Physics of Magnetism

86 CHAPTER 9. MEASUREMENT TECHNIQUES

If the long axis of the rod is along the we are interested in the axial force

exerted on a volume element dV of the sample. Using the relations

where E represents the magnetostatic energy of the sample in the magnetic field, we may
write

where is the magnetic moment of the volume element considered and H is the cor­
responding local field strength. If the sample is homogeneous, all volume elements of
the sample have the same magnetic moment given by For paramagnetic and
diamagnetic samples, it has been shown in Chapters 3 and 6 that the susceptibility is
field-independent. In that case, one may write

After integration along the length of the sample, one finds for the total axial force

where a is the cross-sectional area of the rod-shaped sample perpendicular to the z-axis,
is the field strength at the bottom of the sample located between the magnet poles, and
is the field strength at the top of the sample.
It follows from Eq. (9.1.3) that the force is independent of the direction of and
If is smaller than one tenth of its neglect leads to an error of at most 1 %.
The Gouy method works satisfactorily if the susceptibility is isotropic and field-
independent. The sample rod has to be macroscopically homogeneous and a constant
cross-section is required. Often, the sample consists of a glass tube filled with powder.
In this case, one has to prevent inhomogeneous compression by the field, which can be
done by fixing the powder particles by means of glue.
In the Gouy method, one obtains the susceptibility by measuring the change of weight
after the field in the magnet has been switched on. For practical purposes, it is sometimes
convenient to calibrate the weight increase by means of a standard sample of well-known
susceptibility.

9.2. THE FARADAY METHOD

In the Faraday method, the sample is again placed in an inhomogeneous magnetic field,

the concomitant force being given by