Permeability

Updated February 21, 2007

Click here to go to our companion permittivity page

Click here to go to a page with a table of permeabilities of various materials

Click here to go to our main skin depth page

Click here to go to our physical constants page

This discussion about permeability recently came in from Walt.... thanks!

"Permeability is a magnetic property of space; space either filled with stuff or empty. You've undoubtedly heard of ferromagnetism... the ability of materials to be attracted to a magnet. Permeability is the unit of measure for ferromagnetism. It is also extremely important in the history of electricity and magnetism. Permeability along with the speed of light and a property called permittivity are the three measurable constants of Maxwell's equations.

Materials with unpaired electrons such as iron have microscopic domains that are themselves little magnets. An externally imposed magnetic field, such as produced by an electric current through a coil which is wound around (or next to) the iron can cause the magnetic domains in the iron to line up with each other and the material is said to be magnetized. The alignment is such as to make the entire piece of ferromagnetic material a magnet of the opposite polarity as the driving field. That's why ferromagnetic materials are drawn toward either end of a magnet. It is magnetized at least while the magnetic field is imposed. (If it stays magnetized after striking it, it is a permanent magnet.) The tiny domains of magnetic field are extremely powerful; much more powerful than even the strongest magnet. But in their natural state the domains randomly cancel each other out. A driving magnetic field, although small can trick some of these domains into alignment thus increase the local field by a large factor. (One might think there's a violation of thermodynamics here, but no, the amplification of the magnetic field happens without any opportunity for perpetual motion. Sorry.) The degree to which it increases the magnetic field is the permeability for the material. Permeability is the measure of the amount of ferromagnetism. (Ferromagnetism is a property not a measure.) Some materials have domains that actually fight the external magnetic field. These are called diamagnetic materials. A diamagnetic material is repelled rather than drawn toward a magnet. Alas, diamagnetic materials are no where near as dramatic as ferromagnetic. It takes a huge superconducting magnet to feel the effects of diamagnetism for even the strongest diamagnetic materials. You can see in our table of magnetic materials how unsymmetrical the paramagnetic values are for materials of this universe. Notice that there is no zero value of permeability. Empty space does not fight or aid an applied magnetic field. The important thing to remember about empty space is that it conducts a magnetic field as if it was made of stuff."

Back to our original text... Permeability is a property which is associated with how much a material responds to a magnetic field. The definition is

=B/H

where B is the flux density, and H is the magnetic force.

The permeability of a vacuum is denoted as 0. The units of permittivity are Henries/meter. The permeability of vacuum is exactly 4x10^{-7, which is approximately} 1.25663706E-06. Most materials have permeability very close to that of a vacuum; the common exceptions are materials that some fraction of have iron, chrome, and nickel.

Permeability controls skin depth. The higher the relative permeability, the less an electromagnetic wave will penetrate into the material. Seems kind of backwards, but that is how permeability works!