# 電磁波

## 概念

### 波動理論

${\displaystyle v=\nu \lambda \,\!}$

${\displaystyle u={\frac {1}{2\mu _{0}}}B^{2}+{\frac {\epsilon _{0}}{2}}E^{2}\,\!}$

### 傳播速度

${\displaystyle n=c/v\,\!}$

## 從電磁理論推導

${\displaystyle \nabla \cdot \mathbf {E} =0\,\!}$（1）
${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}$（2）
${\displaystyle \nabla \cdot \mathbf {B} =0\,\!}$（3）
${\displaystyle \nabla \times \mathbf {B} =\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\,\!}$（4）

${\displaystyle \nabla \times \left(\nabla \times \mathbf {E} \right)=\nabla \times \left(-{\frac {\partial \mathbf {B} }{\partial t}}\right)\,\!}$（5）

${\displaystyle \nabla \times \left(\nabla \times \mathbf {E} \right)=\nabla \left(\nabla \cdot \mathbf {E} \right)-\nabla ^{2}\mathbf {E} =-\nabla ^{2}\mathbf {E} \,\!}$（6）

${\displaystyle \nabla \times \left(-{\frac {\partial \mathbf {B} }{\partial t}}\right)=-{\frac {\partial }{\partial t}}\left(\nabla \times \mathbf {B} \right)=-\mu _{0}\epsilon _{0}{\frac {\partial ^{2}\mathbf {E} }{\partial t^{2}}}\,\!}$（7）

 ${\displaystyle \nabla ^{2}\mathbf {E} =\mu _{0}\epsilon _{0}{\frac {\partial ^{2}\mathbf {E} }{\partial t^{2}}}\,\!}$。

 ${\displaystyle \nabla ^{2}\mathbf {B} =\mu _{0}\epsilon _{0}{\frac {\partial ^{2}\mathbf {B} }{\partial t^{2}}}\,\!}$。

${\displaystyle \Box \mathbf {E} =0\,\!}$
${\displaystyle \Box \mathbf {B} =0\,\!}$

${\displaystyle \mathbf {E} =\mathbf {E} _{0}f\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)\,\!}$

${\displaystyle \nabla ^{2}f\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)={\frac {1}{{c_{0}}^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}f\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)\,\!}$

${\displaystyle \nabla \cdot \mathbf {E} =\mathbf {k} \cdot \mathbf {E} _{0}f'\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)=0\,\!}$

${\displaystyle \mathbf {E} \cdot \mathbf {k} =0\,\!}$

${\displaystyle \nabla \times \mathbf {E} ={\hat {\mathbf {k} }}\times \mathbf {E} _{0}f'\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)=-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}$

${\displaystyle \mathbf {B} ={\frac {1}{\omega }}\mathbf {k} \times \mathbf {E} \,\!}$

## 參考文獻

1. ^ Philosophical Transactions of the Royal Society of London, Vol. 90 (1800), pp. 284-292, http://www.jstor.org/stable/info/107057
2. ^ Encyclopædia Britannica Online. James Clerk Maxwell. Encyclopædia Britannica. [2009-08-24]. （原始內容存檔於2009-08-31） （英語）.
3. ^ Encyclopædia Britannica Online. Heinrich Hertz. Encyclopædia Britannica. [2009-08-25]. （原始內容存檔於2009-09-01） （英語）.
4. ^ 馬克士威, 詹姆斯, A dynamical theory of the electromagnetic field (pdf), Philosophical Transactions of the Royal Society of London, 1865, 155: 459–512 [2019-03-19], （原始內容存檔 (PDF)於2011-07-28）
5. ^ Whittaker, E. T., A history of the theories of aether and electricity. Vol 1, Nelson, London, 1951
6. 詹姆士·金斯 (1947) The Growth of Physical Science, link from Internet Archive
7. Griffiths, David J. Introduction to Electrodynamics (3rd ed.). Prentice Hall. 1998: pp. 364–374, 416–471. ISBN 0-13-805326-X.
8. Halliday, David; Robert Resnick, Jearl Walker. Fundamental of Physics 7th. USA: John Wiley and Sons, Inc. 2005. ISBN 0-471-23231-9.
9. ^ Jackson, John David, Classical Electrodynamic 3rd., USA: John Wiley & Sons, Inc., 1999, ISBN 978-0-471-30932-1
10. ^ Hecht, Eugene, Optics 4th, United States of America: Addison Wesley, 2002, ISBN 0-8053-8566-5 （英語）
11. ^ Weinberger, P., John Kerr and his Effects Found in 1877 and 1878 (PDF), Philosophical Magazine Letters: 897–907, [2019-03-19], （原始內容存檔 (PDF)於2020-04-08）
12. ^ Griffiths, David J., Hyperfine splitting in the ground state of hydrogen (PDF), American Journal of Physics, August 1982, 50 (8): pp. 698 [2019-03-19], （原始內容存檔 (PDF)於2020-05-12）