Biomedical Engineering Reference
In-Depth Information
æ
3
χ
H
ö -
1
χ
H
Note that, at low magnetic field,
and (9.3) reduces
coth
=
ç
÷
3
χ
H
è
ø
M
M
s
s
M
s
M
1
to the usual expression M = cH . For large magnetic field,
= -
1
, and 2,
3
χ
H
M
s
M
s
which states that saturation is reached. The diagram M(H) is plotted in Figure 9.8.
If we assume that the paramagnetic beads are monodispersed (all the beads are
identical), Langevin's law may be applied to each bead.
9.2.2  Ferromagnetic Microparticles
The situation is more complex for ferromagnetic beads because ferromagnetic ob-
jects keep a remanent magnetization when the external field vanishes. There is gen-
erally no analytical function for the magnetization and one generally tries to fit the
experimental curve by piecewise continuous polynomials.
9.3  Magnetic Force
A general expression of the magnetic energy of interaction of a particle immersed
in a magnetic field H
is [5, 6]
1
ò � �
E
= -
µ
MHdV
.
(9.4)
0
2
where M
. The
integration is taken over the particle volume. The magnetic force exerted by the
magnetic field on the particle is the gradient of the interaction energy
is the magnetization of the particle in the applied magnetic field H
F
= -Ñ
E
(9.5)
m
m
Figure 9.8  Relation M(H) for the different types of materials.
 
 
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