Biomedical Engineering Reference
In-Depth Information
Most ferrites are polycrystalline. They usually have a high permeability, rel-
atively small losses, and a high electrical resistivity. The saturation magnetic
flux density is lower than in ferromagnetic materials: It is of the order of
0.5 T in a MnZn ferrite instead of 2 T in iron.
Several types of energy have to be taken into account in investigating ferro-
and ferrimagnetic materials:
1. Exchange energy, corresponding to the energy difference between the
elements with parallel spins and those with antiparallel spins.
2. Magnetostatic energy,
associated with free magnetic poles in the
material.
3. Magnetostriction energy, related to the fact that a magnetic material
undergoes an elastic deformation in the direction of magnetization,
which may be positive or negative, corresponding to an elongation or
a contraction, respectively—this deformation is of the order of a few
millionths.
4. Anisotropic energy of the crystal, associated with the difference between
the direction of magnetization and those of easy magnetization.
1.3.3
Electromagnetic Field
In DC situations, the electric field is calculated correctly from the laws of elec-
trostatics. The same is true at extremely low and low frequencies, although the
approximation is less applicable when the frequency increases. Similarly, the
magnetic field is calculated from the laws of magnetostatics in DC situations.
The same is true at extremely low and low frequencies, with however a quality
of approximation decreasing when the frequency increases. Values of the fre-
quency at which the approximation is not valid anymore depend on the geo-
metric, electrical, and magnetic properties of the problem.
When the frequency increases, the electric and magnetic fields cannot be
separated from each other: If one of the fields exists, so does the other. One
cannot consider one field as the source of the other. They are linked to each
other in every situation, and this is described by Maxwell's equations . Maxwell,
a British physicist, formalized the laws of electromagnetics around 1880,
without writing the equations however as we know them today. He made at
this occasion two essential contributions:
1. One was to say that all the former laws, essentially based on experi-
mental measurements made by Gauss, Ampere, Lenz, and others, were
valid but that they had to be considered as a system of equations.
2. The other was to point out that, in the ensemble of these laws, one term
was missing: The displacement current did not appear in the former law
and it was to be added.
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