WikiMili The Free Encyclopedia

The **impedance of free space**, *Z*_{0}, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, *Z*_{0} = |**E**|/|**H**|, where |**E**| is the electric field strength and |**H**| is the magnetic field strength. Its presently accepted value is

A **physical constant**, sometimes **fundamental physical constant** or **universal constant**, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

In physics, **electromagnetic radiation** refers to the waves of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.

- Terminology
- Relation to other constants
- Historical exact value
- Approximation as 120π ohms
- See also
- References and notes
- Further reading

*Z*_{0}= 376.730313667(57) Ω.^{ [1] }

The impedance of free space (that is the wave impedance of a plane wave in free space) is equal to the product of the vacuum permeability *μ*_{0} and the speed of light in vacuum *c*_{0}. Before 2019, the values of both these constants were taken to be exact (they were given in the definitions of the ampere and the metre respectively), and the value of the impedance of free space was therefore likewise taken to be exact. However, with the redefinition of the SI base units which came into force on May 20, 2019, the impedance of free space is subject to experimental measurement because only the speed of light in vacuum *c*_{0} retains an exactly defined value.

In physics, a **plane wave** is a special case of wave or field: a physical quantity whose value, at any moment, is constant over any plane that is perpendicular to a fixed direction in space.

The physical constant *μ*_{0},, commonly called the **vacuum permeability**, **permeability of free space**, **permeability of vacuum**, or **magnetic constant**, is the magnetic permeability in a classical vacuum. *Vacuum permeability* is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field production in a vacuum.

The **speed of light** in vacuum, commonly denoted * c*, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 metres per second. It is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 second. According to special relativity,

The analogous quantity for a plane wave travelling through a dielectric medium is called the * intrinsic impedance * of the medium, and designated *η* (eta). Hence *Z*_{0} is sometimes referred to as the *intrinsic impedance of free space *,^{ [2] } and given the symbol *η*_{0}.^{ [3] } It has numerous other synonyms, including:

A **dielectric** is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing **dielectric polarization**. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

An **optical medium** is material through which electromagnetic waves propagate. It is a form of transmission medium. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. The medium has an *intrinsic impedance*, given by

**Eta** is the seventh letter of the Greek alphabet. Originally denoting a consonant /h/, its sound value in the classical Attic dialect of Ancient Greek was a long vowel, raised to [i] in hellenistic Greek, a process known as iotacism.

*wave impedance of free space*,^{ [4] }*the vacuum impedance*,^{ [5] }*intrinsic impedance of vacuum*,^{ [6] }*characteristic impedance of vacuum*,^{ [7] }*wave resistance of free space*.^{ [8] }

From the above definition, and the plane wave solution to Maxwell's equations,

**Maxwell's equations** are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (*c*) in the vacuum, the "speed of light". Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations that included the Lorentz force law. He also first used the equations to propose that light is an electromagnetic phenomenon.

where

*μ*_{0}is the magnetic constant,*ε*_{0}is the electric constant,*c*_{0}is the speed of light in free space.^{ [9] }^{ [10] }

The reciprocal of *Z*_{0} is sometimes referred to as the *admittance of free space* and represented by the symbol *Y*_{0}.

Between 1948 and 2019, the SI unit the ampere was defined by *choosing* the numerical value of *μ*_{0} to be exactly 4π × 10^{−7} H/m. Similarly, since 1983 the SI metre has been defined relative to the second by *choosing* the value of *c*_{0} to be 299792458 m/s. Consequently,

The **ampere**, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

The **henry** is the SI derived unit of electrical inductance. If a current of 1 ampere flowing through the coil produces flux linkage of 1 weber turn, the coil has a self inductance of 1 henry. The unit is named after Joseph Henry (1797–1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday (1791–1867) in England.

The **metre** or **meter** is the base unit of length in the International System of Units (SI). The SI unit symbol is **m**. The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second.

*exactly*,

or

This chain of dependencies changed when the ampere was redefined on 20 May 2019.

It is very common in textbooks and papers written before about 1990 to substitute the approximate value 120π ohms for *Z*_{0}. This is equivalent to taking the speed of light *c*_{0} to be precisely 3×10^{8} m/s in conjunction with the then-current definition of *μ*_{0} as 4π × 10^{−7} H/m. For example, Cheng 1989 states^{ [3] } that the radiation resistance of a Hertzian dipole is

- (
*not exact*).

This practice may be recognized from the resulting discrepancy in the units of the given formula. Consideration of the units, or more formally dimensional analysis, may be used to restore the formula to a more exact form, in this case to

- ↑ Derived from
*Z*_{0}=*μ*_{0}*c*– "2018 CODATA Value: magnetic constant".*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 2019-05-20. - ↑ Haslett, Christopher J. (2008).
*Essentials of radio wave propagation*. The Cambridge wireless essentials series. Cambridge University Press. p. 29. ISBN 978-0-521-87565-3. - 1 2 David K Cheng (1989).
*Field and wave electromagnetics*(Second ed.). New York: Addison-Wesley. ISBN 0-201-12819-5. - ↑ Guran, Ardéshir; Mittra, Raj; Moser, Philip J. (1996).
*Electromagnetic wave interactions*. Series on stability, vibration, and control of systems. World Scientific. p. 41. ISBN 978-981-02-2629-9. - ↑ Clemmow, P. C. (1973).
*An introduction to electromagnetic theory*. University Press. p. 183. ISBN 978-0-521-09815-1. - ↑ Kraus, John Daniel (1984).
*Electromagnetics*. McGraw-Hill series in electrical engineering. McGraw-Hill. p. 396. ISBN 978-0-07-035423-4. - ↑ Cardarelli, François (2003).
*Encyclopaedia of scientific units, weights, and measures: their SI equivalences and origins*. Springer. p. 49. ISBN 978-1-85233-682-0. - ↑ Ishii, Thomas Koryu (1995).
*Handbook of Microwave Technology: Applications*. Academic Press. p. 315. ISBN 978-0-12-374697-9. - ↑ With ISO 31-5, NIST and the BIPM have adopted the notation
*c*_{0}for the speed of light in free space. - ↑ "Current practice is to use
*c*_{0}to denote the speed of light in vacuum according to ISO 31. In the original Recommendation of 1983, the symbol*c*was used for this purpose." Quote from NIST*Special Publication 330*, Appendix 2, p. 45.

- John David Jackson (1998).
*Classical electrodynamics*(Third ed.). New York: Wiley. ISBN 0-471-30932-X.

The **centimetre–gram–second system of units** is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism.

The **wave impedance** of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields. For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium. In particular, for a plane wave travelling through empty space, the wave impedance is equal to the impedance of free space. The symbol *Z* is used to represent it and it is expressed in units of ohms. The symbol *η* (eta) may be used instead of *Z* for wave impedance to avoid confusion with electrical impedance.

**Coaxial cable**, or **coax** is a type of electrical cable that has an inner conductor surrounded by a tubular insulating layer, surrounded by a tubular conducting shield. Many coaxial cables also have an insulating outer sheath or jacket. The term coaxial comes from the inner conductor and the outer shield sharing a geometric axis. Coaxial cable was invented by English physicist, engineer, and mathematician Oliver Heaviside, who patented the design in 1880.

In electromagnetism, **absolute permittivity**, often simply called **permittivity**, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

In the physical sciences, the **wavenumber** is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.

**Skin effect** is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor, and decreases with greater depths in the conductor. The electric current flows mainly at the "skin" of the conductor, between the outer surface and a level called the **skin depth**. The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. The skin effect is due to opposing eddy currents induced by the changing magnetic field resulting from the alternating current. At 60 Hz in copper, the skin depth is about 8.5 mm. At high frequencies the skin depth becomes much smaller. Increased AC resistance due to the skin effect can be mitigated by using specially woven litz wire. Because the interior of a large conductor carries so little of the current, tubular conductors such as pipe can be used to save weight and cost.

In electromagnetism, **permeability** is the measure of the ability of a material to support the formation of a magnetic field within itself, otherwise known as distributed inductance in Transmission Line Theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter *µ*. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.

In electromagnetics, the **antenna factor** is defined as the ratio of the electric field strength to the voltage *V* induced across the terminals of an antenna. The voltage measured at the output terminals of an antenna is not the actual field intensity due to actual antenna gain, aperture characteristics, and loading effects.

The physical constant ** ε_{0}**, commonly called the

The **electromagnetic wave equation** is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field **E** or the magnetic field **B**, takes the form:

**Antenna measurement** techniques refers to the testing of antennas to ensure that the antenna meets specifications or simply to characterize it. Typical parameters of antennas are gain, radiation pattern, beamwidth, polarization, and impedance.

**Lorentz–Heaviside units** constitute a system of units within CGS, named from Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that the electric constant *ε*_{0} and magnetic constant *µ*_{0} do not appear, having been incorporated implicitly into the unit system and electromagnetic equations. Lorentz–Heaviside units may be regarded as normalizing *ε*_{0} = 1 and *µ*_{0} = 1, while at the same time revising Maxwell's equations to use the speed of light *c* instead.

The word *electricity* refers generally to the movement of electrons through a conductor in the presence of potential and an electric field. The speed of this flow has multiple meanings. In everyday electrical and electronic devices, the signals or energy travel as electromagnetic waves typically on the order of 50%–99% of the speed of light, while the electrons themselves move (drift) much more slowly.

When an electromagnetic wave travels through a medium in which it gets attenuated, it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated. This article describes the mathematical relationships among:

In particle physics and physical cosmology, **Planck units** are a set of units of measurement defined exclusively in terms of five universal physical constants, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units.

In optics, the **Ewald–Oseen extinction theorem**, sometimes referred to as just "extinction theorem", is a theorem that underlies the common understanding of scattering. It is named after Paul Peter Ewald and Carl Wilhelm Oseen, who proved the theorem in crystalline and isotropic media, respectively, in 1916 and 1915. Originally, the theorem applied to scattering by an isotropic dielectric objects in free space. The scope of the theorem was greatly extended to encompass a wide variety of bianisotropic media.

A **loop-gap resonator** (**LGR**) is an electromagnetic resonator that operates in the radio and microwave frequency ranges. The simplest LGRs are made from a conducting tube with a narrow slit cut along its length. The LGR dimensions are typically much smaller than the free-space wavelength of the electromagnetic fields at the resonant frequency. Therefore, relatively compact LGRs can be designed to operate at frequencies that are too low to be accessed using, for example, cavity resonators. These structures can have very sharp resonances making them useful for electron spin resonance (ESR) experiments and precision measurements of electromagnetic material properties.

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.