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 μ0 is known as the magnetic constant or the permeability of free space, and has the exact (defined)[1] value μ0 = 4π×10−7 N·A−2.

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[edit] 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

\mathbf{B}=\mu \mathbf{H}

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[2], but depends also on the history of the material.

Permeability has dimensions inductance per unit length. In SI units, permeability is measured in henries per metre (H/m). 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. 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:

\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}).

The charge q is given in coulombs (C), the velocity v in m/s, so that the force F is in newtons (N):

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}

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.[3] The H field at a distance from a dipole has magnitude proportional to the dipole moment divided by distance cubed[4], which has dimensions current per unit length.

[edit] 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:

\mu_{r} = \frac{\mu}{\mu_{0}}.

In terms of relative permeability, the magnetic susceptibility is:

\chi_m = \mu_r - 1 \,

χm, a dimensionless quantity, is sometimes called volumetric or bulk susceptibility, to distinguish it from χp (magnetic mass or specific susceptibility) and χM (molar or molar mass susceptibility).

[edit] Values for some common materials

Magnetic susceptibility and permeability data for selected materials
Medium Susceptibility (χm) Permeability (μ) x10-6 Magnetic field
Mu-metal 20,000[5] 25,000 N/A2 at 0.002 T
Permalloy 8000[5] 10,000 N/A2 at 0.002 T
Transformer iron with ρ=0.01 µΩ·m 4000[5] 5000 N/A2 at 0.002 T
ferrite (nickel zinc) 20-800 N/A2
ferrite (manganese zinc) >800 N/A2
Steel 700[5] 875 N/A2 at 0.002 T
Nickel 100[5] 125 N/A2 at 0.002 T
Platinum 2.65 × 10−4 1.2569701 N/A2
Aluminum 2.22 × 10−5[6] 1.2566650 N/A2
Hydrogen 8 × 10−9
or 2.2 × 10−9[6]		 1.2566371 N/A2
Vacuum 0 1.2566371 N/A2 (μ0)
Sapphire −2.1 × 10−7 1.2566368 N/A2
Copper −6.4 × 10−6
or −9.2 × 10−6[6]		 1.2566290 N/A2
Water −8.0 × 10−6 1.2566270 N/A2

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 μ0 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 4π × 10−7 H/m exactly.

Ultra high permeability materials

The material with the highest magnetic permeability is Metglas Magnetic Alloy 2714A (Cobalt-based) [7] 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.

[edit] References

  1. ^ The NIST reference on fundamental physical constants
  2. ^ Jackson (1975), p. 190
  3. ^ Jackson, John David (1975). Classical Electrodynamics, 2nd ed., New York: Wiley. ISBN 0-471-43132-X.  p. 182 eqn. (5.57)
  4. ^ Jackson (1975) p. 182 eqn. (5.56)
  5. ^ a b c d e "Relative Permeability", Hyperphysics
  6. ^ a b c Clarke, R. Magnetic properties of materials, surrey.ac.uk
  7. ^ http://www.lessemf.com/278.html

[edit] External links

[edit] See also