A vector quantity that allows Ampère's law to be written in terms of free current density alone as

in a dielectric having a bound current density

where M is the magnetization.Some authors call H the "magnetic field,"and then invent a new term, the "magnetic induction,"for the field B.Not only is this practice unnecessarily confusing, but the use of the term "induction" in this context is inconsistent with the much more widespread use of this word in electrodynamics . In fact, Sommerfeld (1952, p. 45) opines that "The unhappy term 'magnetic field' for H should be avoided as far as possible. It seems to us that this term has led into error none less than Maxwell himself." It is therefore best to simply refer to the field as "H ," or, when necessary for clarity, the "auxiliary magnetic field" (Griffiths 1987, p. 230).
H plays a role in magnetostatics that is analogous to that played by the displacement electric field D in electrostatics. However, H is a more useful in practice than D, since it directly related to the free current, which is what the experimenter controls (whereas B depends on the material being used and possibly also on hysteresis effects in the case of ferromagnetism).
H is defined in cgs by
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where is the permeability of free space.
It should be emphasized that unlike

is not, in general, equal to 0, although in cases of cylindrical, plane, solenoidal, or toroidal symmetry, it turns out that . However, in other cases, one cannot assume that (Griffiths 1987, p. 234).
Inside a ferromagnetic material,

where E is the total free energy and M is again the magnetization.