.0 × 10-6 | 1.2566270 × 10-6 H/m | |
A good 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, corresponding to the in phase and out of phase response.
Note that the magnetic constant has an exact value in SI units (that is, there is no uncertainty in its value),
because the definition of ampere fixes its value to 4p × 10-7 H/m exactly.
Ultra high permeability materials
The material with the highest magnetic permeability is Metglas Magnetic Alloy 2714A (Cobalt-based) 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.
External links
- - a chapter from an online textbook
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See also
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