Magnetism
MAGNETIC FIELD H
An electrical current i flowing in a conductor generates a magnetic field H, which intensity is proportional to the current. For a long and straight conductor (see figure below):
where r is the radial distance from the conductor. The field is a closed loop around the conductor.
Since the current is measured in ampere (A) and the radius in meters (m), the unit of measure of H is the ampere/meter (A/m). This is the unit that should be used in accordance with the international measuring system (SI), but it is still often used the unit of measure of the CGS standard, the oersted (Oe), which is:
1 Oe = 103/4p » 79.58 A/m
MAGNETIC INDUCTION B
While the magnetic field H is only generated by the electrical currents, the magnetic induction B considers all possible field sources, like the field generated by ferromagnetic materials.
In vacuum (and with great approximation in the air), the fields H and B are linked by relationship:
B = m0H
where m0 is the magnetic permeability of vacuum which is 4p×10-7 henry/meter (H/m).
In case the media is not the vacuum but a ferromagnetic material (for example iron), the field B is expressed by a similar relationship:
B = mH = mr0 m0H
where m is the magnetic permeability of the material, conveniently defined as the product of m0 and the relative permeability mr respect to vacuum.
For iron, the maximum value it is about 5000 ¸ 10000, while for some Fe-Ni alloys it can be reach values of the order of 106. The relative permeability depends on the magnetic field H.
The unit of measure of magnetic induction in the SI is the tesla (T), but it is also commonly used the CGS unit, the gauss (G):
1 G = 10-4 T
When considering magnetic fields in air both H or B can be used (even though B is mainly used).
When considering total magnetic field inside ferromagnetic materials, the magnetic induction B must be used.
MAGNETIC FLUX F
The magnetic flux linked with a coil having N winding is defined as:
where A is the area of the surface of each turn and B is the mean field perpendicular to the coil.
The unit of measure of flux is than tesla x square meter (T . m2) which is named Weber (Wb).
The related CGS unit is the maxwell (Mx) :
1 Mx = 10-8 Wb
MAGNETIC MOMENT
The magnetic moment m of a current loop having area A is:
m = iA
The unit of measure is the ampere×m2. The magnetic moment is the elementary unit of the magnetism, like the electrical charge is the elementary unit for the electrostatics.
It is comparable to a small magnet with north and south poles (see picture below).
In atomic scale, magnetic moments are generated by the electrons during their rotation around nuclei and by their spins. Therefore the atomic electrons act as many microscopic magnets inside the material.
These magnets can be randomly located (in this case there is no net magnetism and the material is non magnetic) or they can be rotated in the same direction. In this case, the magnetic moments add up and produce a macroscopic effect, and the material .
Magnetisation M is the sum of all elementary magnetic moments divided by the volume V in which they are contained:
(the symbol S means “sum”). The unit of the magnetisation M is the ampere/meter (A/m), the same of the magnetic field H.
FUNDAMENTAL RELATIONSHIP OF MAGNETIC FIELDS
H, B and M fields are correlated by the fundamental relationship:
B = m0 (H + M) = m0H + J
It should be emphasized that the total magnetic field B is given by the contribution of the field H (related to currents only) and the field M (related to the material only).
The intrinsic magnetisation J, equal to m0M (also named magnetic polarisation), is conveniently used to express M in tesla (or gauss) instead of A/m.
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