How is the dielectric constant of a substance measured? Permittivity

Dielectrić chemical penetratioń capacity medium - a physical quantity characterizing the properties of an insulating (dielectric) medium and showing the dependence of electrical induction on voltage electric field.

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

There are relative and absolute dielectric constants.

The relative dielectric constant ε is dimensionless and shows how many times the force of interaction between two electric charges in a medium is less than in a vacuum. This value for air and most other gases under normal conditions is close to unity (due to 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 dielectric constant of ferroelectrics is tens and hundreds of thousands.

The absolute dielectric constant in foreign literature is denoted by the letter ε; in domestic literature, the combination is predominantly used, where is the electric constant. Absolute dielectric constant is used only in the International System of Units (SI), in which induction and electric field strength are measured in different units. In the SGS system there is no need to introduce absolute dielectric constant. The absolute dielectric constant (like the electrical constant) has the dimension L −3 M −1 T 4 I². In International System of Units (SI) units: =F/m.

It should be noted that the dielectric constant largely depends on the frequency electromagnetic field. This should always be taken into account since reference tables usually contain data for a static field or low frequencies down to a few units of kHz without specifying this fact. At the same time, there are optical methods for obtaining the relative dielectric constant based on the refractive index using ellipsometers and refractometers. Received optical method(frequency 10-14 Hz) the value will differ significantly from the data in the tables.

Consider, for example, the case of water. In the case of a static field (frequency zero), the relative dielectric constant under normal conditions is approximately 80. This is the case down to infrared frequencies. Starting at approximately 2 GHz ε r starts to fall. In the optical range ε r is approximately 1.8. This is quite 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 the mechanism of vision [ source not specified 1252 days] in the earth's atmosphere saturated with water vapor. WITH further growth frequency properties of the medium change again. You can read about the behavior of the relative dielectric constant of water in the frequency range from 0 to 10 12 (infrared region) at (English)

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

The capacitance of the capacitors is determined:

Where ε r- dielectric constant of the substance between the plates, ε O- electrical constant, S- area of ​​the capacitor plates, d- distance between the 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 characteristic impedance of the conductors on the board.

RESISTANCE electrical, physical quantity equal to electrical resistance ( cm. ELECTRICAL RESISTANCE) R of a cylindrical conductor of unit length (l = 1 m) and unit cross-sectional area (S = 1 m 2).. r = R S/l. In Si, the unit of resistivity is Ohm. m. Resistivity can also be expressed in Ohms. cm. Resistivity is a characteristic of the material through which current flows and depends on the material from which it is made. Resistivity equal to r = 1 Ohm. m means that a cylindrical conductor made of this material, length l = 1 m and with a cross-sectional area S = 1 m 2 has a resistance R = 1 Ohm. m. The value of resistivity of metals ( cm. METALS), which are good conductors ( cm. CONDUCTORS), can have values ​​of the order of 10 - 8 – 10 - 6 Ohms. m (for example, copper, silver, iron, etc.). The resistivity of some solid dielectrics ( cm. DIELECTRICS) can reach a value of 10 16 -10 18 Ohm.m (for example, quartz glass, polyethylene, electroporcelain, etc.). The resistivity value of many materials (especially semiconductor materials ( cm. SEMICONDUCTOR MATERIALS)) significantly depends on the degree of their purification, the presence of alloying additives, thermal and mechanical treatments, etc. The value s, the reciprocal of the resistivity, is called conductivity: s = 1/r Specific conductivity is measured in siemens ( cm. SIEMENS (conductivity unit)) per meter S/m. Electrical resistivity (conductivity) is a scalar quantity for an isotropic substance; and tensor - for an anisotropic substance. In anisotropic single crystals, the anisotropy of electrical conductivity is a consequence of the anisotropy of the inverse effective mass ( cm. EFFECTIVE MASS) electrons and holes.

1-6. ELECTRICAL CONDUCTIVITY OF INSULATION

When turning on the insulation of a cable or wire on constant voltage U a current i passes through it, varying with time (Fig. 1-3). This current has constant components - conduction current (i ∞) and absorption current, where γ is the conductivity corresponding to the absorption current; T is the time during which the current i abs drops to 1/e of its original value. For infinitely long time i abs →0 and i = i ∞. The electrical conductivity of dielectrics is explained by the presence in them of a certain amount of free charged particles: ions and electrons.

The most characteristic feature of most electrical insulating materials is ionic electrical conductivity, which is possible due to contaminants inevitably present in the insulation (impurities of moisture, salts, alkalis, etc.). In a dielectric with an ionic conductivity, Faraday's law is strictly observed - the proportionality between the amount of electricity passing through the insulation and the amount of substance released during electrolysis.

As the temperature increases, the resistivity of electrical insulating materials decreases and is characterized by the formula

where_ρ o, A and B are constants for a given material; T - temperature, °K.

A greater dependence of insulation resistance on moisture occurs with hygroscopic insulating materials, mainly fibrous (paper, cotton yarn, etc.). Therefore, fibrous materials are dried and impregnated, as well as protected by moisture-resistant shells.

Insulation resistance can decrease with increasing voltage due to the formation of space charges in the insulating materials. The additional electronic conductivity created in this case leads to an increase in electrical conductivity. There is a dependence of conductivity on voltage in a very strong fields(law of Ya. I. Frenkel):

where γ o - conductivity in weak fields; a is constant. All electrical insulating materials are characterized by certain values ​​of insulation conductivity G. Ideally, the conductivity of insulating materials is zero. For real insulating materials, the conductivity per unit cable length is determined by the formula

In cables with an insulation resistance of more than 3-10 11 ohm-m and communication cables, where losses due to dielectric polarization are significantly greater than thermal losses, conductivity is determined by the formula

Insulation conductivity in communications technology is an electrical parameter of a line that characterizes energy loss in the insulation of cable cores. The dependence of the conductivity value on frequency is shown in Fig. 1-1. The reciprocal of conductivity - insulation resistance, is the ratio of the applied insulation voltage DC(in volts) who is leaking (in amperes), i.e.

where R V is the volumetric insulation resistance, which numerically determines the obstacle created by the passage of current through the thickness of the insulation; R S - surface resistance, which determines the obstacle to the passage of current along the insulation surface.

A practical assessment of the quality of the insulating materials used is the specific volumetric resistance ρ V expressed in ohm-centimeters (ohm*cm). Numerically, ρ V is equal to the resistance (in ohms) of a cube with an edge of 1 cm made of a given material, if the current passes through two opposite faces Cuba. Specific surface resistance ρ S is numerically equal to the surface resistance of the square (in ohms) if current is supplied to the electrodes delimiting two opposite sides of this square.

The insulation resistance of a single-core cable or wire is determined by the formula

Humidity properties of dielectrics

Moisture resistance – this is the reliability of the insulation when it is in an atmosphere of water vapor close to saturation. Moisture resistance is assessed by changes in electrical, mechanical and other physical properties after the material is in an atmosphere with high and high humidity; on moisture and water permeability; on moisture and water absorption.

Moisture permeability – the ability of a material to transmit moisture vapor in the presence of a difference in relative air humidity on both sides of the material.

Moisture absorption – the ability of a material to sorb water when exposed for a long time in a humid atmosphere close to a state of saturation.

Water absorption – the ability of a material to absorb water when immersed in water for a long time.

Tropical resistance and tropicalization equipment protection of electrical equipment from moisture, mold, rodents.

Thermal properties of dielectrics

To characterize the thermal properties of dielectrics, the following quantities are used.

Heat resistance– the ability of electrical insulating materials and products to withstand high temperatures without harm to them and abrupt changes temperature. Determined by the temperature at which a significant change in mechanical and electrical properties For example, in organic dielectrics tensile or bending deformation begins under load.

Thermal conductivity– the process of heat transfer in a material. It is characterized by an experimentally determined thermal conductivity coefficient λ t. λ t is the amount of heat transferred in one second through a layer of material 1 m thick and a surface area of ​​1 m 2 with a temperature difference between the surfaces of the layer of 1 °K. The thermal conductivity coefficient of dielectrics varies over a wide range. The lowest values ​​of λ t have gases, porous dielectrics and liquids (for air λ t = 0.025 W/(m K), for water λ t = 0.58 W/(m K)), high values have crystalline dielectrics (for crystalline quartz λ t = 12.5 W/(m K)). The thermal conductivity coefficient of dielectrics depends on their structure (for fused quartz λ t = 1.25 W/(m K)) and temperature.

Thermal expansion dielectrics are assessed by the temperature coefficient of linear expansion: . Materials with low thermal expansion, as a rule, have higher heat resistance and vice versa. Thermal expansion of organic dielectrics significantly (tens and hundreds of times) exceeds the expansion of inorganic dielectrics. Therefore, the dimensional stability of parts made of inorganic dielectrics during temperature fluctuations is significantly higher compared to organic ones.

1. Absorption currents

Absorption currents are displacement currents of various types of slow polarization. Absorption currents at a constant voltage flow in the dielectric until an equilibrium state is established, changing their direction when the voltage is turned on and off. With an alternating voltage, absorption currents flow during the entire time the dielectric is in the electric field.

In general, electric current j in a dielectric is the sum of the through current j sk and absorption current j ab

j = j sk + j ab.

The absorption current can be determined through the bias current j cm - rate of change of the electrical induction vector D

The through current is determined by the transfer (movement) of various charge carriers in the electric field.

2. Electronic electrical conductivity is characterized by the movement of electrons under the influence of a field. In addition to metals, it is present in carbon, metal oxides, sulfides and other substances, as well as in many semiconductors.

3. Ionic – caused by the movement of ions. It is observed in solutions and melts of electrolytes - salts, acids, alkalis, as well as in many dielectrics. It is divided into intrinsic and impurity conductivity. Intrinsic conductivity is due to the movement of ions obtained during dissociation molecules. The movement of ions in an electric field is accompanied by electrolysis – transfer of a substance between electrodes and its release on the electrodes. Polar liquids are more dissociated and have higher electrical conductivity than non-polar liquids.

In nonpolar and weakly polar liquid dielectrics (mineral oils, silicone liquids), electrical conductivity is determined by impurities.

4. Molion electrical conductivity – caused by the movement of charged particles called molions. It is observed in colloidal systems, emulsions , suspensions . The movement of molions under the influence of an electric field is called electrophoresis. During electrophoresis, unlike electrolysis, no new substances are formed; the relative concentration of the dispersed phase in different layers of the liquid changes. Electrophoretic conductivity is observed, for example, in oils containing emulsified water.

Electrical permeability

Electrical permeability is a quantity characterizing the capacitance of a dielectric placed between the plates of a capacitor. As is known, the capacitance of a flat-plate capacitor depends on the area of ​​the plates (than larger area plates, the greater the capacitance), the distance between the plates or the thickness of the dielectric (the thicker the dielectric, the smaller the capacitance), as well as on the dielectric material, the characteristic of which is the electrical permeability.

Numerically, the electrical permittivity is equal to the ratio of the capacitance of the capacitor with any dielectric of the same air capacitor. To create compact capacitors, it is necessary to use dielectrics with high electrical permittivity. The electrical permittivity of most dielectrics is several units.

Dielectrics with high and ultra-high electrical permeability have been obtained in technology. Their main part is rutile (titanium dioxide).

Figure 1. Electrical permeability of the medium

Dielectric loss angle

In the article "Dielectrics" we looked at examples of including a dielectric in DC and DC circuits. AC. It turned out that in a real dielectric, when it operates in an electric field formed by an alternating voltage, thermal energy is released. The power absorbed in this case is called dielectric losses. In the article “An alternating current circuit containing capacitance” it will be proven that in an ideal dielectric the capacitive current leads the voltage by an angle less than 90°. In a real dielectric, capacitive current leads voltage by an angle less than 90°. The decrease in angle is influenced by leakage current, otherwise called conduction current.

The difference between 90° and the shift angle between voltage and current passing in a circuit with a real dielectric is called the dielectric loss angle or loss angle and is denoted δ (delta). More often it is not the angle itself that is determined, but the tangent of this angle -tan δ.

It has been established that dielectric losses are proportional to the square of the voltage, the frequency of the alternating current, the capacitance of the capacitor and the tangent of the dielectric loss angle.

Consequently, the greater the dielectric loss tangent, tan δ, the more loss energy in the dielectric, the worse the dielectric material. Materials with a relatively large tg δ (of the order of 0.08 - 0.1 or more) are poor insulators. Materials with a relatively small tan δ (about 0.0001) are good insulators.

Permittivity permittivity

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

PERMITTIVITY

DIELECTRIC CONTINUITY, 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 a vacuum:
e =F o /F.
Dielectric constant shows how many times the field is attenuated by the dielectric (cm. DIELECTRICS), quantitatively characterizing the property of a dielectric to be polarized in an electric field.
The value of the relative dielectric constant of a substance, which characterizes the degree of its polarizability, is determined by the polarization mechanisms (cm. POLARIZATION). However, the value largely depends on state of aggregation substances, 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 insignificant and their dielectric constant is close to unity. The polarization of a gas can be purely electronic or dipole if the gas molecules are polar, however, in this case, the electronic polarization is of primary importance. The polarization of various gases is greater, the more larger radius molecules of a gas, 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 gas, which is proportional to pressure and inversely proportional to absolute temperature.
The air in normal conditions e =1.0006, and its temperature coefficient is about 2. 10 -6 K -1 .
Dielectric constant of liquid dielectrics
Liquid dielectrics can consist of non-polar or polar molecules. The e value of non-polar liquids is determined by electronic polarization, so it is small, close to the value of the square of the refraction of light 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 temperature coefficient volumetric expansion of the liquid, but differs in sign.
Polarization of liquids containing dipole molecules, is determined simultaneously by the electronic and dipole-relaxation components. Such liquids have a higher dielectric constant the more more value electric moment of dipoles (cm. DIPOLE) and with what larger number molecules per unit volume. The temperature dependence in the case of polar liquids is complex.
Dielectric constant of solid dielectrics
IN solids ah can take a variety of numeric values according to diversity structural features solid dielectric. In solid dielectrics all types of polarization are possible.
The smallest value of e is found in 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 ion polarizations and have e values ​​that lie within 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 dipole-relaxation polarization in the solid state. e of these materials in to a large extent depends on the temperature and frequency of the applied voltage, obeying the same laws as for dipole liquids.


Encyclopedic Dictionary. 2009 .

See what “dielectric constant” is in other dictionaries:

    The value of e, showing how many times the force of interaction between two electric charges in a medium is less than in a vacuum. In an isotropic medium, e is related to the dielectric susceptibility with the relation: e = 1 + 4pc. Dielectric constant... ... Big Encyclopedic Dictionary

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    DIELECTRIC CONTINUITY, The value e, showing how many times the force of interaction of two electric charges in a medium is less than in a vacuum. The value of e varies widely: hydrogen 1.00026, transformer oil 2.24, ... ... Modern encyclopedia

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    permittivity- A quantity characterizing the dielectric properties of a substance, scalar for an isotropic substance and tensor for an anisotropic substance, the product of which by the electric field strength is equal to the electric displacement. [GOST R 52002 2003]… … Technical Translator's Guide

    Permittivity- DIELECTRIC CONTINUITY, the value e, showing how many times the force of interaction of two electric charges in a medium is less than in a vacuum. The value of e varies widely: hydrogen 1.00026, transformer oil 2.24, ... ... Illustrated Encyclopedic Dictionary

    Permittivity- a quantity characterizing the dielectric properties of a substance, scalar for an isotropic substance and tensor for an anisotropic substance, the product of which by the electric field strength is equal to the electric displacement... Source:... ... Official terminology

    permittivity- absolute dielectric constant; industry permittivity Scalar quantity, characterizing the electrical properties of the dielectric equal to the ratio quantities electrical displacement to the magnitude of the electric field strength... Polytechnic terminological explanatory dictionary

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Books

  • Properties of materials. Anisotropy, symmetry, structure. Per. from English , Newnham R.E. This book is devoted to anisotropy and the relationship between the structure of materials and their properties. It covers a wide range of topics and is a kind introductory course physical properties...

The level of polarizability of a substance is characterized by a special value called dielectric constant. Let's consider what this value is.

Let us assume that the tension uniform field between two charged plates in a vacuum is equal to E₀. Now let's fill the gap between them with any dielectric. which appear at the boundary between the dielectric and the conductor due to its polarization, partially neutralize the effect of charges on the plates. Tension E of this field the tension E₀ will become less.

Experience reveals that when the gap between the plates is sequentially filled with equal dielectrics, the field strengths will be different. Therefore, knowing the value of the ratio of the electric field strength between the plates in the absence of dielectric E₀ and in the presence of dielectric E, one can determine its polarizability, i.e. its dielectric constant. This quantity is usually denoted Greek letterԑ (epsilon). Therefore, we can write:

The dielectric constant shows how many times less of these charges in a dielectric (homogeneous) will be than in a vacuum.

The decrease in the force of interaction between charges is caused by processes of polarization of the medium. In an electric field, electrons in atoms and molecules are reduced in relation to ions, and i.e. appears. those molecules that have their own dipole moment(in particular water molecules) are oriented in the electric field. These moments create their own electric field, counteracting the field that caused their appearance. As a result, the total electric field decreases. In small fields this phenomenon is described using the concept of dielectric constant.

Below is the dielectric constant in vacuum various substances:

Air……………………………....1.0006

Paraffin…………………………....2

Plexiglas (plexiglass)……3-4

Ebonite……………………………..…4

Porcelain……………………………....7

Glass…………………………..…….4-7

Mica……………………………..….4-5

Natural silk............4-5

Slate........................6-7

Amber………………12.8

Water…………………………………...….81

These values ​​of the dielectric constant of substances refer to ambient temperatures in the range of 18–20 °C. Thus, the dielectric constant of solids varies slightly with temperature, with the exception of ferroelectrics.

On the contrary, for gases it decreases due to an increase in temperature and increases due to an increase in pressure. In practice it is taken as one.

Impurities in small quantities have little effect on the level of dielectric constant of liquids.

If two arbitrary point charges are placed in a dielectric, then the field strength created by each of these charges at the location of the other charge decreases by ԑ times. It follows from this that the force with which these charges interact with one another is also ԑ times less. Therefore, for charges placed in a dielectric, it is expressed by the formula:

F = (q₁q₂)/(4πԑₐr²),

where F is the interaction force, q₁ and q₂ are the magnitude of the charges, ԑ is the absolute dielectric constant of the medium, r is the distance between point charges.

The value of ԑ can be shown numerically in relative units(relative to the value of the absolute dielectric constant of vacuum ԑ₀). The value ԑ = ԑₐ/ԑ₀ is called the relative dielectric constant. It reveals how many times the interaction between charges in an infinite homogeneous environment weaker than in a vacuum; ԑ = ԑₐ/ԑ₀ is often called complex dielectric constant. Numerical value the values ​​of ԑ₀, as well as its dimension, depend on which system of units is chosen; and the value of ԑ - does not depend. So, in the SGSE system ԑ₀ = 1 (this fourth basic unit); in the SI system, the dielectric constant of vacuum is expressed:

ԑ₀ = 1/(4π˖9˖10⁹) farad/meter = 8.85˖10⁻¹² f/m (in this system ԑ₀ is a derived quantity).

PERMITTIVITY (dielectric constant) - physical quantity, characterizing the ability of a substance to reduce forces electrical interaction in this substance compared to vacuum. Thus, d.p. shows how many times the forces of electrical interaction in a substance are less than in a vacuum.

D.p. is a characteristic that depends on the structure of the dielectric substance. Electrons, ions, atoms, molecules or their individual parts and larger sections of any substance in an electric field are polarized (see Polarization), which leads to partial neutralization of the external electric field. If the frequency of the electric field is commensurate with the time of polarization of the substance, then in a certain frequency range there is dispersion of the dispersion factor, that is, the dependence of its value on frequency (see Dispersion). The d.p. of a substance depends both on the electrical properties of atoms and molecules, and on their relative position, i.e. the structure of matter. Therefore, the determination of electrical conductivity or its changes depending on environmental conditions is used when studying the structure of a substance, and in particular various tissues of the body (see Electrical conductivity of biological systems).

Various substances (dielectrics), depending on their structure and state of aggregation, have different sizes D. p. (table).

Table. The value of the dielectric constant of some substances

Of particular importance for medical biol research is the study of D. and. in polar liquids. A typical representative of them is water, consisting of dipoles that are oriented in an electric field due to the interaction between the charges of the dipole and the field, which leads to the occurrence of dipole or orientational polarization. The high value of water pressure (80 at t° 20°) determines high degree dissociation of various chemicals in it. substances and good solubility of salts, compounds, bases and other compounds (see Dissociation, Electrolytes). With an increase in the concentration of the electrolyte in water, the value of its DP decreases (for example, for monovalent electrolytes, the DP of water decreases by one when the salt concentration increases by 0.1 M).

Most biol objects belong to heterogeneous dielectrics. When interacting ions of a biological object with an electric field, the polarization of the interfaces is of significant importance (see Biological membranes). In this case, the magnitude of polarization is greater, the lower the frequency of the electric field. Since the polarization of the interface boundaries of a biol, an object depends on their permeability (see) for ions, it is obvious that the effective D. p. in to a greater extent determined by the state of the membranes.

Because the polarization of such a complex heterogeneous object as a biological one has different nature(concentration, macrostructural, orientation, ionic, electronic, etc.), then it becomes clear that with increasing frequency the change in dispersion (dispersion) is sharply expressed. Conventionally, three regions of dispersion of the dynamic frequency are distinguished: alpha dispersion (at frequencies up to 1 kHz), beta dispersion (frequency from several kHz to tens of MHz) and gamma dispersion (frequencies above 10 9 Hz); in biol, objects there is usually no clear boundary between areas of dispersion.

With the deterioration of the function, state of the biol, the object, the dispersion of D. p. at low frequencies decreases until it completely disappears (with tissue death). On high frequencies the value of D.p. does not change significantly.

D.p. are measured in a wide range of frequencies, and depending on the frequency range, measurement methods also change significantly. At frequencies electric current less than 1 Hz, the measurement is carried out using the method of charging or discharging a capacitor filled with the test substance. Knowing the dependence of the charging or discharging current on time, it is possible to determine not only the value electrical capacitance capacitor, but also losses in it. At frequencies from 1 to 3 10 8 Hz for measuring D. and. Special resonance and bridge methods are used, which make it possible to comprehensively study changes in the dynamic properties of various substances in the most complete and comprehensive manner.

In medical-biological research, symmetrical alternating current bridges with direct reading of measured quantities are most often used.

Bibliography: High-frequency heating of dielectrics and semiconductors, ed. A. V. Netushila, M. -L., 1959, bibliogr.; S Edunov B. I. and Fran k-K a m e-n e c k and y D. A. Dielectric constant of biological objects, Usp. physical Sciences, vol. 79, v. 4, p. 617, 1963, bibliogr.; Electronics and cybernetics in biology and medicine, trans. from English, ed. P.K. Anokhina, p. 71, M., 1963, bibliogr.; E m e F. Dielectric measurements, trans. from German, M., 1967, bibliogr.



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