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Encyclopedia > Permittivity

Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. Permittivity relates therefore to a material's ability to transmit (or "permit") an electric field. A physical quantity is either a quantity within physics that can be measured (e. ... A dielectric, or electrical insulator, is a substance that is highly resistant to the flow of electric current and has a relative permittivity greater than unity. ... In electrostatics, the polarization is the vector field that results from permanent or induced electric dipole moments in a dielectric material. ... In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ...

It is directly related to the electric susceptibility. For example, in a capacitor, an increased permittivity allows the same charge to be stored with a smaller electric field (and thus a smaller voltage), leading to an increased capacitance.The permittivity of free space ($varepsilon_0$) is 8.8541878176x10-12 farads per meter (F/m). It has been suggested that this article or section be merged into permittivity. ... A capacitor is a device that stores energy in the electric field created between a pair of conductors on which electric charges of equal magnitude, but opposite sign, have been placed. ... Charge is a word with many different meanings. ... In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ... International danger high voltage symbol. ... The farad (symbol: F) is the SI unit of capacitance. ... The metre, or meter (symbol: m) is the SI base unit of length. ...

In electromagnetism one can define an electric displacement field D, which represents how an electric field E will influence the organization of electrical charges in the medium, including charge migration and electric dipole reorientation. Its relation to permittivity is given by Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess the property of electric charge, and is in turn affected by the presence and motion of such particles. ... The factual accuracy of this article is disputed. ... In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ... Charge is a word with many different meanings. ... The Earths magnetic field, which is approximately a dipole. ...

$mathbf{D}=varepsilon cdot mathbf{E}$

where ε is a scalar if the medium is isotropic or a 3 by 3 matrix otherwise. The term scalar is used in mathematics, physics, and computing basically for quantities that are characterized by a single numeric value and/or do not involve the concept of direction. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. ...

Permittivity, taken as a function of frequency, can take on real or complex value. In general, it is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In a nonlinear medium, the permittivity can depend upon the strength of the electric field. Nonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization P responds nonlinearly to the electric field E of the light. ...

In SI units, permittivity is measured in farads per metre (F/m). The displacement field D is measured in units of coulombs per square metre (C/m2), while the electric field E is measured in volts per metre (V/m). D and E represent the same phenomenon, namely, the interaction between charged objects. D is related to the charge densities associated with this interaction. E is related to the forces and potential differences involved. The permittivity of free space, $varepsilon_0$, is the scale factor that relates the values of D and E in a vacuum. $varepsilon_0$ is equal to 8.8541878176...×10-12 F/m. The units of $varepsilon_0$ in the International System of Units are farads per meter (F/m). In the International System of Units, force is in newtons (N), charge is in coulombs (C), distance is in meters (m), and energy is in joules (J). As in all equations that describe physical phenomena, using a consistent set of units is essential. Cover of brochure The International System of Units. ... The farad (symbol: F) is the SI unit of capacitance. ... The metre, or meter, is a measure of length, approximately equal to 3. ... The coulomb (symbol: C) is the SI unit of electric charge. ... A square metre (US spelling: square meter) is by definition the area enclosed by a square with sides each 1 metre long. ... Josephson junction array chip developed by NIST as a standard volt. ... The metre, or meter, is a measure of length, approximately equal to 3. ...

## Vacuum permittivity

It has been suggested that electric susceptibility be merged into this article or section. (Discuss)

The permittivity of a material is usually given relative to that of vacuum, as a relative permittivity, $varepsilon_{r}$ (also called dielectric constant in some cases). The actual permittivity is then calculated by multiplying the relative permittivity by $varepsilon_{0}$: Image File history File links Please see the file description page for further information. ... It has been suggested that this article or section be merged into permittivity. ... The dielectric constant Îµr (represented as or K in some cases) is defined as the ratio: where Îµs is the static permittivity of the material in question, and Îµ0 is the vacuum permittivity. ...

$varepsilon = varepsilon_r varepsilon_0 = (1+chi_e)varepsilon_0$

where $,chi_e$ is the electric susceptibility of the material. It has been suggested that this article or section be merged into permittivity. ...

Vacuum permittivity $varepsilon_{0}$ (also called permittivity of free space) is the ratio D/E in vacuum. It also appears in Coulomb's law as a part of the Coulomb force constant, $frac{1}{ 4 pi epsilon_0}$, which expresses the attraction between two unit charges in vacuum. In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ...

$varepsilon_0 = frac{1}{c^2mu_0} approx$ 8.8541878176 × 10-12 F/m (C2/Jm),

where c is the speed of light and μ0 is the permeability of vacuum. All three of these constants are exactly defined in SI units. The farad (symbol: F) is the SI unit of capacitance. ... The metre, or meter (symbol: m) is the SI base unit of length. ... The coulomb (symbol: C) is the SI unit of electric charge. ... The joule (symbol: J) is the SI unit of energy, or work with base units of kgÂ·mÂ²/sÂ² (NÂ·m). ... The metre, or meter (symbol: m) is the SI base unit of length. ... Cherenkov effect in a swimming pool nuclear reactor. ... In electromagnetism, permeability is the degree of magnetisation of a material that responds linearly to an applied magnetic field. ... Cover of brochure The International System of Units. ...

## Permittivity in media

In the common case of isotropic media, D and E are parallel vectors and $varepsilon$ is a scalar, but in general anisotropic media this is not the case and $varepsilon$ is a rank-2 tensor (causing birefringence). The permittivity $varepsilon$ and magnetic permeability μ of a medium together determine the phase velocity v of electromagnetic radiation through that medium: Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... In physics and in vector calculus, a spatial vector is a concept characterized by a magnitude, which is a scalar, and a direction (which can be defined in a 3-dimensional space by the Euler angles). ... The term scalar is used in mathematics, physics, and computing basically for quantities that are characterized by a single numeric value and/or do not involve the concept of direction. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... A calcite crystal laid upon a paper with some letters showing the double refraction Birefringence, or double refraction, is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals, depending on... In electromagnetism, permeability is the degree of magnetisation of a material that responds linearly to an applied magnetic field. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... Electromagnetic radiation can be conceptualized as a self propagating transverse oscillating wave of electric and magnetic fields. ...

$varepsilon mu = frac{1}{v^2}$

When an electric field is applied to a medium, a current flows. The total current flowing in a real medium is in general made of two parts: a conduction and a displacement current. The displacement current can be thought of as the elastic response of the material to the applied electric field. As the magnitude of the electric field is increased, the displacement current is stored in the material, and when the electric field is decreased the material releases the displacement current. The electric displacement can be separated into a vacuum contribution and one arising from the material by In electricity, current refers to electric current, which is the flow of electric charge. ... Electrical conduction is the movement of electrically charged particles through matter. ... Displacement current is a quantity related to a changing electric field; it is not a real current (movement of charge) in a vacuum, but it has the units of current, as movement of charge does, and has an associated magnetic field. ...

$mathbf{D} = varepsilon_{0} mathbf{E} + mathbf{P} = varepsilon_{0} mathbf{E} + varepsilon_{0}chimathbf{E} = varepsilon_{0} mathbf{E} left( 1 + chi right),$

where P is the polarization of the medium and χ its electric susceptibility. It follows that the relative permittivity and susceptibility of a sample are related, $varepsilon_{r} = chi + 1$. In electrostatics, the polarization is the vector field that results from permanent or induced electric dipole moments in a dielectric material. ... It has been suggested that this article or section be merged into permittivity. ...

### Complex permittivity

A dielectric permittivity spectrum over a wide range of frequencies. ε' and ε'' denote the real and the imaginary part of the dielectric function, respectively. Various processes are labeled on the image: ionic and dipolar relaxation, and atomic and electronic resonances at higher energies.

As opposed to the response of a vacuum, the response of normal materials to external fields generally depends on the frequency of the field. This frequency dependence reflects the fact that a material's polarization does not respond instantaneously to an applied field. The response must always be causal (arising after the applied field). For this reason permittivity is often treated as a complex function of the frequency of the applied field ω, $varepsilon rightarrow widehat{varepsilon}(omega)$. The definition of permittivity therefore becomes Image:Dielectric responses. ... Image:Dielectric responses. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...

$D_{0}e^{i omega t} = widehat{varepsilon}(omega) E_{0} e^{i omega t},$

where D0 and E0 are the amplitudes of the displacement and electrical fields, respectively, $i=sqrt{-1}$ is the imaginary unit. The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity or dielectric constant $varepsilon_{s}$ (also $varepsilon_{DC}$): In mathematics, the imaginary unit (sometimes also represented by the Latin or the Greek iota) allows the real number system to be extended to the complex number system . ... The dielectric constant Îµr (represented as or K in some cases) is defined as the ratio: where Îµs is the static permittivity of the material in question, and Îµ0 is the vacuum permittivity. ...

$varepsilon_{s} = lim_{omega rightarrow 0} widehat{varepsilon}(omega).$

At the high-frequency limit, the complex permittivity is commonly referred to as ε. At the plasma frequency and above, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity is a good approximation for altering fields of low frequencies, and as the frequency increases a measurable phase difference δ emerges between D and E. The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate fields strength (E0), D and E remain proportional, and

$widehat{varepsilon} = frac{D_0}{E_0}e^{idelta} = |varepsilon|e^{idelta}.$

Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way:

$widehat{varepsilon}(omega) = varepsilon'(omega) - ivarepsilon''(omega) = frac{D_0}{E_0} left( cosdelta - isindelta right).$

In the equation above, $varepsilon''$ is the imaginary part of the permittivity, which is related to the rate at which energy is absorbed by the medium (converted into thermal energy, etcetera). The real part of the permittivity, $varepsilon'$.

The complex permittivity is usually a complicated function of frequency ω, since it is a sumperimposed description of dispersion phenomena occurring at multiple frequencies. The dielectric function $varepsilon(omega)$ must have poles only for frequencies with positive imaginary parts, and therefore satisfies the Kramers-Kronig relations. However, in the narrow frequency ranges that are often studied in practice, the permittivity can be approximated as frequency-independent or by model functions. Dispersion of a light beam in a prism. ... In mathematics and physics, the Kramers-Kronig relations describe the relation between the real and imaginary part of a certain class of complex-valued functions. ...

At a given frequency, the imaginary part of $widehat{varepsilon}$ leads to absorption loss if it is positive (in the above sign convention) and gain if it is negative. More generally, the imaginary parts of the eigenvalues of the anisotropic dielectric tensor should be considered.

### Classification of materials

Materials can be classified according to their permittivity. Those with a permittivity that has a negative real part $varepsilon'$ are considered to be metals, in which no propagating electromagnetic waves exist. Those with a positive real part are dielectrics. Hot metal work from a blacksmith Look up Metal in Wiktionary, the free dictionary. ... A dielectric, or electrical insulator, is a substance that is highly resistant to the flow of electric current and has a relative permittivity greater than unity. ...

A perfect dielectric is a material that exhibits a displacement current only, therefore it stores and returns electrical energy as if it were an ideal capacitor. In the case of lossy medium, i.e. when the conduction current is not negligible, the total current density flowing is: A capacitor is a device that stores energy in the electric field created between a pair of conductors on which electric charges of equal magnitude, but opposite sign, have been placed. ...

$J_{tot} = J_c + J_d = sigma E - i omega varepsilon_0 varepsilon_r E = i omega varepsilon_0 widehat{varepsilon} E$

where

σ is the conductivity of the medium;
εr is the relative permittivity.

The size of the displacement current is dependent on the frequency ω of the applied field E; there is no displacement current in a constant field. Electrical conductivity is a measure of how well a material accommodates the transport of electric charge. ...

In this formalism, the complex permittivity $widehat{varepsilon}$ is defined as:

$widehat{varepsilon} = varepsilon_r + i frac{sigma}{varepsilon_0 omega}$

### Dielectric absorption processes

In general, the absorption of electromagnetic energy by dielectrics is covered by a few different mechanisms that influence the shape of the permittivity as a function of frequency:

• Relaxation effects associated with permanent and induced molecular dipoles. At low frequencies the field changes slowly enough to allow dipoles to reach equilibrium before the field has measurably changed. For frequencies at which dipole orientations cannot follow the applied field due to the viscosity of the medium, absorption of the field's energy leads to energy dissipation. The mechanism of dipoles relaxing is called dielectric relaxation and for ideal dipoles is described by classic Debye relaxation
• Resonance effects, which arise from the rotations or vibrations of atoms, ions, or electrons. These processes are observed in the neighborhood of their characteristic absorption frequencies.

The word relaxation can mean the following: The opposite of stress or tension; the aim of recreation and leisure activities. ... The pitch drop experiment at the University of Queensland. ... In physics, dielectric relaxation refers to the relaxation reponse of a dielectric medium to an external field of microwave frequencies. ... Debye relaxation is the dielectric relaxation response of an ideal, noninteracting population of dipoles to an alternating external electric field. ... The Tacoma Narrows Bridge (shown twisting) in Washington collapsed spectacularly, under moderate wind, in part because of resonance. ...

### Quantum-mechanical interpretation

Quantum-mechanically speaking, there are distinct regions of atomic and molecular interactions, microscopically, that account for the macroscopic behavior we label as permittivity. At low frequencies in polar dielectrics, molecules are polarized by an applied electric field, which induces periodic rotations.

For example, at the microwave frequency, the microwave field causes the periodic rotation of water molecules, sufficient to break hydrogen bonds. The field does work against the bonds and the energy is absorbed by the material in terms of heat, which is why microwave ovens work very well for materials containing water. There are two maximums of the imaginary component (the absorptive index) of water, one at the microwave frequency, and the other at far ultraviolet (UV) wavelengths.

At UV and above, and at high frequencies in general, the frequencies are too high for molecules to relax in, and thus the energy is purely absorbed by atoms, exciting electron energy levels. At the plasma frequency, the electrons are fully ionized, and will conduct electricity. At moderate frequencies, where the energy content is not high enough to affect electrons directly, yet too high for rotational aspects, the energy is absorbed in terms of resonant molecular vibrations. In water, this is where the absorptive index starts to drop sharply, and the minimum of the imaginary permittivity is at the frequency of blue light (optical regime). This is why water is blue, and also why sunlight does not damage water-containing organs such as the eye. This article or section is missing references or citation of sources. ...

While carrying out a complete ab initio or first-principles modelling is now computationally possible, it has not been widely applied yet. Thus, a phenomological model is accepted as being an adequate method of capturing experimental behaviors. The Debye model and the Lorentz model use a 1st order and 2nd order (respectively) lumped system parameter linear representation (such as an RC and an LRC resonant circuit). The current version of the article or section reads like an advertisement. ... Debye relaxation is the dielectric relaxation response of an ideal, noninteracting population of dipoles to an alternating external electric field. ... In geometry, the hyperboloid model, also known as the Minkowski model or the Lorentz model, is a model of hyperbolic geometry in which the points are points on one sheet of a hyperboloid of two sheets. ...

## Permittivity measurements

The dielectric constant of a material can be found by a variety of static electrical measurements. The complex permittivity is evaluated over a wide range of frequencies by using different variants of dielectric spectroscopy, covering nearly 21 orders of magnitude from 10-6 to 1015 Hz. Also, by using cryostats and ovens, the dielectric properties of a medium can be characterized over an array of temperatures. In order to study systems for such diverse exciting fields, a number of measurement setups are used, each adequate for a special frequency range. A dielectric permittivity spectrum over a wide range of frequencies. ... Cryocoolers are refrigerators used to reach cryogenic temperatures. ...

Please improve and expand this section. There may be comments on what is required on the requests for expansion page or on this article's talk page.
• Low-frequency time domain measurements (10-6-103 Hz)
• Low frequency frequency domain measurements (10-5-106 Hz)
• Reflective coaxial methods (106-1010 Hz)
• Transmission coaxial method (108-1011 Hz)
• Quasi-optical methods (109-1010 Hz)
• Fourier-transform methods (1011-1015 Hz)

A dielectric, or electrical insulator, is a substance that is highly resistant to the flow of electric current and has a relative permittivity greater than unity. ... The dielectric constant Îµr (represented as or K in some cases) is defined as the ratio: where Îµs is the static permittivity of the material in question, and Îµ0 is the vacuum permittivity. ... A dielectric permittivity spectrum over a wide range of frequencies. ... ...

• Theory of Electric Polarization: Dielectric Polarization, C.J.F. Böttcher, ISBN 0-44441-579-3
• Dielectrics and Waves edited by A. von Hippel, Arthur R., ISBN 0-89006-803-8

Results from FactBites:

 Permittivity - Wikipedia, the free encyclopedia (1708 words) Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. In SI units, permittivity is measured in farads per metre (F/m). The complex permittivity is usually a complicated function of frequency ω, since it is a sumperimposed description of dispersion phenomena occurring at multiple frequencies.
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