The H field corresponds to what is called the magnetic field strength.
It is measured in amps / meter (A/m). That is to say it is caused by a
current and exists in the space around the current independent of the
material occupying the space. H will generally be stronger near to the
current and will diminish in strength with distance from the current.
In free space or in air the B field represents magnetic flux density
which is given in units of Tesla by B = µ?.H where µ? is the absolute
magnetic permeability of free space and = 4p10^-7. More magnetic flux
can be produced by the same H value in certain (magnetic) materials,
notably iron, and this is accounted by introducing another factor, the
relative permeability µr, giving B = µ?.µr.H for magnetic materials. µr
can take values of over 1000 which makes iron very attractive to use in
devices (like transformers) which employ magnetic fields. Without using
iron such devices would be physically much larger.
Thanks &Regards.
Nirmal Singh
Askiitians Faculty