Permeability (electromagnetism)
The term was coined by William Thomson, 1st Baron Kelvin in 1872,[1] and used alongside permittivity by Oliver Heaviside in 1885.
In SI units, permeability is measured in henries per meter (H/m), or equivalently in newtons per ampere squared (N/A2).
In the macroscopic formulation of electromagnetism, there appear two different kinds of magnetic field: 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] where the proportionality factor μ is the permeability, which depends on the material.
The SI units of μ are volt-seconds per ampere-meter, equivalently henry per meter.
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] assuming B and H are parallel.
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.
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.
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] 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).
[35] For passive magnetic levitation a relative permeability below 1 is needed (corresponding to a negative susceptibility).
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.
By Euler's formula, the complex permeability can be translated from polar to rectangular form, The ratio of the imaginary to the real part of the complex permeability is called the loss tangent, which provides a measure of how much power is lost in material versus how much is stored.
