Re: What is the H field?

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.