Linear Magnetic Materials
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Just like that for Linear Dielectrics we also have Linear Magnetic Materials for which the Magnetization M is proportional to the applied field. The applied field is taken to be the H field because that is the field which is measured in the Lab. This is unlike the case for electrostatics where the E-field is the applied field . So we have M=χmH where χm is called the Magnetic susceptibility. Since B=μ0( H + M )=μH where μ is the permeability of the material we have μ=μ0(1 + χm). As in Dielectrics it is also possible to define a relative permeability μr=μ/μ0=(1 + χm).
Since in the linear magnetic materials both the H field and the Magnetization M are proportional to the B- field, it may appear that in this case as ∇.B=0 this implies ∇.H=0. This is wrong, for the same reason as in Dielectrics where Curl E=0 does not imply Curl D=0. This is because at the boundary the proportionality changes and a careful examination of the corresponding integral forms of the law show that both M and H have non zero divergences except in the case when the entire space is filed with a single magnetic material in which case there are no boundaries. For linear materials since the bound current Jb=∇ X M and M =χm H
we have Jb=χm Jfree.
The most important and widely used magnetic materials are however Ferromagnetic materials. These are non linear magnetic materials containing permanent magnetic dipoles associated with unpaired electrons in odd electron atoms just as in Paramagnetism. However the difference in this case is that there is a very strong
interaction between neighbouring dipoles due to quantum mechanical reasons. For this reason neighbouring dipoles tend to point the same way even in the absence of an external magnetic field. In small regions the dipole orientation is almost 100 % due to this reason. These are called Ferromagnetic domains and the entire region may be described by a single total dipole moment vector called the magnetic domain vector .
There are a large number of such domains in a Ferromagnetic material with randomly oriented domain vectors subject to random thermal vibrations. When a a Ferromagnetic material is subjected to an external magnetic field the domain vectors tend to align
together and this causes domains to merge and grow and for string fields the entire material may be described by a single domain and results in a very strong Magnetization. When the external field is switched off some of the domain vectors stay aligned and gives rise to permanent magnetization. This is called Hysteresis .
Normally random thermal motion determined by the Temperature of the material compete with domain alignments. However at a certain critical temperature called the Curie Temperature the alignment of domain vectors are favored over random thermal motions. For IRON this is T= 770 deg Centigrade above which it is Paramagnetic wit no domain formations and below the Curie Temperature it is Ferromagnetic. The transition between the Paramagnetic phase and the Ferromagnetic phase is thermodynamically alike to a liquid-solid phase transition in materials, like water-ice transition. The properties of Magnetic materials are decided by quantum mechanics and is a subject of frontline research in Condensed mater physics.
This ends our discussion on the Electric and Magnetic effects of static charges and steady currents. The second part of the course will deal with dynamic situations where charge densities and currents are functions of time and we will see
that this would unify the Electric and Magnetic aspects into a single framework of Electrodynamics involving time dependent electric and magnetic fields and described by a set of 4 equations
called the Maxwell's equation. It was Maxwell that unified the
apparently different phenomena into a single framework. You will also see how Electrodynamics is intimately connected to
the Special Theory of Relativity.
Hysteresis link:
http://www.tpub.com/content/chemical-biological/TM-1-1500-335-23/css/TM-1-1500-335-23_208.htm
http://en.wikipedia.org/wiki/Ferromagnetism
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