真空电容率本文重定向自 真空电容率

${\displaystyle \epsilon _{0}\approx 8.854\ 187\ 817\dots \ \times 10^{-12}}$ 法拉

${\displaystyle \epsilon _{0}\ {\stackrel {def}{=}}\ {\frac {1}{\mu _{0}{c_{0}}^{2}}}}$

${\displaystyle \epsilon _{0}\approx 8.854\ 187\ 817\ldots \times 10^{-12}}$ 安培24千克-1-3（或者法拉／米）。

${\displaystyle \mathbf {D} \ {\stackrel {def}{=}}\ \epsilon _{0}\mathbf {E} +\mathbf {P} \,\!}$

历史背景

单位理想化

${\displaystyle F={\frac {k_{\mathrm {e} }Q^{2}}{r^{2}}}\,\!}$

${\displaystyle F={\frac {{q_{s}}^{2}}{r^{2}}}\,\!}$

${\displaystyle F=\;k'_{\mathrm {e} }{q'_{s}}^{2}/4\pi r^{2}\,\!}$

${\displaystyle F=q^{2}/4\pi \epsilon _{0}r^{2}\,\!}$

${\displaystyle q_{s}=q/{\sqrt {4\pi \epsilon _{0}}}\,\!}$

ε0数值的设定

${\displaystyle \nabla \cdot \mathbf {E} =0\,\!}$
${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}$
${\displaystyle \nabla \cdot \mathbf {B} =0\,\!}$
${\displaystyle \nabla \times \mathbf {B} =\epsilon _{0}\mu _{0}{\frac {\partial \mathbf {E} }{\partial t}}\,\!}$ ;

${\displaystyle \nabla \times (\nabla \times \mathbf {B} )=\epsilon _{0}\mu _{0}{\frac {\partial (\nabla \times \mathbf {E} )}{\partial t}}\,\!}$

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

${\displaystyle \nabla \times (\nabla \times \mathbf {B} )=\nabla (\nabla \cdot \mathbf {B} )-\nabla ^{2}\mathbf {B} \,\!}$

${\displaystyle \nabla \times (\nabla \times \mathbf {B} )=-\nabla ^{2}\mathbf {B} \,\!}$

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

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

${\displaystyle c_{0}=1/{\sqrt {\epsilon _{0}\mu _{0}}}\,\!}$

注释

1. ^ 取第二个麦克斯韦方程（法拉第方程）的旋度，并将第四个麦克斯韦方程${\displaystyle \nabla \times \mathbf {B} =\epsilon _{0}\mu _{0}{\frac {\partial \mathbf {E} }{\partial t}}}$代入，则可得到
{\displaystyle {\begin{aligned}\nabla \times (\nabla \times \mathbf {E} )&=-{\frac {\partial (\nabla \times \mathbf {B} )}{\partial t}}\\&=-\epsilon _{0}\mu _{0}{\frac {\partial ^{2}\mathbf {E} }{\partial t^{2}}}\\\end{aligned}}}
应用一个矢量恒等式，再代入第一个麦克斯韦方程${\displaystyle \nabla \cdot \mathbf {E} =0}$，即得
{\displaystyle {\begin{aligned}\nabla \times (\nabla \times \mathbf {E} )&=\nabla (\nabla \cdot \mathbf {E} )-\nabla ^{2}\mathbf {E} \\&=-\nabla ^{2}\mathbf {E} \\\end{aligned}}}
这样，就可以得到光波的电场波动方程
${\displaystyle \nabla ^{2}\mathbf {E} -\epsilon _{0}\mu _{0}{\frac {\partial ^{2}\mathbf {E} }{\partial t^{2}}}=0}$

参考文献

1. CODATA. Electric constant. 2006 CODATA recommended values. NIST. [2007-08-08].
2. ^ 引述自 NIST（国家标准与技术学院）：现行的惯例是按照ISO 31的建议，用 ${\displaystyle c_{0}}$ 来标记在真空的光速。原本的1983年建议书主张采用 ${\displaystyle c}$ 来做此用途。
3. ^ NIST對於公尺的定義 (html). NIST.
4. ^ NIST對於安培的定義 (html). NIST.
5. ^ CODATA報告 (pdf). NIST.
6. ^ Cardarelli, François. Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins 2nd. Springer. 2004. ISBN 9781852336820.
7. ^ John David Jackson. Classical electrodynamics Third. New York: Wiley. 1999: Appendix on units and dimensions; pp. 775 et seq.。. ISBN 047130932X.怎样选择独立单位的叙述
8. ^ 物理术语部分真空指出，近似真空和自由空间的一个主要分歧源点，是来自于无法达到0气压。但是，还有其它非理想性的可能源点。参阅，例如，Di Piazza, Antonino; K. Hatsagortsyan & C. Keitel, Light diffraction by a strong standing electromagnetic wave, Phys.Rev.Lett., 2006, 97: 083603Gies, Holger; J. Jaeckel & A. Ringwald, Polarized light propagating in a magnetic field as a probe for millicharged fermions, Phys. Rev. Letts., 2006, 97: 140402
9. ^ Astrid Lambrecht (Hartmut Figger, Dieter Meschede, Claus Zimmermann Eds.). Observing mechanical dissipation in the quantum vacuum: an experimental challenge；在物理書 Laser physics at the limits. Berlin/New York: Springer. 2002: 197. ISBN 3540424180.
10. ^ Walter Dittrich & Gies H. Probing the quantum vacuum: perturbative effective action approach. Berlin: Springer. 2000. ISBN 3540674284.
11. ^ 对于这类修正，CIPM RECOMMENDATION 1 (CI-2002)p. 195的建议是：
♦ …在每一个案例里，为了要处理真实发生的事件，像衍射、地心引力，或不完美的真空等等，任何必要的修正都必须仔细执行。
除此以外，
♦ …科学家认为米是单位固有长度（proper length）。米的定义，只适用于一个足够小的区域内，这样，可以忽略重力场的不均匀性。
CIPM是国际重量和度量会议（International Committee for Weights and Measures）的首字母缩略字。