1.1.5 Magnetostatic interactions

Magnetostatic interactions represent the way the elementary magnetic moments interact over `long' distances within the body. In fact, the magnetostatic field at a given location within the body depends on the contributions from the whole magnetization vector field, as we will see below. Magnetostatic interactions can be taken into account by introducing the appropriate magnetostatic field ${\mathbf{H}_\text{m}}$ according to Maxwell equations for magnetized media:

$$\begin{cases} \nabla\cdot{\mathbf{H}_\text{m}}=-\nabla\cdot\... ...abla\times{\mathbf{H}_\text{m}}=\mathbf{0} \end{cases} \quad,$$ (1.45)

with the following conditions at the body discontinuity surface $\partial \Omega$

$$\begin{cases} \textbf{n}\cdot\left[{\mathbf{H}_\text{m}}\rig... ...xt{m}}\right]_{\partial \Omega}= \mathbf{0} \end{cases} \quad.$$ (1.46)

In Eqs. (1.45)-(1.46), we have denoted with $\textbf{n}$ the outward normal to the boundary $\partial \Omega$ of the magnetic body, and with $[{\mathbf{H}_\text{m}}]_{\partial \Omega}$ the jump of the vector field ${\mathbf{H}_\text{m}}$ across $\partial \Omega$.