# Magnetic permeability

## Matter inside magnetic fields

Up to now we examined the action of force between a current through a wire and magnets. As we have seen, electric current is the cause of magnetic fields. The matter surrounding us is made out of atoms, which consist of positively charged protons, neutrons and negatively charged electrons. Moving charges cause magnetic fields and magnetic fields influence charged particles. Electrons and protons don't stick together, but move around each other. The mass of protons is much higher than those of the electrons and so the movement of the electrons is stronger than those of the protons. The moving charges of atoms interact therefore inevitably with magnetic fields. Let's ignore the mathematics of quantum physics and have a look at the macroscopic effects of matter inside magnetic fields.

## Magnetic constant

As well as a current through a wire amplifies or weakens magnetic fields, matter effects those fields, too. The index characterizing those influence is the magnetic constant. We have seen those constant before at formula [3.17] as the ratio between the magnetic flux density B and the magnetic field strength H. Inside a vacuum with no atoms around, we get a value of:

μ0 = 4 * π * 10-7 N/A2 ≈ 1,2566 * 10-6 N/A2

## Relative permeability

The permeability of a substance is often given in relation to the magnetic constant in free space. The relative permeability μr is the ratio between the permeability of the substance μ and the permeability of free space μ0:

## Diamagnetic materials

Materials with a relative permeability μr < 1 are called diamagnetic. As we will see at the chapter about induction, matter is always diamagnetic in principle. A relative permeability lower than 1 means the magnetic field is weakened inside the material. Caused by that, an action of force pointing to lower field strength takes place. Simplified: Diamagnetic materials are repulsed by magnetic fields, no matter if the north or south pole of a magnet is moved towards them.

## Paramagnetic materials

Inside paramagnetic materials, then relative permeability μr is greater than 1. In macroscopic dimensions, those materials are free of charge, because the number of protons equals the number of electrons. Concerning the movement of the electrons around the atomic nuclei, a magnetic moment is generated. Those magnetic moment can't be observed at macroscopic scales, because the single moments are not arranged in parallel but in different directions. Therefore the sum of those magnetic moments is zero.
If a paramagnetic material is exposed to an external magnetic field, the magnetic moment of some atoms start pointing in parallel to the direction of the external field. Those arrangement of the "magnetic spins" causes an enforcement of the magnetic field insides the material. In principle, the mechanism of weakening the strength of the external field takes place, too, but the paramagnetic effect is stronger than that.
Paramagnetic materials are attracted by areas of higher field strength of external magnetic fields. There is no matter if a north or south pole of a magnet is moved towards them.

## Ferromagnetc materials

If there is μr >> 1, a material is called ferromagnetic. The magnetic moments of those atoms or molecules are very distinctive, meaning the paramagnetic effects inside of those materials are very strong.
Ferromagnetic materials are attracted to magnets, the force always points to the direction of higher field strength. The best known ferromagnetic material is iron and from the Latin word for iron (ferrum), the name was created.