Permeability describes the effect of material in determining the magnetic flux density. All else being equal, magnetic flux density increases in proportion to permeability.
To illustrate the concept, consider that a particle bearing charge
moving at velocity
gives rise to a magnetic flux density:
is the unit vector pointing from the charged particle to the field point
is this distance, and “
” is the cross product. Note that
increases with charge and speed, which makes sense since moving charge is the source of the magnetic field. Also note that
is inversely proportional to
, indicating that
decreases in proportion to the area of a sphere surrounding the charge, also known as the inverse square law. The remaining factor,
, is the constant of proportionality that captures the effect of material. We refer to
as the permeability of the material. Since
can be expressed in units of
/m2 and the units of
are m/s, we see that
must have units of henries per meter (H/m). (To see this, note that
, H/m) describes the effect of material in determining the magnetic flux density.
In free space, we find that the permeability
It is common practice to describe the permeability of materials in terms of their relative permeability:
which gives the permeability relative to the minimum possible value; i.e., that of free space. Relative permeability for a few representative materials is given in Appendix 10.2.
is approximately 1 for all but a small class of materials. These are known as magnetic materials, and may exhibit values of
as large as
106. A commonly-encountered category of magnetic materials is ferromagnetic material, of which the best-known example is iron.
- “Permeability (electromagnetism)” on Wikipedia.
- Section 7.16 (“Magnetic Materials”).
- Appendix 10.2 (“Permeability of Some Common Materials”).
Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 CC BY-SA 4.0
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