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CHAPTER 8. SOME BASIC CONCEPTS AND UNITS
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
the permeability has, similar to the permeability in
and the magnetic field 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
Introrepresents the molar mass of the material, expressed in
ducing everywhere numerical values {..} by substituting
and crossing out the units in the numerator and denominator, we obtain from Eq. (8.15) the equation
between numerical values:
CHAPTER 8. SOME BASIC CONCEPTS AND UNITS
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
the permeability has, similar to the permeability in
and the magnetic field 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
Introrepresents the molar mass of the material, expressed in
ducing everywhere numerical values {..} by substituting
and crossing out the units in the numerator and denominator, we obtain from Eq. (8.15) the equation
between numerical values: