Electrodynamics/Magnetization

From Wikibooks, open books for an open world
< Electrodynamics
Jump to: navigation, search

Magnetic Moment[edit]

Magnetization Field[edit]

We can define two new vector fields to help aide us in further studies of magnetics. The first new field is the magnetization field M. This field represents the magnetic moment per unit volume of a magnetized substance. The second, H is known occasionally as the "magnetic field strength" and is used here primarily as a simplifying agent.

Magnetization[edit]

We can define the magnetic moment in terms of the magnetization as:

\mathbf{m} = \mathbf{M}(\mathbf{r}')dV'
\mathbf{A}(\mathbf{r}') = -\int \mathbf{M}(\mathbf{r})' \times \nabla \frac{1}{|\mathbf{r} - \mathbf{r}'|}dV'
\mathbf{A}(\mathbf{r}) = \int \frac{\nabla \times \mathbf{M}(\mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|}dV'
\mathbf{j}_M = \nabla \times \mathbf{M}

H Field[edit]

\mathbf{H} = \mathbf{B} - 4\pi\mathbf{M}
\nabla \times \mathbf{H} = 4 \pi \mathbf{j}_M
\oint_C \mathbf{H} \cdot d\mathbf{l} = 4 \pi \int_C\mathbf{j}_F \cdot \mathbf{n}dA