PlanetPhysics/Auxiliary Field H

The auxiliary field, {\mathbf H} is defined from the magnetic field {\mathbf B}, the magnetization {\mathbf M} and the permeability of free space $$\mu_0$$.

$${\mathbf H} = \frac{\mu_0} - {\mathbf M}$$

Confusion sometimes arises because the {\mathbf H} field was named the magnetic field or magnetic field intensity in the past, while {\mathbf B} was denoted as the magnetic flux density or magnetic induction. Similar to Thermodynamics, where we can talk about macroscopic phenomenon and solve problems without dealing with microscopic properties, the {\mathbf H} field is a macroscopic field like the electric displacement {\mathbf D}.

{\mathbf References}

[1] Magnetic field, Wikipedia

[2] Jackson, D. "Classical Electrodynamics", John Wiley and Sons, Inc., 1975.

[3] Griffiths, D. "Introduction to Electrodynamics", Prentice-Hall, Inc., 1999.