Relative permeability

In physics, in particular in magnetostatics, the relative permeability is an intrinsic property of a magnetic material. It is usually denoted by &mu;r. For simple magnetic materials, using SI units, &mu;r is related to the proportionality constant between the magnetic flux density B and the magnetic field H, namely B = &mu;r &mu;0 H, where &mu;0 is the magnetic constant. The relative permeability describes the ease by which a magnetic medium may be magnetized.

A related quantity is the magnetic susceptibility, related to the magnetic permeability in cgs units by:
 * $$\mu=1+4\pi \chi \, \ \mathrm {cgs} \ ; $$

and in SI units by:
 * $$\mu = \mu_0 \ ( 1+\chi ) \, \ \mathrm{SI\ units} \ ; $$

where &mu;0 is the magnetic constant.

The force exerted between two long parallel wires conducting a current and separated by a magnetizable medium, the magnetostatic force between the wires is changed by a factor &mu;r. Empirically it is observed that the force may increase or decreases due to the presence of the magnetic medium, hence the relative permittivity  &mu;r may be greater than or less than 1.

For simple media, if &mu;r < 1, the medium is termed diamagnetic; if > 1 paramagnetic. Only classical vacuum has &mu;r = 1 (exact). It should be noted that the use of a constant as the relative permeability of a substance is an approximation, even for quantum vacuum. A more complete representation recognizes that all media exhibit departures from this approximation, in particular, a dependence on field strength, a dependence upon the rate of variation of the field in both time and space, and a dependence upon the direction of the field. In many materials these dependencies are slight; in others, like ferromagnets, they are pronounced.