Free space (electromagnetism): Difference between revisions
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===Classical case=== | ===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 | 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> | ::ε<sub>0</sub> ≈ 8.854 187 817... × 10<sup>−12</sup> F m<sup>−1</sup> | ||
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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. | 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 | 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.}} | ||
Another consequence is that the ratio of electric to magnetic field strengths in an [[electromagnetic wave]] propagating in free space is a | </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 a 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. | ::Z<sub>0</sub> = 376.730 313 461... ohms. | ||
Revision as of 18:55, 24 November 2010
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,[1] 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.[2] 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.[3] The description of free space varies somewhat among authors, with some authors requiring only the absence of substances with electrical properties,[4] or of charged matter (ions and electrons, for example).[5]
Classical case
In the classical case, free space is characterized by the electrical permittivity ε0 and the magnetic permeability μ0 with an exact value provided by NIST as the electric constant and a defined value as the magnetic constant respectively.[1]
- ε0 ≈ 8.854 187 817... × 10−12 F m−1
- μ0 = 4π × 10−7 ≈ 12.566 370 614... x 10−7 N A−2
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 ε0 and μ0 via the relation:[6]
Using the defined valued for the speed of light provided by NIST as:
- c0 = 299 792 458 m s −1,
and the already mentioned defined value for μ0, this relationship leads to the exact value given above for ε0.
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 a exact value provided by NIST as the characteristic impedance of free space:
- Z0 = 376.730 313 461... ohms.
It also can be noted that the electrical permittivity ε0 and the magnetic permeability μ0 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).[7]
References
- ↑ 1.0 1.1 Werner S. Weiglhofer and Akhlesh Lakhtakia (2003). “§4.1: The classical vacuum as reference medium”, Introduction to complex mediums for optics and electromagnetics. SPIE Press. ISBN 0819449474.
- ↑ Ramamurti Shankar (1994). Principles of quantum mechanics, 2nd ed.. Springer, p. 507. ISBN 0306447908.
- ↑ Werner Vogel, Dirk-Gunnar Welsch (2006). Quantum optics, 3rd ed.. Wiley-VCH, p. 337. ISBN 3527405070.
- ↑ RK Pathria (2003). The Theory of Relativity, Reprint of Hindustan 1974 2nd ed.. Courier Dover Publications, p. 119. ISBN 0486428192.
- ↑ (1992) Christopher G. Morris, editor: Academic Press dictionary of science and technology. Academic, p. 880. ISBN 0122004000.
- ↑ Albrecht Unsöld, B. Baschek (2001). “§4.1: Electromagnetic radiation, Equation 4.3”, The new cosmos: an introduction to astronomy and astrophysics, 5th ed.. Springer, p. 101. ISBN 3540678778.
- ↑ A. Pramanik (2004). “§1.3 The principle of superposition”, Electro-Magnetism: Theory and Applications. PHI Learning Pvt. Ltd, pp. 37-38. ISBN 8120319575.