Relative permittivity

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The relative permittivity of a material is the permittivity (absolute) expressed as the ratio relative to the permittivity of the vacuum.

Permitivity is a material property that influences the Coulomb force between two point charges in the material. Relative permittivity is a factor where the electric field between the cost is reduced relative to the vacuum.

Likewise, the relative permittivity is the ratio of the capacitance of a capacitor using the material as dielectric, compared to the same capacitor having the vacuum as the dielectric. Relative permittivity is also commonly known as the dielectric constant , the term left in physics and engineering and in chemistry.

Video Relative permittivity

Definisi

Permitivitas relatif biasanya dilambangkan sebagai ? _r (?) (kadang-kadang ? atau K ) under didefinisikan sebagai

${\ displaystyle \ varepsilon _ {r} (\ omega) = {\ frac {\ varepsilon (\ omega)} {\ varepsilon _ 0}} ,} Â Â$

where ? (?) is the absolute permittivity of the complex-dependent frequency of the material, and? ₀ is the permittivity of the vacuum.

Permitivitas relatif adalah nomor tanpa dimensi yang secara umum bernilai kompleks; bagian nyata dan imajinernya dinotasikan sebagai:

${\ displaystyle \ varepsilon _ {r} (\ omega) = \ varepsilon _ {r} '(\ omega) -i \ varepsilon r' '(\ omega).} Â Â$

The relative permittivity of the media is related to its electrical vulnerability, ? _e , such as ? _r (?) = 1? _e .

In anisotropic media (such as non-cubic crystals) relative permittivity is the second rank tensor.

The relative permittivity of a material for zero frequency is known as static relative permittivity .

Terminology

The historical term for relative permittivity is the dielectric constant . It's still commonly used, but has been abandoned by standard organizations, because of its ambiguity, as some older writers use it for absolute permittivity. Permitivity can be quoted either as a static property or as a frequency dependent variant. It has also been used to refer only real components? ' _r of relatively complex-rewarded permittivity.

Physics

In the causal theory of waves, permittivity is a complex quantity. The imaginary part corresponds to the phase shift of the polarization P relative to E and leads to the electromagnetic attenuation of the wave through the medium. By definition, the relative permittivity of the vacuum equals 1, ie? Ã, = Ã,? ₀ , although there is a theoretical nonlinear quantum effect in a vacuum present in high field strength.

The following table gives some typical values.

Maps Relative permittivity

Measurement

Relative static permittivity, ? _r , can be measured for the static electric field as follows: first the capacitance of the test capacitor, C ₀ , measured by the vacuum between the plates. Then, using the capacitor and the same distance between the plates, the capacitance C with the dielectric between the plates is measured. The relative permittivity can be calculated as

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{Â Â Â Â Â Â Â Â Â Â ? Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ C Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ ÂÂ <Â> <Â> Â Â Â Â Â Â Â ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ, Â Â Â Â Â Â Â Â Â ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â . Â Â Â Â Â Â Â Â Â Â Â Â Â Â {\ displaystyle \ varepsilon _ {r} = {\ frac {C} {C_ {0}}}.} Â Â}

For the time-variance electromagnetic field, this quantity becomes frequency dependent. Indirect technique to calculate ? _r is the conversion of radio frequency S-parameter measurement results. Description of the S-parameter conversion frequently used for frequency dependency determination ? _r of the dielectric can be found in this bibliographic source. Alternatively, resonance-based effects can be used at fixed frequencies.

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Apps

Energy

Relative permittivity is an important part of information when designing capacitors, and in other circumstances where the material may be expected to introduce the capacitance into the circuit. If a material with a relatively high permittivity is placed in an electric field, the magnitude of the field will be reduced measurably in the dielectric volume. This fact is usually used to increase the capacitance of a particular capacitor design. Layers beneath the engraved conductors on printed circuit boards (PCBs) also act as dielectrics.

Communications

Dielectric is used in RF transmission line. In coaxial cables, polyethylene can be used between the center conductor and the outer shield. It can also be placed inside waveguides to form filters. Optical fiber is an example of dielectric waveguides . They consist of dielectric material deliberately doped with impurities so as to control precisely the value ? _r in a cross section. It controls the refractive index of the material and therefore also the optical transmission mode. However, in this case technically the important relative permittivity, as they are not operated within the electrostatic boundary.

Environment

The relative permittivity of air changes with temperature, humidity, and air pressure. Sensors can be constructed to detect changes in capacitance caused by changes in relative permittivity. Most of these changes are caused by the effects of temperature and humidity because the barometer pressure is quite stable. By using the change in capacitance, along with the measured temperature, relative humidity can be obtained by using the engineering formula.

Chemistry

The relative static permittivity of a solvent is a relative measure of its chemical polarity. For example, water is very polar, and has a relative static permittivity of 80.10 at 20 Ã, Â ° C while n -hexane is non-polar, and has a relative static permeability of 1.89 at 20Ã, ° C. This information is important when designing the separation, sample preparation and chromatography techniques in analytical chemistry.

Correlations must, however, be treated with caution. For example, has dichloromethane a value? _r of 9.08 (20 Ã, Â ° C) and slightly less water soluble (13 g/L or 9.8 mL/L at 20 Ã, Â ° C); at the same time, tetrahydrofuran has? _r = 7.52 at 22 Â ° C, but it is completely soluble with water. In the case of tetrahydrofuran, the oxygen atom may act as a hydrogen bond acceptor; where dichloromethane can not form hydrogen bonds with water.

This is even more pronounced when comparing the values ​​of acetic acid (6.2528) and the value of iodethane (7.6177). Great numerical values? _r is not surprising in the second case, because the iodine atom is easily polarized; Nevertheless, this does not imply that it is polar, also (electronic polarizability applies over the orientational in this case).

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Lossy media

Securing burning, the same is to complete untuk allowivitas absolutely, permitivitas relatif untuk material lossy dapat diformulasikan sebagai:

${\ displaystyle \ varepsilon _ r} = \ varepsilon _ r} '- {\ frac {i \ sigma} {\ omega \ varepsilon _ {0 }}},} Â Â$

in terms of "dielectric conductivity"? (unit S/m, siemens per meter), which "summarizes all the dissipative effects of the material, it may be the actual [electrical] conductivity caused by migrating carriers and may also refer to the energy loss associated with the dispersion of? real permittivity]] (, p. 8) Expanding corner frequency? = 2? C/? and electric constants ₀ = 1/(Ã,Âμ ₀ c ² ), reducing to:

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{          ?                 Â                           =                  ?                 Â                      ?                -           me         ?         ?         ?         ,               {\ displaystyle \ varepsilon _ {r} = \ varepsilon _ {r} '- i \ sigma \ lambda \ kappa,}  Â}

Where? is the wavelength, c is the speed of light in a vacuum and ? = Ã,Âμ ₀ c/2? ? 60.0 S ^-1 = 60,0? is the new constant introduced (the reciprocal unit of siemens, or ohms, so that it is substantially independent of the unit).

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Metal

Permitivity is usually related to the dielectric material, but the metal is described as having an effective permittivity, with a relatively relative permittivity equal to one. In low frequency regions, extending from radio frequencies to far infrared regions and terahertz, the plasma frequency of electrons is much greater than the frequency of electromagnetic propagation, so that the complex index n of a practical metal is a pure imaginary number.. In a low-frequency regime, the relative permittivity is also almost purely imaginary: it has an enormous imaginary value associated with relatively insignificant conductivity and real value.

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See also

src: file.scirp.org

References

Source of the article : Wikipedia