# Magnetic Permeability

Magnetic permeability or simply permeability is the ease with which a material can be magnetized. It is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately 1.257 x 10-6 Henry per meter (H/m) in free space (a vacuum). In other materials it can be much different, often substantially greater than the free-space value, which is symbolized µ0.

Materials that cause the lines of flux to move farther apart, resulting in a decrease in magnetic flux density compared with a vacuum, are called diamagnetic. Materials that concentrate magnetic flux by a factor of more than one but less than or equal to ten are called paramagnetic; materials that concentrate the flux by a factor of more than ten are called ferromagnetic. The permeability factors of some substances change with rising or falling temperature, or with the intensity of the applied magnetic field.

In engineering applications, permeability is often expressed in relative, rather than in absolute, terms. If µ0 represents the permeability of free space (that is, 4π X10-7H/m or 1.257 x 10-6 H/m) and µ represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, µr, is given by:

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

For non-ferrous metals such as copper, brass, aluminum etc., the permeability is the same as that of "free space", i.e. the relative permeability is one. For ferrous metals however the value of µr may be several hundred. Certain ferromagnetic materials, especially powdered or laminated iron, steel, or nickel alloys, have µr that can range up to about 1,000,000. Diamagnetic materials have µr less than one, but no known substance has relative permeability much less than one. In addition, permeability can vary greatly within a metal part due to localized stresses, heating effects, etc.

When a paramagnetic or ferromagnetic core is inserted into a coil, the inductance is multiplied by µr compared with the inductance of the same coil with an air core. This effect is useful in the design of transformers and eddy current probes.