*Experiments with magnets and our surroundings*

**Twelve Fundamentals of Magnetism**

**8. Permeability, µ [webers per
ampere-turn-meter, Wb/(At*m)]**

**a. Links for this topic**

http://en.wikipedia.org/wiki/Permeability_(electromagnetism)

**b. What is it?**

The permeability of a material is a measure of its ability to support a magnetic field within itself. It can be thought of as the effective multiplication of an external magnetic field by the alignment of the magnetic domains within the material.

**c. Its unit**

Permeability, µ = B/H, the ratio of the flux density to the magnetic field intensity. It is often seen as B = µ*H. (µ is the lower case Greek letter mu.) Its units are webers per ampere-turn-meter (Wb/(At*m)) or newtons per ampere squared (N/A

^{2}). It can be seen as the slope of the B-H curve for a type of material. As H varies, the slope of B usually varies non-linearly. This is what causes some difficulty in designing magnetic circuits since B does not vary linearly with H for strongly magnetic materials. However, for most non-magnetic materials, its permeability is linear. See the diagrams below:

Here, we see how µ varies for different types of materials.

µ_{f }is the permeability of ferromagnetic material (strongly magnetic, but saturates, is non-linear)

(note, µ_{f }should look more like what we see below)

µ_{p }is the permeability of paramagnetic material (slightly magnetic, is linear)

µ_{0 }is the permeability of a vacuum (non-magnetic, is linear)

µ_{d }is the permeability of diamagnetic material (slightly anti-magnetic, is linear)

Here, we see how both µ_{f }and B vary with respect to H for a ferromagnetic material, such as iron.

Since B = µ*H, when µ is non-linear, B will also be non-linear.

**d. How is it used?**

The permeability of a material is the product of the material's relative permeability with the permeability of a vacuum: µ = µ

_{r}* µ_{0 }

i. µ_{r}is the relative permeability of the material, which usually ranges from 1 (for a vacuum) to 4,000 for an electrical steel

ii. In some special cases, the relative permeability can range from

0 for a superconductive material, to

0.9998 for a diamagnetic material, to

1,000,000 for special ferromagnetic alloys

ii. µ_{r}~ 1 for most materials, such as a vacuum, air, wood, plastic, skin, copper, aluminum, silver, gold, etc

iii. µ_{r}has no units since it is a relative term

iv. µ_{0}(mu naught) = 4*pi*10^{-7}and is approximately equal to 1/800,000 Wb/(At*m)

**e. An example in a vacuum**

In a vacuum where µr = 1, so µ = µ

_{r}* µ_{0}= 4*pi*10^{-7}, a field intensity of 796 At/m (often rounded to 800 At/m) is needed to create a flux density of 1mT within the vacuum. Since the permeability of a vacuum does not change, B is a linear function with respect to H. If you double H, B will double. So it would take about 800,000 At/m to create a flux density of 1 T within the vacuum.