# 電磁輻射

（重定向自電磁波輻射

## 概念

### 波動模型

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

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

### 粒子模型和量子理論

${\displaystyle E=h\nu \,\!}$

${\displaystyle p={\frac {E}{c}}={\frac {h\nu }{c}}={\frac {h}{\lambda }}\,\!}$

### 傳播速度

${\displaystyle E=h\nu \,\!}$

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

## 熱輻射

${\displaystyle {U \over V}={\frac {8\pi ^{5}(kT)^{4}}{15(hc)^{3}}}\,\!}$

${\displaystyle C_{V}={\frac {32\pi ^{5}k^{4}T^{3}}{15(hc)^{3}}}\,\!}$

## 从电磁理论推导

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

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

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

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

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

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

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

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

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

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

## 輻射的影響

### 人體影響

X光伽馬射線屬於電離輻射，會使生物的基因損壞或突變，甚至導致癌症。這些電磁波輻射允許劑量由法律確定。

## 参考文献

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] （英语）.
3. ^ Encyclopædia Britannica Online. Heinrich Hertz. Encyclopædia Britannica. [2009-08-25] （英语）.
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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
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10. ^ Hecht, Eugene, Optics 4th, United States of America: Addison Wesley, 2002, ISBN 0-8053-8566-5 （英语）
11. ^ Weinberger, P., John Kerr and his Effects Found in 1877 and 1878 (PDF), Philosophical Magazine Letters: 897–907
12. ^ Richard Phillips Feynman; A. Zee. QED: The Strange Theory of Light and Matter. Princeton University Press. 2006. ISBN 0-691-12575-9.
13. ^ George Greenstein; Arthur Zajonc. The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics. Jones & Bartlett Learning. 2006. ISBN 978-0-7637-2470-2.
14. ^ French, Anthony, An Introduction to Quantum Physics, W. W. Norton, Inc., 1978
15. ^ （英文）國際純粹與應用化學聯合會．"photoionization"．《化学术语总目录》在线版．
16. Griffiths, David J. Introduction to Quantum Mechanics(2nd ed.). Prentice Hall. 2004: pp. 348–359. ISBN 0-13-111892-7.
17. ^ Griffiths, David J., Hyperfine splitting in the ground state of hydrogen (PDF), American Journal of Physics, August 1982, 50 (8): pp. 698
18. ^ 飯島　純夫、電磁場が染色体に及ぼす影響[永久失效連結]、山梨医大誌 14 (1)，1 - 5，1999。
19. ^ WHOファクトシートNo.263,"電磁界と公衆衛生:「超低周波電磁界とがん」", 2001年10月 [1]PDF
20. ^ Electromagnetic fields and public health: mobile phones. Fact sheet N°193. World Health Organization. June 2011 [5 November 2013].
21. ^ http://www.nies.go.jp/kanko/tokubetu/setsumei/sr-035-2001b.html
22. ^ 国際非電離放射線防護委員会(ICNIRP), "時間変化する電界、磁界及び電磁界による曝露を制限するためのガイドライン（300 GHz まで）", 1998年4月[2] 页面存档备份，存于互联网档案馆
23. ^ 総務省 電波利用ホームページ 電波環境の保護[3]