Dielectric

A dielectric, or electrical Insulator , is a substance that is highly resistant to the flow of Electric Current . Although a Vacuum is also an excellent dielectric, the following discussion applies primarily to physical substances.

EXPLANATION

When an electric field is applied to a dielectric medium, a . The Displacement Current can be thought of as the elastic response of the dielectric material to the applied electric field. As the magnitude of the electric field is increased, the displacement is stored in the dielectric material, and when the electric field is decreased the material releases displacement current. The electric displacement can be separated into a vacuum contribution and one arising from the dielectric 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 dielectric are related,

arepsilon_{r} = \chi + 1

.

Complex permittivity in dielectrics

Apart from a vacuum, the response of normal dielectrics to external fields generally depends on the Frequency of the field. This frequency dependence is because 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

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Dielectric