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 the field, and thereby reduce the total electric field inside the material. A physical Quantity is a physical property that can be quantified In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can A dielectric is a nonconducting substance ie an insulator. The term was coined by William Whewell in response to a request from Michael Faraday. In Classical electromagnetism, the polarization density (or electric polarization, or simply polarization) is the Vector field that expresses Thus, permittivity relates to a material's ability to transmit (or "permit") an electric field.

It is directly related to electric susceptibility. The electric susceptibility χe of a Dielectric material is a measure of how easily it polarizes in response to an Electric field. 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. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical Capacitance is a measure of the amount of Electric charge stored (or separated for a given Electric potential.

1 Explanation
2 Vacuum permittivity
3 Permittivity in media
4 Measurement
5 References and notes
6 See also
7 External links
8 Suggested readings
9 External links

Explanation

In electromagnetism, the electric displacement field D represents how an electric field E influences the organization of electrical charges in a given medium, including charge migration and electric dipole reorientation. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, the electric displacement field (also called electrical field/flux density is a Vector field \mathbf{D} that appears in Maxwell's equations In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a Its relation to permittivity in the very simple case of linear, homogeneous, isotropic materials with instantaneous response to changes in electric field is

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

where the permittivity ε is a scalar. Isotropy is uniformity in all directions Precise definitions depend on the subject area In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or If the medium is not isotropic, the permittivity is a second rank tensor. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually

In general, permittivity isn't 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 on the strength of the electric field. Nonlinear optics (NLO is the branch of Optics that describes the behaviour of Light in nonlinear media, that is media in which the dielectric polarization Permittivity as a function of frequency can take on real or complex values.

In SI units, permittivity is measured in farads per metre (F/m). This is about the capacitance unit of measure For the charge unit see Faraday (unit. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International 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). The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. M^2 redirects here For other uses see M². CM2 redirects here The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International D and E describe the interaction between charged objects. D is related to the charge densities associated with this interaction, while E is related to the forces and potential differences.

Vacuum permittivity

Main article: vacuum permittivity

Vacuum permittivity $\varepsilon_{0}$ (also called permittivity of free space or the electric constant) is the ratio D/E in free space. Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes

$\varepsilon_0 \ \stackrel{\mathrm{def}}{=}\ \frac{1}{{c}^2\mu_0} \approx$ 8. 8541878176… × 10⁻¹² F/m (or C²N^-1m^-2),

c (or c₀) is the speed of light in free space. This is about the capacitance unit of measure For the charge unit see Faraday (unit. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical ^[1]

μ 0

is the magnetic constant. The vacuum permeability, referred to by international standards organizations as the magnetic constant, and denoted by the symbol μ 0 (also

Constants c and μ₀ are defined in SI units to have exact numerical values (see NIST), shifting responsibility of experiment to the determination of the meter and the ampere. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second (The approximation in the value of ε₀ stems from π being an irrational number. In Mathematics, an irrational number is any Real number that is not a Rational number — that is it is a number which cannot be expressed as a fraction ) The electric constant ε₀ also appears in Coulomb's law as a part of the Coulomb force constant, 1 / ( 4π ε₀ ), which expresses the force between two unit charges separated by unit distance in vacuum. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical

The linear permittivity of a homogeneous material is usually given relative to that of free space, as a relative permittivity $\varepsilon_{r}$ (also called dielectric constant, although this sometimes only refers to the static, zero-frequency relative permittivity). Measurement The relative static permittivity εr can be measured for static Electric fields as follows first the Capacitance of a test In an anisotropic material, the relative permittivity may be a tensor. The actual permittivity is then calculated by multiplying the relative permittivity by $\varepsilon_{0}$ :

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

where

$\,\chi_e$ is the electric susceptibility of the material. The electric susceptibility χe of a Dielectric material is a measure of how easily it polarizes in response to an Electric field.

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). Isotropy is uniformity in all directions Precise definitions depend on the subject area In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or Anisotropy (pronounced with stress on the third syllable ˌænaɪˈsɒtrəpi is the property of being directionally dependent as opposed to Isotropy, which means homogeneity History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray The permittivity $\varepsilon$ and magnetic permeability $μ$ of a medium together determine the phase velocity v of electromagnetic radiation through that medium:

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

When an external electric field is applied to a real medium, a current flows. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. The phase velocity (or phase speed) of a Wave is the rate at which the phase of the wave propagates in space Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. The total current flowing within the medium consists of two parts: a conduction and a displacement current. Electrical conduction is the movement of electrically charged particles through a Transmission medium ( Electrical conductor) Displacement current is a quantity that arises in a changing electric field The displacement current can be thought of as the elastic response of the material to the applied electric field. As the magnitude of the externally applied electric field is increased, an increasing amount of energy is stored in the electric displacement field within the material. If the electric field is subsequently decreased, the material will release the stored electrostatic energy. The displacement current reflects the resulting change in electrostatic energy stored within the material. Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical The electric displacement can be separated into a vacuum contribution and one arising from the material by

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

where

P is the polarization of the medium

χ

its electric susceptibility. In Classical electromagnetism, the polarization density (or electric polarization, or simply polarization) is the Vector field that expresses The electric susceptibility χe of a Dielectric material is a measure of how easily it polarizes in response to an Electric field.

It follows that the relative permittivity and susceptibility of a sample are related, $\varepsilon_{r} = \chi + 1$ .

Complex permittivity

A dielectric permittivity spectrum over a wide range of frequencies. ε′ and ε″ denote the real and the imaginary part of the permittivity, respectively. Various processes are labeled on the image: ionic and dipolar relaxation, and atomic and electronic resonances at higher energies. From the Dielectric spectroscopy page [1] of the research group of Dr. Kenneth A. Mauritz. Dielectric Spectroscopy (sometimes called impedance spectroscopy) measures the Dielectric properties of a medium as a function of Frequency

As opposed to the response of a vacuum, the response of normal materials to external fields generally depends on the frequency of the field. Frequency is a measure of the number of occurrences of a repeating event per unit Time. 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) which can be represented by a phase difference. For this reason permittivity is often treated as a complex function (since complex numbers allow specification of magnitude and phase) of the frequency of the applied field $ω$ , $\varepsilon \rightarrow \widehat{\varepsilon}(\omega)$ . The definition of permittivity therefore becomes

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

where

D 0

and

E 0

are the amplitudes of the displacement and electrical fields, respectively,

i ² = −1 is the imaginary unit. Definition By definition the imaginary unit i is one solution (of two of the Quadratic equation

It is important to realise that the choice of sign for time-dependence dictates the sign convention for the imaginary part of permittivity. The signs used here correspond to those commonly used in physics, whereas for the engineering convention one should reverse all imaginary quantities.

The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity $\varepsilon_{s}$ (also $\varepsilon_{DC}$ ):

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

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 ( $E 0$ ), D and E remain proportional, and

$\widehat{\varepsilon} = \frac{D_0}{E_0}e^{i\delta} = |\varepsilon|e^{i\delta}.$

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:

$\widehat{\varepsilon}(\omega) = \varepsilon'(\omega) + i\varepsilon''(\omega) = \frac{D_0}{E_0} \left( \cos\delta + i\sin\delta \right).$

where

$\varepsilon''$ is the imaginary part of the permittivity, which is related to the dissipation (or loss) of energy within the medium.

$\varepsilon'$ is the real part of the permittivity, which is related to the stored energy within the medium.

The complex permittivity is usually a complicated function of frequency ω, since it is a superimposed description of dispersion phenomena occurring at multiple frequencies. In Optics, dispersion is the phenomenon in which the Phase velocity of a wave depends on its frequency The dielectric function $\varepsilon(\omega)$ must have poles only for frequencies with positive imaginary parts, and therefore satisfies the Kramers–Kronig relations. The Kramers–Kronig relations are mathematical properties connecting the real and imaginary parts of any complex function which is analytic However, in the narrow frequency ranges that are often studied in practice, the permittivity can be approximated as frequency-independent or by model 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. In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes

In the case of solids, the complex dielectric function is intimately connected to band structure. The primary quantity that characterize the electronic structure of any crystalline material is the probability of photon absorption, which is directly related to the imaginary part of the optical dielectric function ε(ω). In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena The optical dielectric function is given by the fundamental expression:^[2]

$\epsilon(\omega)=1+\frac{8\pi^2e^2}{m^2}\sum_{c,v}\int_{}^{} W_{cv}(E) \left[ \phi (\hbar \omega - E)-\phi( \hbar \omega +E) \right ] \, dx \ .$

In this expression, W_cv ( E ) represents the product of the Brillouin zone-averaged transition probability at the energy E with the joint density of states,^[3]^[4] J_cv ( E ); φ is a broadening function, representing the role of scattering in smearing out the energy levels. In Mathematics and Solid state physics, the first Brillouin zone is a uniquely defined Primitive cell of the Reciprocal lattice in the In statistical and Condensed matter physics, the density of states ( DOS) of a system describes the number of states at each energy level that are available ^[5] In general, the broadening is intermediate between Lorentzian and Gaussian;^[6]^[7] for an alloy it is somewhat closer to Gaussian because of strong scattering from statistical fluctuations in the local composition on a nanometer scale. The Cauchy–Lorentz distribution, named after Augustin Cauchy and Hendrik Lorentz, is a continuous Probability distribution. Carl Friedrich Gauss (1777 &ndash 1855 is the Eponym of all of the topics listed below

Classification of materials

Materials can be classified according to their permittivity and conductivity, σ. Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an Electric current. Materials with a large amount of loss inhibit the propagation of electromagnetic waves. In this case, generally when $\frac{\sigma}{\omega\varepsilon}\gg1$ , we consider the material to be a good conductor. Dielectrics are associated with lossless or low-loss materials, where $\frac{\sigma}{\omega\varepsilon}\ll1$ . Those that do not fall under either limit are considered to be general media. A perfect dielectric is a material that has no conductivity, thus exhibiting only a displacement current. Therefore it stores and returns electrical energy as if it were an ideal capacitor. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors

Lossy medium

In the case of lossy medium, i. e. when the conduction current is not negligible, the total current density flowing is:

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

where

σ is the conductivity of the medium;

ε is the real part of the permittivity. Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an Electric current.

$\widehat{\varepsilon}$ is the complex 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.

In this formalism, the complex permittivity is defined as:

$\widehat{\varepsilon} = \varepsilon + i \frac{\sigma}{\omega}$

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. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. The mechanism of dipoles relaxing is called dielectric relaxation and for ideal dipoles is described by classic Debye relaxation. Dielectric relaxation is the momentary delay (or lag in the Dielectric constant of a material Debye relaxation is the Dielectric relaxation response of an ideal noninteracting population of Dipoles to an alternating external Electric field.

Resonance effects, which arise from the rotations or vibrations of atoms, ions, or electrons. In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's These processes are observed in the neighborhood of their characteristic absorption frequencies.

The above effects often combine to cause non-linear effects within capacitors. For example, dielectric absorption refers to the inability of a capacitor that has been charged for a long time to completely discharge when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, real capacitors will develop a small voltage, a phenomenon that is also called soakage or battery action. For some dielectrics, such as many polymer films, the resulting voltage may be less than 1-2% of the original voltage. However, it can be as much as 15 - 25% in the case of electrolytic capacitors or supercapacitors. An electrolytic capacitor is a type of Capacitor that uses an ionic conducting liquid as one of its plates Electric double-layer capacitors, also known as supercapacitors, electrochemical double layer capacitors ( EDLCs) or ultracapacitors

Quantum-mechanical interpretation

In terms of quantum mechanics, permittivity is explained by atomic and molecular interactions. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by

At low frequencies, molecules in polar dielectrics 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. Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0 A hydrogen bond results from a Dipole-dipole force between an Electronegative atom and a Hydrogen atom bonded to Nitrogen, Oxygen The field does work against the bonds and the energy is absorbed by the material as heat. In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature This is why microwave ovens work very well for materials containing water. There are two maxima of the imaginary component (the absorptive index) of water, one at the microwave frequency, and the other at far ultraviolet (UV) frequency.

At moderate frequencies, the energy is too high to cause rotation, yet too low to affect electrons directly, and is absorbed in the form 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. Eyes are organs that detect Light, and send signals along the Optic nerve to the visual areas of the brain [2]

At high frequencies (such as UV and above), molecules cannot relax, and the energy is purely absorbed by atoms, exciting electron energy levels. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J

While carrying out a complete ab initio (that is, first-principles) modelling is now computationally possible, it has not been widely applied yet. Ab Initio Software Corporation was founded in the mid 1990's by the former CEO of Thinking Machines Corporation Sheryl Handler, and several other former employees 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). 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

Measurement

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. Dielectric Spectroscopy (sometimes called impedance spectroscopy) measures the Dielectric properties of a medium as a function of Frequency Also, by using cryostats and ovens, the dielectric properties of a medium can be characterized over an array of temperatures. A Cryostat (cryo=cold and stat=stable is a vessel similar in construction to a Vacuum flask, or Dewar used to maintain cold Cryogenic 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.

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)

References and notes

^ Current practice of international standards organizations such as NIST and BIPM is to use c₀ to denote the speed of light in vacuum according to ISO 31. Time domain is a term used to describe the analysis of mathematical functions or physical signals with respect to Time. Frequency domain is a term used to describe the analysis of Mathematical functions or signals with respect to frequency The International Bureau of Weights and Measures ( Bureau international des poids et mesures, in French) is an international Standards organization, one International Standard ISO 31 ( Quantities and units International Organization for Standardization, 1992 is the most widely respected style guide for the In the original Recommendation of 1983, the symbol c was used for this purpose. See NIST Special Publication 330, Appendix 2, p. 45
^ Peter Y. Yu, Manuel Cardona (2001). Fundamentals of Semiconductors: Physics and Materials Properties. Berlin: Springer, pp. 261 ff. ISBN 3540254706.
^ José García Solé, Jose Solé, Luisa Bausa, (2001). An introduction to the optical spectroscopy of inorganic solids. Wiley, Appendix A1, pp, 263ff. ISBN 0470868856.
^ John H. Moore, Nicholas D. Spencer (2001). Encyclopedia of chemical physics and physical chemistry. Taylor and Francis, pp. 105 ff. ISBN 0750307986.
^ Solé and Bausa, pp. 10 ff. ISBN 3540254706.
^ Hartmut Haug, Stephan W. Koch (1994). Quantum Theory of the Optical and Electronic Properties of Semiconductors. World Scientific, pp. 196 ff. ISBN 9810218648.
^ Manijeh Razeghi (2006). Fundamentals of Solid State Engineering. Birkhauser, pp. 383 ff. ISBN 0387281525.

External links

Electromagnetism, a chapter from an online textbook

Dictionary

-noun

(physics) A property of a dielectric medium that determines the forces that electric charges placed in the medium exert on each other.

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Contents

Explanation

Vacuum permittivity

Permittivity in media

Complex permittivity

Classification of materials

Lossy medium

Quantum-mechanical interpretation

Measurement

References and notes

See also

External links

Suggested readings

External links

Dictionary

permittivity

-noun