English
Noun
 A property of a dielectric medium that determines the
forces that electric
charges placed in the medium exert on each other.
Translations
property of a dielectric medium
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. Thus, permittivity relates to a
material's ability to transmit (or "permit") an electric
field.
It is directly related to
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.
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. Its
relation to permittivity in the very simple case of linear,
homogeneous,
isotropic
materials with instantaneous response to changes in electric field
is
 \mathbf=\varepsilon \mathbf
where the permittivity ε is a
scalar.
If the medium is not isotropic, the permittivity is a second rank
tensor.
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. 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). 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 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
Vacuum permittivity \varepsilon_ (also
called permittivity of free space or the electric constant) is the
ratio D/E in
free
space.
 \varepsilon_0 \ \stackrel\ \frac \approx 8.8541878176…
× 10−12 F/m (or C2N1m2),
 c (or c0) is the speed of
light in free space.
 \mu_0 is the magnetic
constant.
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 approximation in the
value of ε0 stems from π being an
irrational
number.) 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.
The linear permittivity of a homogeneous material
is usually given relative to that of free space, as a relative
permittivity \varepsilon_ (also called
dielectric
constant, although this sometimes only refers to the static,
zerofrequency relative permittivity). In an anisotropic material,
the relative permittivity may be a tensor. The actual permittivity
is then calculated by multiplying the relative permittivity by
\varepsilon_:
 \varepsilon = \varepsilon_r \varepsilon_0 =
(1+\chi_e)\varepsilon_0
where
 \,\chi_e is the electric
susceptibility of the material.
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 rank2
tensor (causing
birefringence). The
permittivity \varepsilon and
magnetic permeability \mu of a medium together determine the
phase
velocity v of
electromagnetic
radiation through that medium:
When an external electric field is applied to a
real medium, a
current
flows. The total current flowing within the medium consists 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 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. The electric displacement can be
separated into a vacuum contribution and one arising from the
material by
 \mathbf = \varepsilon_ \mathbf + \mathbf = \varepsilon_ \mathbf
+ \varepsilon_\chi\mathbf = \varepsilon_ \mathbf \left( 1 + \chi
\right),
where
 P is the
polarization of the medium
 \chi its electric
susceptibility.
It follows that the relative permittivity and
susceptibility of a sample are related, \varepsilon_ = \chi +
1.
Complex permittivity
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) 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 \omega, \varepsilon
\rightarrow \widehat(\omega). The definition of permittivity
therefore becomes
 D_e^ = \widehat(\omega) E_ e^,
where
 D_ and E_ are the amplitudes of the displacement and electrical
fields, respectively,
 i 2 = −1 is the imaginary
unit.
It is important to realise that the choice of
sign for timedependence 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 lowfrequency limit of permittivity,
also called the static permittivity \varepsilon_ (also
\varepsilon_):
 \varepsilon_ = \lim_ \widehat(\omega).
At the highfrequency 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 \delta 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_), D and E remain proportional, and
 \widehat = \frace^ = \varepsilone^.
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(\omega) = \varepsilon'(\omega) + i\varepsilon(\omega)
= \frac \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. 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 frequencyindependent or by model functions.
At a given frequency, the imaginary part of
\widehat 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 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). The optical dielectric function is given by the
fundamental expression:

 \epsilon(\omega)=1+\frac\sum_\int_^ W_(E) \left[ \phi (\hbar
\omega  E)\phi( \hbar \omega +E) \right ] \, dx \
.
In this expression, Wcv ( E ) represents the
product of the
Brillouin
zoneaveraged transition probability at the energy E with the
joint
density
of states, Jcv ( E ); φ is a broadening function, representing
the role of scattering in smearing out the energy levels. In
general, the broadening is intermediate between
Lorentzian and
Gaussian;
for an alloy it is somewhat closer to Gaussian because of strong
scattering from statistical fluctuations in the local composition
on a nanometer scale.
Classification of materials
Materials can be classified according to their
permittivity and
conductivity,
σ. Materials with a large amount of loss inhibit the propagation of
electromagnetic waves. In this case, generally when \frac\gg1, we
consider the material to be a good conductor. Dielectrics are
associated with lossless or lowloss materials, where \frac\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.
Lossy medium
In the case of lossy medium, i.e. when the
conduction current is not negligible, the total current density
flowing is:
 J_ = J_c + J_d = \sigma E  i \omega \varepsilon E = i \omega
\widehat E
where
 σ is the conductivity
of the medium;
 ε is the real part of the permittivity.
 \widehat 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 + i \frac
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 above effects often combine to cause
nonlinear 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 12% of the original voltage.
However, it can be as much as 15  25% in the case of
electrolytic
capacitors or
supercapacitors.
Quantummechanical interpretation
In terms of
quantum
mechanics, permittivity is explained by
atomic and
molecular interactions.
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. The field does work against the bonds and the energy is
absorbed by the material as
heat. 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 watercontaining organs such as the
eye.
http://www.dartmouth.edu/~etrnsfer/water.htm
At high frequencies (such as UV and above),
molecules cannot relax, and the energy is purely absorbed by atoms,
exciting
electron
energy levels.
While carrying out a complete
ab initio (that
is, firstprinciples) 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 1storder and 2ndorder (respectively) lumped
system parameter linear representation (such as an RC and an LRC
resonant circuit).
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. 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.
 Lowfrequency time domain
measurements (10−6−103 Hz)
 Lowfrequency frequency
domain measurements (10−5−106 Hz)
 Reflective coaxial methods (106−1010 Hz)
 Transmission coaxial method (108−1011 Hz)
 Quasioptical methods (109−1010 Hz)
 Fouriertransform methods (1011−1015 Hz)
References and notes
Suggested readings
 Theory of Electric Polarization: Dielectric Polarization,
C.J.F. Böttcher, ISBN 0444415793
 Dielectrics and Waves edited by A. von Hippel, Arthur R., ISBN
0890068038
 Dielectric Materials and Applications edited by Arthur von
Hippel, ISBN 0890068054.
permittivity in Bulgarian: Диелектрична
проницаемост
permittivity in Catalan: Permitivitat
permittivity in Czech: Permitivita
permittivity in German: Permittivität
permittivity in Spanish: Permitividad
permittivity in Esperanto: Elektra
konstanto
permittivity in French: Permittivité
permittivity in Korean: 유전율
permittivity in Indonesian: Permittivitas
permittivity in Italian: Costante
dielettrica
permittivity in Hebrew: מקדם דיאלקטרי
permittivity in Lithuanian: Dielektrinė
skvarba
permittivity in Dutch: Permittiviteit
permittivity in Japanese: 誘電率
permittivity in Norwegian: Permittivitet
permittivity in Polish: Przenikalność
elektryczna
permittivity in Slovak: Permitivita
permittivity in Slovenian: Dielektričnost
permittivity in Finnish: Permittiivisyys
permittivity in Swedish:
Permittivitet