The dielectric constant the dielectric constant

the value of ε, showing how many times the force of interaction of two electric charges in a medium is less than in vacuum. In an isotropic medium, ε is related to the dielectric susceptibility χ by the relation: ε = 1 + 4π χ. The permittivity of an anisotropic medium is a tensor. The permittivity depends on the frequency of the field; in strong electric fields, the permittivity begins to depend on the field strength.

DIELECTRIC PERMITTIVITY, a dimensionless quantity e, showing how many times the interaction force F between electric charges in a given medium is less than their interaction force F o in vacuum:
e \u003d F about / F.
The dielectric constant shows how many times the field is weakened by the dielectric (cm. DIELECTRIC), quantitatively characterizing the property of a dielectric to be polarized in an electric field.
The value of the relative permittivity of a substance, which characterizes the degree of its polarizability, is determined by the mechanisms of polarization (cm. POLARIZATION). However, the value to a large extent also depends on the state of aggregation of the substance, since during transitions from one state to another, the density of the substance, its viscosity and isotropy change significantly (cm. ISOTROPY).
Dielectric constant of gases
Gaseous substances are characterized by very low densities due to long distances between molecules. Due to this, the polarization of all gases is negligible and the dielectric constant they are close to unity. The polarization of a gas can be purely electronic or dipole if the gas molecules are polar, but in this case, too, the electron polarization is of primary importance. The polarization of various gases is the greater, the larger the radius of the gas molecule, and is numerically close to the square of the refractive index for this gas.
The dependence of a gas on temperature and pressure is determined by the number of molecules per unit volume of the gas, which is proportional to the pressure and inversely proportional to the absolute temperature.
Air under normal conditions has e = 1.0006, and its temperature coefficient has a value of about 2. 10 -6 K -1 .
Dielectric constant of liquid dielectrics
Liquid dielectrics can be composed of non-polar or polar molecules. The e value of non-polar liquids is determined by the electron polarization, so it is small, close to the value of the square of light refraction, and usually does not exceed 2.5. The dependence of e of a non-polar liquid on temperature is associated with a decrease in the number of molecules per unit volume, i.e., with a decrease in density, and its temperature coefficient is close to the temperature coefficient of the volume expansion of the liquid, but differs in sign.
The polarization of liquids containing dipole molecules is determined simultaneously by the electronic and dipole-relaxation components. Such liquids have the greater the dielectric constant, the greater the value of the electric moment of the dipoles (cm. DIPOLE) and the greater the number of molecules per unit volume. The temperature dependence in the case of polar liquids is complex.
Dielectric constant of solid dielectrics
AT solids can take on a variety of numerical values ​​in accordance with the diversity structural features solid dielectric. In solid dielectrics, all types of polarization are possible.
The smallest value of e has solid dielectrics, consisting of non-polar molecules and having only electronic polarization.
Solid dielectrics, which are ionic crystals with dense packing of particles, have electronic and ionic polarizations and have e values ​​that lie in a wide range (e rock salt - 6; e corundum - 10; e rutile - 110; e calcium titanate - 150).
e of various inorganic glasses, approaching the structure of amorphous dielectrics, lies in a relatively narrow range from 4 to 20.
Polar organic dielectrics have a dipole-relaxation polarization in the solid state. e of these materials depends to a large extent on the temperature and frequency of the applied voltage, obeying the same laws as for dipole liquids.

Relative permittivity environment ε - dimensionless physical quantity characterizing the properties of an insulating (dielectric) medium. Associated with the effect of polarization of dielectrics under the action of electric field(and with the dielectric susceptibility of the medium characterizing this effect). The value of ε shows how many times the force of interaction of two electric charges in a medium is less than in vacuum. The relative permittivity of air and most other gases under normal conditions is close to unity (because of their low density). For most solid or liquid dielectrics, the relative permittivity ranges from 2 to 8 (for a static field). The dielectric constant of water in a static field is quite high - about 80. Its values ​​are large for substances with molecules that have a large electric dipole. The relative permittivity of ferroelectrics is tens and hundreds of thousands.

Practical use

The permittivity of dielectrics is one of the main parameters in the design of electrical capacitors. The use of materials with a high dielectric constant can significantly reduce the physical dimensions of capacitors.

The permittivity parameter is taken into account when designing printed circuit boards. The value of the dielectric constant of the substance between the layers in combination with its thickness affects the value of the natural static capacitance of the power layers, and also significantly affects the wave resistance of the conductors on the board.

Frequency dependency

It should be noted that the permittivity depends to a large extent on the frequency of the electromagnetic field. This should always be taken into account, since handbook tables usually contain data for a static field or low frequencies up to several units of kHz without indicating this fact. At the same time, there are also optical methods for obtaining the relative permittivity from the refractive index using ellipsometers and refractometers. The value obtained by the optical method (frequency 10 14 Hz) will differ significantly from the data in the tables.

Consider, for example, the case of water. In the case of a static field (frequency is zero), the relative permittivity under normal conditions is approximately 80. This is the case up to infrared frequencies. Starting around 2 GHz εr starts to fall. In the optical range εr is approximately 1.8. This is consistent with the fact that in the optical range the refractive index of water is 1.33. In a narrow frequency range, called optical, dielectric absorption drops to zero, which actually provides a person with a mechanism of vision in the earth's atmosphere saturated with water vapor. As the frequency increases further, the properties of the medium change again.

Dielectric Constant Values ​​for Some Substances

Relative permittivity

Relative permittivity environment ε is a dimensionless physical quantity that characterizes the properties of an insulating (dielectric) medium. It is connected with the effect of polarization of dielectrics under the action of an electric field (and with the value of the dielectric susceptibility of the medium characterizing this effect). The value of ε shows how many times the interaction force of two electric charges in a medium is less than in vacuum. The relative permittivity of air and most other gases under normal conditions is close to unity (because of their low density). For most solid or liquid dielectrics, the relative permittivity ranges from 2 to 8 (for a static field). The dielectric constant of water in a static field is quite high - about 80. Its values ​​are large for substances with molecules that have a large electric dipole. The relative permittivity of ferroelectrics is tens and hundreds of thousands.

Measurement

Relative permittivity of a substance εr can be determined by comparing the capacitance of a test capacitor with a given dielectric (C x) and the capacitance of the same capacitor in vacuum (C o):

Practical use

The permittivity of dielectrics is one of the main parameters in the design of electrical capacitors. The use of materials with a high dielectric constant can significantly reduce the physical dimensions of capacitors.

The capacitance of capacitors is determined:

where εr is the permittivity of the substance between the plates, ε o- electric constant, S- the area of ​​the capacitor plates, d- distance between plates.

The permittivity parameter is taken into account when designing printed circuit boards. The value of the dielectric constant of the substance between the layers in combination with its thickness affects the value of the natural static capacitance of the power layers, and also significantly affects the wave resistance of the conductors on the board.

Frequency dependency

It should be noted that the permittivity depends to a large extent on the frequency of the electromagnetic field. This should always be taken into account, since handbook tables usually contain data for a static field or low frequencies up to several units of kHz without indicating this fact. At the same time, there are also optical methods for obtaining the relative permittivity from the refractive index using ellipsometers and refractometers. The value obtained by the optical method (frequency 10 14 Hz) will differ significantly from the data in the tables.

Consider, for example, the case of water. In the case of a static field (frequency is zero), the relative permittivity under normal conditions is approximately 80. This is the case up to infrared frequencies. Starting around 2 GHz εr starts to fall. In the optical range εr is approximately 1.8. This is consistent with the fact that in the optical range the refractive index of water is 1.33. In a narrow frequency range, called optical, dielectric absorption drops to zero, which actually provides a person with a mechanism of vision in the earth's atmosphere saturated with water vapor. As the frequency increases further, the properties of the medium change again. The behavior of the relative permittivity of water in the frequency range from 0 to 10 12 (infrared) can be read at (eng.)

Notes

see also

• Vacuum permittivity (electrical constant)

Dielectric Constant Values ​​for Some Substances

The dielectric constant environment - a physical quantity that characterizes the properties of an insulating (dielectric) medium and shows the dependence of electric induction on the strength of an electric field.

It is determined by the effect of polarization of dielectrics under the action of an electric field (and with the value of the dielectric susceptibility of the medium characterizing this effect).

There are relative and absolute permittivities.

The relative permittivity ε is dimensionless and shows how many times the interaction force of two electric charges in a medium is less than in vacuum. This value for air and most other gases under normal conditions is close to unity (because of their low density). For most solid or liquid dielectrics, the relative permittivity ranges from 2 to 8 (for a static field). The dielectric constant of water in a static field is quite high - about 80. Its values ​​are large for substances with molecules that have a large electric dipole moment. The relative permittivity of ferroelectrics is tens and hundreds of thousands.

The absolute permittivity in foreign literature is denoted by the letter , in the domestic literature, the combination is mainly used ε ε 0 (\displaystyle ~(\varepsilon )(\varepsilon )_(0)), where is the electric constant. Absolute permittivity is used only in the International System of Units (SI), in which induction and electric field strength are measured in different units. In the CGS system, there is no need to introduce the absolute permittivity. The absolute dielectric constant (as well as the electric constant) has the dimension L −3 M −1 T 4 I². In units of the International System of Units (SI) : [ ε 0 (\displaystyle ~(\varepsilon )_(0))]= / .

Encyclopedic YouTube

• 1 / 5

  Generally speaking, the permittivity is a tensor determined from the following relations (the notation uses the Einstein convention):

  D i = ε 0 ε i j E j (\displaystyle ~D_(i)=\varepsilon _(0)\varepsilon _(ij)E_(j)) D = ε a E (\displaystyle ~\mathbf (D) =(\boldsymbol (\varepsilon ))_(a)\mathbf (E) ) E = E 1 e 1 + E 2 e 2 + E 3 e 3 (\displaystyle ~\mathbf (E) =E_(1)\mathbf (e) _(1)+E_(2)\mathbf (e) _ (2)+E_(3)\mathbf (e) _(3))- electric field strength vector, D = D 1 e 1 + D 2 e 2 + D 3 e 3 (\displaystyle ~\mathbf (D) =D_(1)\mathbf (e) _(1)+D_(2)\mathbf (e) _ (2)+D_(3)\mathbf (e) _(3))- electric induction vector, ε a = ε 0 ((ε a) i j) (\displaystyle ~(\boldsymbol (\varepsilon ))_(a)=\varepsilon _(0)((\varepsilon _(a))_(ij))) is the absolute permittivity tensor.

  E = E 0 e i ω t ⇒ ∂ E ∂ t = i ω E (\displaystyle ~\mathbf (E) =\mathbf (E) _(0)e^(i\omega t)\ \Rightarrow \ (\frac (\partial \mathbf (E) )(\partial t))=i\omega \mathbf (E) )

  Measurement

  Relative permittivity of a substance εr can be determined by comparing the capacitance of a test capacitor with a given dielectric (C x) and the capacitance of the same capacitor in vacuum (C o):

  ε r = C x C 0 . (\displaystyle \varepsilon _(r)=(\frac (C_(x))(C_(0))).)

  Practical use

  The permittivity of dielectrics is one of the main parameters in the development of electrical capacitors. The use of materials with a high dielectric constant can significantly reduce the physical dimensions of capacitors.

  The capacitance of capacitors is determined:

  C = ε r ε 0 S d , (\displaystyle C=\varepsilon _(r)\varepsilon _(0)(\frac (S)(d)),)

  where εr is the permittivity of the substance between the plates, ε o- electric constant, S- the area of ​​the capacitor plates, d- distance between plates.

  The dielectric constant parameter is taken into account when developing printed circuit boards. The value of the dielectric constant of the substance between the layers in combination with its thickness affects the value of the natural static capacitance of the power layers, and also significantly affects the wave resistance of the conductors on the board.

  
  
  

  We advise you to read

  • Psychological characteristics of children in adolescence
  • Transferring a child to another school - the procedure and necessary documents Whether to transfer a child to another school
  • Chlamydia urogenital - description, causes, symptoms (signs), diagnosis, treatment Treatment of urogenital chlamydia
  • The benefits and significance of hydroamino acid threonine for the human body L threonine what