# 高斯磁定律

## 理论方程形式

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

${\displaystyle \oiint }$${\displaystyle {\mathbb {S} }}$${\displaystyle \mathbf {B} \cdot {\rm {d}}\mathbf {s} =0}$

## 磁矢势

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

${\displaystyle \nabla \times (\nabla \phi )=0\,\!}$

## 磁单极子

${\displaystyle \nabla \cdot \mathbf {B} =\mu _{0}\rho _{m}\,\!}$

## 毕奥-萨伐尔定律

${\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\int _{\mathbb {V} '}d^{3}r'\mathbf {J} (\mathbf {r} ')\times {\frac {\mathbf {r} -\mathbf {r} '}{|\mathbf {r} -\mathbf {r} '|^{3}}}\,\!}$

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

${\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\nabla \times \int _{\mathbb {V} '}d^{3}r'{\frac {\mathbf {J} (\mathbf {r} ')}{|\mathbf {r} -\mathbf {r} '|}}\,\!}$

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

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

## 参考文献

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. 2008: pp. 9. ISBN 978-0-691-12456-8.