Auxillary Field

Magnetic field arising from free current alone. Analogous to electric displacement for magnetostatics

$\vec{H}=\frac{1}{{\mu }_0}\vec{B}-\vec{M}=\frac{\vec{B}}{{\mu }_0(1+{\chi }_b)}=\frac{\vec{B}}{\mu }$

• ${\mu }_0$ is the magnetic constant
• $\vec{B}$ is the magnetic field
• $\vec{M}$ is the magnetization
• ${\chi }_b$ is the magnetic susceptibility of the material
• $\mu$ is the permeability of the material

$\nabla \times \vec{H}={\vec{J}}_f+{\partial }_t\vec{D}$