# 電磁輻射

## 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

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

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

## 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）

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

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

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

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

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

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

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

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

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

## 輻射的影響

### 人體影響

X光伽馬射線屬於游離輻射，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。

## 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 [2015-04-23], （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, [2015-04-24], （原始內容存檔 (PDF)於2020-04-08）
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. ^ 國際純化學和應用化學聯合會．"photoionization"．《化學術語總目錄》在線版．（英文）
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 [2010-04-30], （原始內容 (PDF)存檔於2020-05-12）
18. ^ 飯島　純夫、電磁場が染色體に及ぼす影響[永久失效連結]、山梨醫大誌 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]. （原始內容存檔於2016-05-25）.
21. ^ http://www.nies.go.jp/kanko/tokubetu/setsumei/sr-035-2001b.html
22. ^ 國際非電離放射線防護委員會(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]頁面存檔備份，存於網際網路檔案館
23. ^ 総務省 電波利用ホームページ 電波環境の保護[3]