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Magnetic Permeability:  Why Are Some Materials Attracted By A Magnet And Others Are Not?

Two magnets attract to each other because their fields interact.  Usually materials that are not magnets do not have a net external field, and obviously, they do not attract to things; however, some metal alloys can have a net field created by applying an external field.  This induced field is only present when the external drive field is applied.

A permanent magnet is “attracted” to a ferrous work-piece because magnetism is “induced” in the work-piece.  The magnetism is induced by the magnetic field emanating from the permanent magnet.  (A work-piece is what the magnet or magnetic field is acting on.  This could be the steel door skin of a refrigerator, a nail, a metal plate used in a magnetic latch, etc.)  A magnet is not attracted to a piece of wood because no internal field in induced in the wood.  With no induced internal field in the wood, there is no field interaction and no attraction.

So, a magnetic field can be induced in a piece of steel.  As stated above, an external magnetic field is needed to do this.  That is why two pieces of steel do not attract to each other.  They do not induce fields in each other. No field, no interaction, no attraction.

The degree of the induced magnetism is related to the ferrous material’s magnetic permeability, and it is expressed as a unit-less value designated by the Greek letter, mu (μ).  The higher the material’s permeability, the greater the magnetic induction and the resulting force of attraction.  As shown below, a material’s permeability is not constant and does have a limit.

Materials that are not attracted to a magnet like air, wood, plastic, brass, etc., have a permeability of, essentially, 1.  There is no magnetism induced in them by an external magnetic field, and therefore, they are not attracted by a magnet.  Ferrous, Nickel, and Cobalt alloys have a high permeability (μ), and thereby, magnetic fields can be induced in them when exposed to an external magnetic field.


WARNING for Engineers!             First order equation:      B = μH


Induced Magnetism in an Alloy (B) = Alloy’s Permeability (μ) X External Applied Drive Field (H)


Figure 1:  Mild Steel Example

Figure 1: Mild Steel Example

In the CGS unit system:

B is in (Gauss)    Permeability (unit-less) External Field strength (Oersted)


Mild Steel Example:

Induced (Internal Field) = ~ 15,000 Gauss = (30) x 500 Oersted

The 15,000 Gauss field induced in the mild steel interacts with the applied magnetic field, and there is attraction.

In Figure 1, it can be observed how the Flux lines are denser in the steel, showing the induced field, as well as how the Flux Lines “bend” in the steel alloy.  The steel’s magnetic properties bias or interact with the magnet’s magnetic flux lines (Field).



Permeability - Wood

Figure 2: Wood Example

Wood Example:

Induced (Internal Field) = 500 Gauss (1) x 500 Oersted

The only field in the wood is from the externally applied magnetic field and no new field is induced to interact with the applied field.  No Attraction!

In Figure 2, it can be observed how the Flux Lines are not biased by the wood at all, and there is no induced field. The Flux Lines do not “bend” in the wood and pass through as if it is not there.  There is no Field to Field interaction and no attraction.

The permeability of a material is not constant, and for a given temperature, it changes based on the intensity of the applied external magnetic field (H).  The relative aspect of permeability is more apparent when illustrated with a graph depicting a material’s permeability relative to the applied external field. (Refer to Figure 3)

Magnetic Induction - Permeability Plot

Figure 3

Oftentimes, technical books will list a material’s magnetic permeability as a constant, but this is far from accurate and is very misleading.  For instance, Image 3 is a plot for mild Steel C-1018, and it illustrates the Induced Magnetism (G) for various applied Field Strength levels (H).  It also depicts the corresponding magnetic permeability at each applied field strength level.  The permeability for C-1018 may be advertised as 100 (in the CGS unit system), but this is the peak value, and it is less than 20 over most of the curve.

A material’s permeability is important, because it allows one to anticipate the performance of a magnet when used in a design.  For instance, a customer may want to pick up automobile exhaust tubing with a magnetic end effector on a robot-arm.  When the tube is made from an aluminized mild steel alloy the magnet handling device may work just fine; however, when the tube is 410 SS, the tube may be dropped.   The force of attraction between the handling magnet and the tube is greater with the aluminized mild steel than the 410 SS because the mild steel has a higher permeability than the 410 SS.


Key Points:

  • A ferrous material is attracted to a permanent magnet because the permanent magnet induces magnetism within the ferrous material. The permanent magnet’s field and the newly induced field in the ferrous part interact and attract.
  • Magnetic Permeability is the characteristic of a material which represents the establishment of an induced internal magnetic field by an external magnetic field. The magnetic permeability is the proportionality between the Induced Field (B) and the applied Field Strength (H).

permeability illustration

  • A material’s permeability indicates how easily an external magnetic field can induce an internal field in the material. The higher the internal field, the higher the force of attraction.
  • A material’s permeability is not constant and changes based on number a of factors. The effective permeability of a material can change with the temperature, how it was processed, the intensity of the applied drive field, humidity, etc.

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