The ratio of the magnetic flux density, B, in a medium to the external magnetic field strength, H, i.e.
The permeability of free space is designated μ0 and is termed the magnetic constant. In the system of SI units it has the value 4π ×10–7 henry/metre. In other systems, such as the CGS and MKS systems, it has been given different values. Using Maxwell’s equations it can be shown that
where ε0 is the permittivity of free space and c is the speed of light.
The relative permeability, μr, is the ratio of the magnetic flux density in a medium to the magnetic flux density in free space for the same value of external magnetic field strength, i.e.
For most materials μr is a constant. Diamagnetic materials have a value of μr less than unity. Paramagnetic materials have a value just greater than unity (see diamagnetism; paramagnetism). Ferromagnetic materials have values of μr that are very much greater than unity and that depend on the magnetic flux density (see ferromagnetism; magnetic hysteresis).
The incremental permeability is the permeability measured when a small alternating magnetic field is superimposed on a large steady one.