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Electric Susceptibility

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Define Electric Susceptibility

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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.

Overview

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

Where,

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

Where,

ε = εᵣε₀

εᵣ = (1 + Xₑ)

Dielectric Constant

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

Where,

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)

Also,

D = εE and P = XeE

Substituting this values in Equation 1 we get,

εE = ε₀E + XeE

ε = ε₀ + Xe

ε / ε₀ = 1 + Xe / ε₀

But,

ε / ε₀ = Dielectric Constant (K)

This is the required relation; clearly, the value for all-dielectric materials is greater than 1.

Dielectric Material

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.

FAQ (Frequently Asked Questions)

1. What is the relation between Permittivity and Susceptibility?

Ans: According to many physicians, permittivity is considered as the ability to resist the external electric field. This means a substance that has a high permittivity requires a high external electric field in order to get polarized. On the other hand, susceptibility is considered as the ability of a substance to get polarized. Thus, a substance that has a high susceptibility can get polarized very easily. Therefore it is clear that both the quantities are inversely proportional to each other. But if you are considering both the quantities on the basis of mathematical terms, then both are linearly dependent on each other.

2. What is Dielectric Polarization?

Ans: At the time of the electric field getting applied to a capacitor, the dielectric material or the electric insulator starts getting polarized. Through this process, the negative charges that are present in the material shift themselves towards the positive electrode and the positive charges present within the material shift towards the negative electrode. Since the charges are not free to move around within the insulator, the polarization effect that opposes the applied field is seen drawing charges onto the electrodes. This phenomenon helps in storing energy in the capacitor. The above process is known as dielectric polarization in physics terms.