|MadSci Network: Physics|
There are two kinds of sources of magnetic field, one is current, the other is the self-spin of electron. Consider a current in vacuum, things are very simple. B is always proportional to the strength of the current, H is also always proportional to the strength of the current. B=mu0*H. mu0 is a physical constant not dependent on any material. You can just regard B and H as the same thing with different units. Let's denote this B and H as B0 and H0. However, if you keep the current, but fill the whole space uniformly with a material, and you measure B again, you will find B is different from B0. For some material B is larger, for some material B is smaller, but at different positions B is always proportional to B0 by a factor of mu_r. This mu_r is called relative permeability. The reason B is different from B0 is that the material cotains non-paired electrons which are like small magnets due to their self-spin. These small magnets line up with the imposed field B0 and the total field B is changed. For different materials, the density of non-paired electrons and their interactions are different, therefore their reactions to the imposed magnetic field are different, which results in different relative permittivity for different materials. Now it is clear that in material the magnetic field B can be decomposed into two parts: one is cuased by some independent current source, which we deonte as B0; the other is caused by the self-spin of non-paired electrons in the material, which is of course B-B0. Maybe for some history reason or some people did not like B0, so they invented another physical quantity H which is always B0/mu0. In the above discussions we only considered the situation where the whole space is filled with one material. However, in most practical cases, different parts of the space are filled with different materials. In this case, there is no easy way to calculate the magnetic field given the current. However, people found the rule that govens the natural phenomenon can still be written in a simple and beautiful form if H is used, this form is called Maxwell's equations. They are a set of differential equations which describe the relations among E, D,H and B. Since in this case mu_r is a function of the position, you cannot eliminate H from the Maxwell's equations without changing its simple form. You can still regard H as some intermediate variable without physical significance, but it is so extensively used in electromagnetics and people are so familiar with it that it is generally regarded a physical quantity.
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