The electric susceptibility is generally defined as the constant of proportionality (what can possibly be a matrix); these are related to an Electric Field E to the induced dielectric polarization density P. Electric susceptibility, which is also known as dielectric susceptibility, is considered to be a dimensionless proportionality constant which is responsible for indicating the degree of polarization of a dielectric material, this phenomenon happens in response to an applied electric field. Electric susceptibility is directly proportional to the polarization of a material.
Electric susceptibility is considered to be a quantitative measure to the extent to which an electric field applied to a dielectric constant causes polarization. When this phenomenon occurs, there is a slight displacement of positive and negative charges within the material. Most of the dielectric materials have similar properties, such as the polarization P is directly proportional to the electric field strength E; this property is common in every dielectric material. Therefore, the ratio of P and E (P/E) is considered constant. This constant generally expresses the intrinsic value of the material.
In the centimeter-gram-second system (cgs), the electric susceptibility, xₑ, is defined by a ratio that is xₑ = P/E. In the meter-kilogram-second system, electric susceptibility is defined slightly differently because the constant permittivity of a vacuum, ε₀, gets included here. The expression comes out something like this
xₑ = P/(ε₀E).
In both systems, electric susceptibility always remains a positively dimensionless number. Due to the slight difference in the definition of cgs and mks, electric susceptibility values of particular materials under the mks system get 4π times more than the cgs system.
Electric Susceptibility Formula
The formula of electric susceptibility is derived as follow:
P = ε₀XₑE
P = It is considered as the polarization density.
ε₀ = It is considered as the electric permittivity of free space.
Xₑ = It is considered as the electric susceptibility.
E = It represents the electric field.
The susceptibility is proved to be related to its relative permittivity, also known as dielectric constant εᵣ by:
Xₑ = εᵣ - 1
Therefore in the case of vacuum,
Xₑ = 0
During this time, the electric displacement D also becomes equal to the polarization density P by:
D = ε₀E + P = ε₀(1 + Xₑ) E = εᵣ
ε = εᵣε₀
εᵣ = (1 + Xₑ)
A dielectric is considered to be a material that has poor electrical conductivity but has the ability to store electric charge in it. It is capable of storing an electric charge because of dielectric polarization.
The dielectric constant of a material can be defined as the ratio of the permittivity of the substance to the permittivity of the free space.
It shows how capable a material is to hold sufficient electric flux within it.
The dielectric constant is mathematically expressed as
k = ε/ε₀
K= Dielectric Constant.
ε = The permittivity of a substance.
ε₀ = The permittivity of free space.
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Relationship between Electric Susceptibility and Dielectric Constant
The Dielectric Constant is responsible for indicating the extent to which a particular substance can conduct electricity through it.
Electric susceptibility is responsible for indicating the extent to which a given substance gets polarised when it is kept in an electric field. If the substance gets polarised more than normal, then the substance will start creating an internal field which will, in turn, oppose the external field; this, in turn, will reduce the electric flux present within the material. This is why electric susceptibility affects the electric permittivity of a medium.
So the relationship between dielectric constant and susceptibility conveys that the greater the level of polarisation lower will be the electric permittivity.
Relation between Susceptibility and Dielectric Constant
D = ε₀ (E+P). ………(1)
D = εE and P = XeE
Substituting this values in Equation 1 we get,
εE = ε₀E + XeE
ε = ε₀ + Xe
ε / ε₀ = 1 + Xe / ε₀
ε / ε₀ = Dielectric Constant (K)
This is the required relation; clearly, the value for all-dielectric materials is greater than 1.
The dielectric material is considered to be a non-metallic material. They have high resistance capability, temperature coefficient of resistance negative, and large insulation resistance. In simple words, dielectric materials are considered to be non-conducting materials which do not allow electrical flow to pass through it easily. These are poor insulators that store electric charges despite passing them.
If you place a dielectric material in the electric field, the electricity will not flow within that material. Electric charges slightly shift from their average equilibrium positions, which causes dielectric polarization.