# 高斯磁定律

## 理論方程式形式

$\nabla\cdot\mathbf{B} = 0\,\!$

$\oint_{\mathbb{S}} \mathbf{B} \cdot \mathrm{d}\mathbf{a} = 0\,\!$

## 磁向量勢

$\mathbf{B} = \nabla\times\mathbf{A}\,\!$

$\nabla\times(\nabla \phi)=0\,\!$

## 磁單極子

$\nabla\cdot\mathbf{B} = \mu_0\rho_m\,\!$

## 必歐-沙伐定律

$\mathbf{B}(\mathbf{r}) = \frac{\mu_0}{4\pi} \int_{\mathbb{V}'} d^3r' \mathbf{J}(\mathbf{r}')\times \frac{\mathbf{r} - \mathbf{r}'}{|\mathbf{r} - \mathbf{r}'|^3}\,\!$

$\frac{\mathbf{r} - \mathbf{r}'}{|\mathbf{r} - \mathbf{r}'|^3} = - \nabla\left(\frac{1}{|\mathbf{r} - \mathbf{r}'|}\right)\,\!$

$\mathbf{B}(\mathbf{r}) = \frac{\mu_0}{4\pi} \nabla\times\int_{\mathbb{V}'} d^3r' \frac{\mathbf{J}(\mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|}\,\!$

$\nabla\cdot(\nabla\times\mathbf{A})=0\,\!$

$\nabla\cdot\mathbf{B}=0\,\!$

## 參考文獻

1. ^ 1.0 1.1 Jackson, John David. Classical Electrodynamic 3rd. USA: John Wiley & Sons, Inc. 1999: pp. 237, 273. ISBN 978-0-471-30932-1.
2. ^ Griffiths, David J. Introduction to Electrodynamics (3rd ed.). Prentice Hall. 1998: pp. 321. ISBN 0-13-805326-X.
3. ^ Joannopoulos John D.; Johnson, Steve G.;Winn, Joshua N. and Meade, Robert D. Photonic Crystals: Molding the Flow of Light 2nd. Princeton, NJ USA: Princeton University Press. 2008pp. 9: . ISBN 978-0-691-12456-8.