Magnetic Intensity and Permeability}
When matter is placed in a magnetic field, its atoms respond to the
applied field by either adding their own magnetic fields to that
of the applied field (ferromagnetic and paramagnetic materials)
or by subtracting from it (diamagnetic materials).
This extra magnetism produced by the material is described in
a rather confusing way, so pay close attention.
The first important concept is the
magnetization 
,
defined to be the net magnetic dipole moment per unit volume
in the material:
The total magnetic field inside such a material is
related to the applied external field and the
magnetization by
The magnetic field strength 
is a quantity which has the same units as but depends
only on the strength of the external magnetic field:
Note that has units of magnetization, not units of magnetic
field.
The magnetic susceptibility 
gives the ratio between and :
If is large, it means that the atoms inside the material
respond strongly to the applied magnetic field, while if it is small
it means that the magnetism of the atoms in an applied field is
not very important.
Finally, we introduce the permeability 
(not the same as the magnetic moment ) which is related to the susceptibility
by
This quantitity gives a simple relation between the total
magnetic field in the material and the magnetic field strength :
