# What are the dimensions of the magnetic permeability

## Permeability (magnetism)

Physical size
Surname magnetic conductivity
Size type Tensor
Formula symbol of size μ
Size and
System of units
unit dimension
SI
H · m-1
= N * A-2
= m kg s−2 · A−2
L · M · T-2 · I-2

The magnetic permeability (also magnetic conductivity), which is closely related to magnetic susceptibility, is the derived SI quantity that determines the permeability of matter to magnetic fields. In other words, the ratio of the magnetic flux density is calledB. for magnetic field strengthH Permeability.

### In a vacuum

In a vacuum there is the relationship between the magnetic flux density B.0 and the magnetic field strength H0 by given, where μ0 as Permeability of vacuum, magnetic constant, magnetic field constant or induction constant. In SI units it is exactly due to the definition of the ampere

μ0 = 4 · π · 10-7 H · m-1
= 4 · π · 10-7N / A-2
= 4 · π · 10-7m kg s−2 · A−2
= 1,256 637 061 4 … · 10-6 m kg s−2 · A−2

By setting μ0 The electric field constant is also an exact valueε0 exactly known, since both constants are about the speed of light in a vacuum c0 to related.

### In matter

The permeability in matter is composed of the permeability of the vacuum and the permeability numberμr

It follows for the material equations:

μ = μ0μr Occasionally, μr also referred to as relative and μ as absolute permeability. The permeability number for most substances (such as air) is μr = 1. For iron, for example, the permeability number is much higher, depending on the type of iron used, μr Assume values ​​around 2000 to 5000. This is related to the atomic nature, see ferromagnetism.

Diamagnetic materials have a permeability number a little less than one, the permeability number of paramagnetic materials is slightly greater than one. Ferromagnetic materials have a very high permeability, but this is dependent on the external magnetic field, since the alignment of the so-called elementary magnets in the material increases the external field. One of the existing permeability definitions clearly shows the gradient of the hysteresis loop of a magnetic material.

The permeability numberμr, which is ≫1 for soft magnetic materials and quantifies the permeability of a material to a magnetic field compared to diamagnetic or paramagnetic materials, is defined a total of eleven times with different calculations for technical applications in DIN 1324 Part 2. In addition to the permeability μ as the quotient of the magnetic flux density B. in Tesla (T) and magnetic field strength H In amperes per meter (A / m), the other definitions given in the table apply.

A problem with the assumed constant permeability can be seen on the basis of the hysteresis curve. The permeability μ corresponds to the slope .

Due to the magnetic saturation and the magnetic remanence, the permeability is not constant, but only approximately linear in partial sections. Considerations were therefore made to obtain a universal representation of permeability from the multitude of definitions. One possible form of this representation would be Differential permeability as a function of the field strength H and the rate of change of the field strength .

With this regulation, the permeability would not only provide information about the very specific operating case (as is common today), but would also be the function of the field strength H and take into account the pre-stressing of the material.

Since a specific, comprehensive formula for the dependence of the permeability on other factors is not known, the section considered in an application is classified according to linearity (non-linearity), homogeneity (inhomogeneity) and isotropy (anisotropy).

In the general case, the magnetic conductivity in matter is a tensor and thus also describes the mentioned non-linearity, inhomogeneity and anisotropy of the material. Only in the special (simplified) case, when linearity, homogeneity and isotropy is given, is the permeability a scalar.

The complex permeability is used to compare different ferrites depending on the frequency f: With the real part μs'of the complex permeability, the inductance can be calculated and with the imaginary part μs'' the resistance of the complex impedance of the component. The copper resistance of a winding must also be added.

• Definition of parameters for ferrites