Electric Susceptibility| Definition and Simple Explanation

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Electric susceptibility (χ_e) is a quantitative measure of how much an electric field applied to a dielectric substance generates polarisation.
The electric susceptibility is a dimensionless constant

When a dielectric is placed in an electric field, it acquires a polarization that depends on the field. The electric susceptibility χe relates the polarization to the electric field.
The polarization vector P is proportional to the total applied electric field intensity E and is in the same direction as E.

P=χ_eε₀E

• P is a polarization vector
• χ_e is electric susceptibility
• ε₀ is the permittivity of free space

Relation between Electric Susceptibility and Dielectric constant (Relative Permittivity)

The ratio of the force between two-point charges at a specific distance apart in free space or vacuum to the force between the same two-point charges placed at the same distance in the specified medium is defined as relative permittivity or dielectric constant.

P ∝ E
P = χ_eε₀E
χ_e = P/ε₀E
ε_r=1+χ_e
χ_e = ε_r-1 (ε_r is relative perimitivity or dielectric contant)
P = Eε₀ (ε_r-1)

Dielectric Material

Dielectric materials are nonconductors or insulators that can sustain an electric field with little power dissipation. When put in an electric field, dielectrics, unlike metals, do not conduct electricity. Dielectric polarization happens instead. This generates an internal electric field, which reduces the dielectric’s total electric field.
Ceramics, paper, mica, and glass are examples of solid dielectric materials. Distilled water and transformer oil are examples of liquid dielectric materials. Nitrogen, dry air, helium, oxides of various metals, and so on are examples of gas dielectrics.

Dielectric Constant or Relative Permivitity

The dielectric constant, also known as permittivity, is a material’s ability to store charge or function as a capacitor in an electric field. The absolute values for this property should be as low as possible for a material to be called an electrical insulator. A dielectric constant is a dimensionless number.
The vacuum dielectric constant is one.

An alternate definition of the dielectric constant is the material’s permittivity. Permittivity characterizes a substance’s influence on an electric field: the higher the permittivity, the more the material tends to reduce any field set up in it.
Therefore, the dielectric constant (ε_r) is the ratio of the dielectric permittivity (ε) to the permittivity of a vacuum (ε₀), hence the higher the polarisation created by a material in a given applied field, the greater the dielectric constant.

ε_r = ε/ε₀

Electric Susceptibility in Simple Terms

Electric susceptibility is a property of a material that describes how easily it can become polarized when an electric field is applied to it. In other words, it measures how responsive a material is to an electric field. If a material has a high electric susceptibility, it is easy to polarize, while a material with low electric susceptibility is difficult to polarize.

Think of electric susceptibility as a measure of how “electrically sensitive” a material is. Some materials, like metals, are not very sensitive to electric fields and have a low electric susceptibility, while others, like certain types of glass, are very sensitive to electric fields and have a high electric susceptibility.

Electric susceptibility is an important property of materials in many areas of science and engineering, including electronics, optics, and telecommunications. It helps us understand how materials behave in electric fields, and it is used to design and optimize devices that use or generate electric fields.

Electric Susceptibility Significance in Daily Life

Electric susceptibility has several practical applications in daily life. For example:

1. Capacitors: Electric susceptibility is an important property in the design and function of capacitors, which are used in many electronic devices, such as radios, televisions, and computers. Capacitors store electric charge and release it when needed, and their electric susceptibility determines how much charge they can store.
2. Optics: Electric susceptibility plays a role in the optical properties of materials, including how they absorb and transmit light. It is a key factor in the design of lenses, mirrors, and other optical components used in cameras, telescopes, and microscopes.
3. Insulators: Materials with high electric susceptibility are often used as insulators in electrical equipment to prevent electrical current from flowing where it shouldn’t. Examples include the insulating material used in electrical wires and the rubber or plastic insulation on electrical appliances.
4. Dielectrics: Dielectric materials, which have high electric susceptibility, are commonly used in the construction of capacitors and other electrical components. These materials can store electric energy and have very low electrical conductivity.

In summary, electric susceptibility is an important property of materials that has many practical applications in daily life, from the design of electronic devices to the construction of insulators and optical components.

Solved Problems of Electric Susceptibility

Problem 1: A capacitor has a capacitance of 50 microfarads and a voltage rating of 1000 volts. What is the electric susceptibility of the dielectric material used in the capacitor?

Solution: We can use the formula for the capacitance of a parallel-plate capacitor with a dielectric material:

C = εA/d

where C is the capacitance, ε is the electric permittivity of the dielectric material, A is the area of the plates, and d is the distance between the plates.

Rearranging this formula to solve for ε, we get:

ε = Cd/A

Substituting the given values, we get:

ε = (50 x 10^-6 F) x (1000 V) / (A)

We don’t know the area A, but we can use the fact that the electric susceptibility χ is equal to ε – ε0 / ε0, where ε0 is the electric permittivity of free space. For most practical purposes, ε0 can be taken as 8.85 x 10^-12 F/m.

So we have:

χ = (ε – ε0) / ε0

We can substitute the value of ε we calculated and ε0, and we get:

χ = [(50 x 10^-6 F x 1000 V) / A – 8.85 x 10^-12 F/m] / 8.85 x 10^-12 F/m

Simplifying this expression, we get:

χ = 5639 / A – 1

We don’t know the area A, so we cannot calculate χ directly. However, we can see that χ increases as A decreases, and vice versa.

Problem 2: A parallel-plate capacitor has a capacitance of 1.5 nF when it is empty, and a capacitance of 2.0 nF when it is filled with a dielectric material. What is the electric susceptibility of the dielectric material?

Solution: We can use the formula for the capacitance of a parallel-plate capacitor with a dielectric material:

C = εA/d

where C is the capacitance, ε is the electric permittivity of the dielectric material, A is the area of the plates, and d is the distance between the plates.

We can write the ratio of the capacitance with and without the dielectric as:

C/C0 = ε/ε0

where C0 is the capacitance without the dielectric and ε0 is the electric permittivity of free space.

Substituting the given values, we get:

2.0 nF / 1.5 nF = ε / 8.85 x 10^-12 F/m

Solving for ε, we get:

ε = (2.0 nF / 1.5 nF) x 8.85 x 10^-12 F/m

Simplifying this expression, we get:

ε = 11.8 x 10^-12 F/m

Now we can calculate the electric susceptibility χ using the formula χ = (ε – ε0) / ε0:

χ = (11.8 x 10^-12 F/m – 8.85 x 10^-12 F/m) / 8.85 x 10^-12 F/m

Simplifying this expression, we get:

χ = 0.333

Therefore, the electric susceptibility of the dielectric material is 0.333.

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