Define Electric Susceptibility
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 polarisation 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 polarisation of a dielectric material, this phenomenon happens in response to an applied electric field. Electric susceptibility is directly proportional to the polarisation 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 polarisation. 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 polarisation 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 polarisation 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 polarisation 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 polarisation.
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.
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 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 polarisation.
Types of Dielectric Material
By considering the type of molecules present in the dielectric materials they can be classified into two categories - polar Dielectric Material and Non-polar Dielectric Material. Let us further discuss these two types of dielectric materials.
Polar Dielectric Material:- Due to the asymmetric shape of the molecules, the possibility of the coincidence between the positive and the negative type of molecules is kept at zero. Dipole moments do exist in this type of dielectric material.
If an external electrical field is applied to the material, then in such case the charged molecules will assemble themselves in a similar direction of the electric field. When this electric field is removed, random dipole moments will again be observed in this material and the net dipole moment will go to zero. H2O and CO2 are two famous types of polar dielectric substances.
Non-Polar Dielectric Material:- In this type of dielectric material, both the positive and negative charged molecules of the material will coincide with each other within the non-polar dielectrics. They do not have any permanent dipole moment in their molecules. These molecules show a certain level of symmetry in their structure and form. Gaseous dielectric substances like H2, O2, N2 are common examples of Non-Polar Dielectric Material.
Some Examples of Dielectric Materials and their Real-Life Application and Uses
Examples
Some examples of solid dielectric materials can be ceramics, paper, mica, glass, etc.
Distilled water and transformer oil can be used as an example of liquid dielectric materials.
Nitrogen (N2), Oxygen (O2), helium, dry air and various kinds of metal and non-metal oxides (CO2) are all types of gaseous dielectric solutions. A perfect vacuum is also dielectric in nature.
Applications:-
Dielectric materials are used in capacitors, as they have the ability to store energy.
Dielectric liquids, such as mineral oils, are used in electrical transformers, and they assist in the cooling process.
Used to improve the performance of various semiconductor devices.
FAQs on Electric Susceptibility
1. What is meant by electric susceptibility in physics?
In physics, electric susceptibility (χe) is a dimensionless proportionality constant that indicates the degree to which a dielectric material can be polarised when an external electric field is applied. A higher value of electric susceptibility means the material polarises more easily, which in turn reduces the total electric field inside it.
2. What is the formula for electric susceptibility?
The formula for electric susceptibility (χe) relates the polarisation density (P) of the material to the applied electric field strength (E). The relationship is given by:
P = ε₀ χe E
Where:
- P is the polarisation density (dipole moment per unit volume).
- ε₀ is the permittivity of free space.
- χe is the electric susceptibility.
- E is the applied electric field.
3. What is the difference between electric susceptibility and relative permittivity (dielectric constant)?
Electric susceptibility and relative permittivity (K or εr) both describe a material's response to an electric field, but they are defined differently. The relationship between them is linear: K = 1 + χe.
- Electric Susceptibility (χe) measures how easily a material can be polarised.
- Relative Permittivity or Dielectric Constant (K) measures the factor by which the electric field is reduced inside the material compared to a vacuum. It represents the material's ability to store electrical energy.
4. Why is electric susceptibility a dimensionless quantity?
Electric susceptibility (χe) is a ratio of two quantities with the same units, making it dimensionless. It is defined as the ratio of the polarisation density (P) to the product of the vacuum permittivity (ε₀) and the electric field strength (E). Since both P and ε₀E have the same units of charge per unit area (C/m²), their ratio cancels out, resulting in a pure number with no dimensions.
5. What is the key difference between an insulator and a dielectric material?
While all dielectric materials are insulators, not all insulators are effective dielectrics. The primary difference lies in their behaviour in an electric field:
- An insulator is a material that simply resists the flow of electric current due to a lack of free charge carriers.
- A dielectric material is an insulator that becomes polarised when placed in an external electric field. This means its constituent molecules form dipoles that align with the field, allowing it to store electrical energy.
6. How does introducing a dielectric with high susceptibility affect a capacitor?
Introducing a dielectric material with high electric susceptibility into a capacitor significantly increases its capacitance. When the dielectric is placed between the capacitor plates, it becomes polarised, creating an internal electric field that opposes the external field from the charges on the plates. This opposition reduces the overall electric field and, consequently, the potential difference between the plates for the same amount of charge. Since capacitance is defined as C = Q/V, a decrease in potential difference (V) for a fixed charge (Q) results in an increased capacitance.
7. What is the difference between atomic polarisability and electric susceptibility?
Atomic polarisability and electric susceptibility both describe polarisation, but at different scales.
- Atomic Polarisability (α) is a microscopic quantity. It refers to the ability of a single atom or molecule to form an electric dipole when subjected to an electric field.
- Electric Susceptibility (χe) is a macroscopic quantity. It describes the collective polarisation behaviour of the entire bulk material, representing the cumulative effect of all the individual atomic dipoles within it.
8. How does temperature generally affect the electric susceptibility of a dielectric?
For most polar dielectric materials, electric susceptibility is inversely proportional to temperature. As the temperature of the material increases, the random thermal motion of its molecules becomes more vigorous. This increased thermal agitation disrupts the alignment of the molecular dipoles with the external electric field, making the material harder to polarise. Consequently, the electric susceptibility decreases as temperature rises.
