Information About

Permittivity
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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 ( arepsilon_0) is 8.8541878176x10-12 Farad s per Meter (F/m).


EXPLANATION


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

:\mathbf{D}= arepsilon \cdot \mathbf{E}

where ε is a Scalar if the medium is Isotropic or a 3 by 3 Matrix otherwise.

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.

In SI units, permittivity is measured in Farad s per Metre (F/m). The displacement field D is measured in units of Coulomb s per Square Metre (C/m2), while the electric field '''E''' is measured in Volt s 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, arepsilon_0 , is the scale factor that relates the values of D and '''E''' in a vacuum. arepsilon_0 is equal to 8.8541878176...×10-12 F/m. The units of arepsilon_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.


VACUUM PERMITTIVITY


The permittivity of a material is usually given relative to that of vacuum, as a relative permittivity, arepsilon_{r} (also called Dielectric Constant in some cases). The actual permittivity is then calculated by multiplying the relative permittivity by arepsilon_{0}:

: arepsilon = arepsilon_r arepsilon_0 = (1+\chi_e) arepsilon_0

where \,\chi_e is the Electric Susceptibility of the material.

Vacuum permittivity arepsilon_{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 ''', rac{1}{ 4 \pi \epsilon_0} , which expresses the attraction between two unit charges in vacuum.

: arepsilon_0 = rac{1}{c^2\mu_0} = 8.8541878176\ldots imes 10^{-12} \ \mathrm{F/m},

where c is the Speed Of Light and \mu_0 is the Permeability of vacuum. All three of these constants are exactly defined in SI units.


PERMITTIVITY IN MEDIA


In the common case of Isotropic media, D and '''E''' are parallel Vector s and arepsilon is a Scalar , but in general Anisotropic media this is not the case and arepsilon is a rank-2 Tensor (causing Birefringence ). The permittivity arepsilon and magnetic Permeability \mu of a medium together determine the Phase Velocity ''v'' of Electromagnetic Radiation through that medium:

: arepsilon \mu = rac{1}{v^2}

When an electric field is applied to a medium, a 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

:\mathbf{D} = arepsilon_{0} \mathbf{E} + \mathbf{P} = arepsilon_{0} \mathbf{E} + arepsilon_{0}\chi\mathbf{E} = arepsilon_{0} \mathbf{E} \left( 1 + \chi ight),

where P is the Polarization of the medium and \chi its Electric Susceptibility . It follows that the relative permittivity and susceptibility of a sample are related, arepsilon_{r} = \chi + 1.


Complex permittivity


Opposed to 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 \omega, arepsilon ightarrow \widehat{ arepsilon}(\omega). The definition of permittivity therefore becomes

:D_{0}e^{i \omega t} = \widehat{ arepsilon}(\omega) E_{0} e^{i \omega t},

where D_{0} and E_{0} 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 arepsilon_{s} (also arepsilon_{DC}):

: arepsilon_{s} = \lim_{\omega ightarrow 0} \widehat{ arepsilon}(\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 measureable 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_{0}), D and '''E''' remain proportional, and