Physics of Magnetism

CHAPTER 8. SOME BASIC CONCEPTS AND UNITS 77

The magnetic induction B is connected with the magnetic field strength H by the

equation

where is the magnetic permeability. As the magnetic induction is expressed in

and the magnetic field in the permeability has, similar to the permeability in

vacuum the unit which is also called henry per meter, that is,

The relative permeability is of course a dimensionless number.

The simplest circuit which is able to generate a magnetic field is a planar circular

conductor carrying an electric current. In fact, such a current loop can be considered as the

most elementary unit of magnetism, as we saw already in Chapter 2. If a current loop has

an area A and carries a current I, the corresponding magnetic moment is The

unit of magnetic moment can therefore be taken as ampere square meter When

expressed in these units, the Bohr magneton introduced in Eq. (2.1.2) has a magnitude of

The magnetization can be defined as the magnetic moment per volume

where p is the number of moments per volume. With in and in this gives

for the unit of magnetization. When M is defined in this manner, one has the same

units for the magnetization and the magnetic field strength.

In practice, it is more appropriate to define the magnetization as the magnetic moment

per mass. The magnetization is then defined by

where is the number of magnetic moments per mass. With in and in this

leads to for the unit of magnetization. The advantage of this choice of unit is

that we do not need to know the volume of the sample of which we wish to determine the

magnetization but only its mass, the latter being easily obtained by weighing the sample.

For comparison let us introduce the magnetic moment of Bohr magnetons, where

is Avogadro’s constant: molecules (or formula units) which are contained

in one mole of material:

We have the following relation between the various types of magnetizations

where represents the molar mass of the material, expressed in Intro­
ducing everywhere numerical values {..} by substituting
and cross­
ing out the units in the numerator and denominator, we obtain from Eq. (8.15) the equation
between numerical values: