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The relative permeability
µr of a material "somehow" describes the
interaction of magnetic (i.e. more or less all) materials and magnetic fields
H, e.g. vial the equations Þ |
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B is the magnetic flux
density or magnetic induction, sort of replacing H in
the Maxwell equations whenever materials are encountered. |
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L is the inductivity of a linear
solenoid (also called coil or inductor) with length l,
cross-sectional area A, and number of turns t, that
is "filled" with a magnetic material with
µr. |
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n is still the index of refraction; a quantity that
"somehow" describes how electromagnetic fields with extremely high
frequency interact with matter.
For all practical purposes, however, µr = 1 for optical
frequencies |
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Magnetic fields inside magnetic
materials polarize the material, meaning that the vector sum of magnetic
dipoles inside the material is no longer zero. |
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The decisive quantities are the magnetic dipole moment m, a
vector, and the magnetic Polarization
J, a vector, too. |
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Note: In contrast to dielectrics, we define an
additional quantity, the magnetization M by simply
including dividing J by µo. |
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The magnetic dipoles to be polarized are either
already present in the material (e.g. in Fe, Ni or Co, or more
generally, in all paramagnetic materials, or are induced by the magnetic
fields (e.g. in diamagnetic materials). |
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The dimension of the magnetization
M is [A/m]; i.e. the same as that of the magnetic
field. |
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The magnetic polarization
J or the magnetization M are not given by some magnetic surface charge, because
Þ. |
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a negative or positive electric charge |
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The equivalent of "Ohm's
law", linking current density to field strength in conductors is the
magnetic Polarization law: |
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| M |
= |
(µr - 1) · H |
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| M |
:= |
cmag · H |
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The decisive material parameter is cmag = (µr – 1) =
magnetic susceptibility. |
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The "classical" induction
B and the magnetization are linked as shown. In essence,
M only considers what happens in the material, while
B looks at the total effect: material plus the field that induces
the polarization. |
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Magnetic polarization mechanisms are
formally similar to dielectric polarization mechanisms, but the physics can be
entirely different. |
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| Atomic mechanisms of
magnetization are not directly analogous to the dielectric case |
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Magnetic moments originate from: |
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The intrinsic magnetic dipole moments
m of elementary particles with spin is measured in units of the
Bohr magnetonmBohr. |
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h · e
4p · m*e |
= 9.27 ·
10–24 Am2 |
| me
= |
2 · h · e · s
4p · m*e |
= 2 · s ·
m Bohr |
= ± mBohr |
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The magnetic moment me
of the electron is Þ |
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Electrons "orbiting" in an atom can be
described as a current running in a circle thus causing a magnetic dipole
moment; too |
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The total magnetic moment of an atom
in a crystal (or just solid) is a (tricky to obtain) sum of all contributions
from the electrons, and their orbits (including bonding orbitals etc.), it is
either: |
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Zero - we then have a diamagnetic
material. |
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Magnetic field induces dipoles,
somewhat analogous to elctronic polarization in dielectrics.
Always very weak effect (except for superconductors)
Unimportant for technical purposes |
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In the order of a few Bohr magnetons - we have a
essentially a paramagnetic material. |
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Magnetic field induces some order to
dipoles; strictly analogous to "orientation polarization" of
dielectrics.
Always very weak effect
Unimportant for technical purposes |
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In some
ferromagnetic materials spontaneous ordering of magnetic moments occurs
below the Curie (or Neél) temperature. The important families are |
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- Ferromagnetic materials ÝÝÝÝÝÝÝ
large µr, extremely important.
- Ferrimagnetic materials ÝßÝßÝßÝ
still large µr, very important.
- Antiferromagnetic materials ÝßÝßÝßÝ
µr » 1, unimportant
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Ferromagnetic materials:
Fe, Ni, Co, their alloys
"AlNiCo", Co5Sm, Co17Sm2,
"NdFeB" |
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There is characteristic temperature
dependence of µr for all cases |
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© H. Föll
