Free space (electromagnetism): Difference between revisions

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#REDIRECT [[Vacuum (classical)]]
 
Free space usually refers to a perfect vacuum, devoid of all particles. The term is most often used in classical electromagnetism where it refers to a reference state,<ref name=Weiglhofer>{{cite book|title=Introduction to complex mediums for optics and electromagnetics |author=Werner S. Weiglhofer and Akhlesh Lakhtakia |year=2003 |url=http://books.google.com/books?id=QtIP_Lr3gngC&pg=PA34&hl=en#v=onepage&q&f=false|publisher=SPIE Press |isbn=0819449474 |chapter=§4.1: The classical vacuum as reference medium }}</ref> and in quantum physics where it refers to the ground state of the electromagnetic field, which is subject to fluctuations about a dormant zero average-field condition.<ref name=Shankar>{{cite book|title=Principles of quantum mechanics |author=Ramamurti Shankar |url=http://books.google.com/books?id=2zypV5EbKuIC&pg=PA507#v=onepage&q=free%20space&f=false |pages=p. 507 |isbn=0306447908 |year=1994 |edition=2nd ed. |publisher=Springer}}</ref> The classical case of vanishing fields implies all fields are source-attributed, while in the quantum case field moments can arise without sources from virtual phonon creation and destruction.<ref name=Vogel>{{cite book |title=Quantum optics |author=Werner Vogel, Dirk-Gunnar Welsch |url=http://books.google.com/books?id=qRtnP1dPGmQC&pg=PA337&hl=en#v=onepage&q&f=false |pages=p. 337 |publisher=Wiley-VCH |year=2006 |edition=3rd ed.  |isbn=3527405070}}</ref> The description of free space varies somewhat among authors, with some authors requiring only the absence of substances with electrical properties,<ref name=Pathria>{{cite book|title=The Theory of Relativity |author= RK Pathria |url=http://books.google.com/books?id=Ma4ZFefVKIYC&pg=PA119&hl=en#v=onepage&q&f=false |pages=p. 119 | |year=2003 |isbn=0486428192 |publisher=Courier Dover Publications |edition=Reprint of Hindustan 1974 2nd ed.}}</ref> or of charged matter (ions and electrons, for example).<ref name=Morris>{{cite book |title=Academic Press dictionary of science and technology |editor=Christopher G. Morris, editor |publisher=Academic |url=http://books.google.com/books?id=nauWlPTBcjIC&pg=PA880&hl=en#v=onepage&q&f=false|pages=p. 880 |year=1992 |isbn=0122004000}}</ref>
 
===Classical case===
In the classical case, free space is characterized by the electrical permittivity ε<sub>0</sub> and the magnetic permeability μ<sub>0</sub> with an exact value provided by [[NIST]] as the [http://physics.nist.gov/cgi-bin/cuu/Value?ep0 ''electric constant''] and a defined value as the [http://physics.nist.gov/cgi-bin/cuu/Value?mu0 ''magnetic constant''] respectively.<ref name=Weiglhofer/>
 
::ε<sub>0</sub> ≈ 8.854 187 817... × 10<sup>−12</sup> F m<sup>−1</sup>
 
::μ<sub>0</sub> = 4π × 10<sup>−7</sup> ≈ 12.566 370 614... x 10<sup>−7</sup> N A<sup>−2</sup>
 
where the approximation is not a physical uncertainty (such as a measurement error) but a result of the inability to express these [[irrational numbers]] with a finite number of digits.
 
One consequence of these electromagnetic properties coupled with [[Maxwell's equations]] is that the [[speed of light]] in free space is related to ε<sub>0</sub> and μ<sub>0</sub> via the relation:<ref name=Baschek>
 
{{cite book |title= The new cosmos: an introduction to astronomy and astrophysics |author=Albrecht Unsöld, B. Baschek |url=http://books.google.com/books?id=nNnmR8ljctoC&pg=PA101 |pages=p. 101 |chapter=§4.1: Electromagnetic radiation, Equation 4.3 |isbn=3540678778 |year=2001 |publisher=Springer |edition=5th ed.}}
 
</ref>
 
::<math>c_0 = 1/\sqrt{\mu_0 \varepsilon_0}\ . </math>
 
Using the defined valued for the [http://physics.nist.gov/cgi-bin/cuu/Value?c speed of light] provided by NIST as:
 
::c<sub>0</sub> = 299 792 458 m s <sup>−1</sup>,
 
and the already mentioned defined value for μ<sub>0</sub>, this relationship leads to the exact value given above for ε<sub>0</sub>.
 
Another consequence of these electromagnetic properties is that the ratio of electric to magnetic field strengths in an [[electromagnetic wave]] propagating in free space is an exact value provided by NIST as the [http://physics.nist.gov/cgi-bin/cuu/Value?z0 characteristic impedance of free space]:
 
::Z<sub>0</sub> = 376.730 313 461... ohms.
 
It also can be noted that the electrical permittivity ε<sub>0</sub> and the magnetic permeability μ<sub>0</sub> do not depend upon direction, field strength, polarization, or frequency. Consequently, free space is isotropic, linear, non-dichroic, and dispersion free. Linearity, in particular, implies that the fields and/or potentials due to an assembly of charges is simply the addition of the fields/potentials due to each charge separately (that is, the  principle of superposition applies).<ref name=Pramanik>
{{cite book |title=Electro-Magnetism: Theory and Applications |author=A. Pramanik |url=http://books.google.com/books?id=gnEEwy12S5cC&pg=PT23 |pages=pp. 37-38 |chapter=§1.3 The principle of superposition |isbn=8120319575 |year=2004 |publisher=PHI Learning Pvt. Ltd}}</ref>
 
==References==
{{reflist}}

Latest revision as of 13:47, 27 March 2011

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