Dielectric Constant in Vacuum

Introduction

The dielectric constant is a critical concept which is used in the field of electricity. Different materials have a massive property to hold huge electric charges for long durations. This property of the material is called dielectric.

What is Dielectric?

A material that has poor electrical conductivity but owns the capability to store an electrical charge is called dielectric material. There are many dielectric materials like vacuum, metal, air or water. It is important to increase capacitance in a circuit of capacitance in those circuits’ dielectrics play a major role.

What is Dielectric Constant?

The dielectric constant evaluates the capacity of a dielectric material to reserve energy in an electric field. It is also known as relative permittivity.

• It is defined as the proportion of the permittivity of the material to the permittivity of the free space.

• It also explains the flux density generated at a point in the field due to electric field intensity.

Dielectric Constant Formula

The mathematical expression for the dielectric constant is given below −

$$\mathrm{K=\frac{\epsilon}{\epsilon_0}}$$

where K is the dielectric constant

$\mathrm{\epsilon}$ is the permittivity of the material

$\mathrm{\epsilon_o}$ is the permittivity of the free space

Dielectric Constant Units

It has no unit and dimension as it is a ratio of two like quantities.

Dielectric Constant Symbol

The specific inductive capacity, called the dielectric constant, is symbolised by the Greek letter Kappa, K.

The Theory Behind Dielectric Constant

It is a primary variable needed to specify a capacitor. An electronic device used to store charge is called a capacitor, which is formed by putting a dielectric insulating plate in between the metal conducting plates.

• This dielectric material layer determines the efficiency and capacity of a capacitor to store charge. Thus, it is advised to select the finest dielectric material.

• This property of dielectric is considered important in the working of a capacitor.

• The dielectric constant can also be explained as the ratio of the electric field without a dielectric $\mathrm{(E_0)}$ to the resultant electric field with a dielectric (E).

$$\mathrm{K=\frac{E_0}{E}}$$

• $\mathrm{E_0}$ is always greater or equal to E. Therefore, the value of the dielectric constant K is always greater than 1.

• More the value of K large amounts of charge will be stored in the capacitor.

• The relation of capacitance of a capacitor with dielectric C and capacitor without dielectric $\mathrm{C_0}$ is

$$\mathrm{C=KC_0}$$

Thus, if dielectric material is filled in the space between the plate of capacitors, then the value of its capacitance will get increased by the value of the dielectric constant.

The formula of capacitance for parallel plate capacitor is

$$\mathrm{C=\frac{K \varepsilon_0A}{d}}$$

Here,

• C refers to the capacitance of the parallel plate capacitor

• K refers to the dielectric constant

• $\mathrm{\varepsilon_0}$ refers to the permittivity of free space

• A refers to the area of the parallel plate capacitor

• d is the distance between parallel plates

From the above expression, it is understood that the capacitance can be increased by enhancing the value of the dielectric constant and by reducing the distance between the parallel plates.

Dielectric Constant Value

The value of a dielectric constant is different for distinct dielectric materials that are given below −

S. No.	Dielectric Material	Dielectric Constant Value
1	Teflon	2.1
2	Concrete	4.5
3	Air	1.00059
4	Vacuum	1
5	Water	80
6	Silicon	11.68
7	Diamond	5.5 - 10

Table-1: Dielectric constant for different dielectric materials

Factors Affecting Dielectric Constant

There are several factors that affect the value of the dielectric constant that are described below −

Temperature

At low temperatures, the adjustment of the molecules of dielectric material is difficult. But if the temperature is increased, there is an increase in the dipole moment of the material which increases the value of the dielectric constant. This temperature at which the dielectric constant starts increasing is referred to as the transition temperature. If the temperature is raised above the transition temperature, then there is a continuous decrease in the dielectric constant.

Frequency

If the frequency of the external voltage is increased, the dielectric constant value turns non-linear.

Applied Voltage

If alternating current voltage is supplied then the value of the dielectric constant will get increased whereas its value gets decreased if the direct current voltage is supplied.

Humidity or Moisture

With the increase in humidity or moisture, the value of the dielectric constant decreases.

Heating Effect

If the dielectric material is heated, there is a motion in the molecules of the material which leads to the dissemination of the energy that is considered a dielectric loss. This loss in the form of heat occurs when a dielectric material is provided with electrical energy.

Structure and Morphology

The dielectric constant is affected by the structure and morphology of the material.

Conclusion

The present tutorial gives a brief description of the dielectric constant which is also known as the historic term used for relative permittivity. For zero frequency the permittivity of the material is regarded as the static or frequency-based variant.

In addition, the factors affecting dielectric constant have been briefly provided. Different expressions of this constant with respect to several physical quantities have been stated in this tutorial. This tutorial may be useful for understanding the permittivity of different dielectric materials.

FAQs

Q1. What do you understand about the polarization of a dielectric material?

Ans. When an external electric field is applied, electric dipoles are produced in the dielectric material; this process is known as the polarization of a dielectric material.

Q2. Explain how relative permittivity affects the environment.

Ans. When there is a change in the humidity, temperature and barometric pressure, the air in the atmosphere gets affected which influences relative permittivity and hence changes the value of capacitance. With the help of sensors, these changes can be measured.

Q3. Define ionic polarization.

Ans. The movement of positive or negative ions in the opposite direction when an external electric field is applied is known as ionic polarization.

Q4. What do you mean by ferroelectric materials?

Ans. When an external electrical field is not applied, materials which show electronic polarization are known as ferroelectric materials. For example, Barium Titanate $\mathrm{(BaTiO_3)}$ and Potassium Dihydrogen Phosphate $\mathrm{(KH_2 PO_4)}$

Q5. If a capacitor is placed in a vacuum the area of the cross-section of the plates is $\mathrm{6m^{2}}$ and the distance between them is 3m. Calculate the capacitance of the capacitor. $\mathrm{(\varepsilon_0=8.85\times 10^{−12}Fm^{−1})}$

Ans. Given:

Area of the cross-section of plates=$\mathrm{6m^{2}}$

Distance between the plates=3m

The capacitor is placed in a vacuum,K=1

$$\mathrm{(\varepsilon_0=8.85\times 10^{−12}Fm^{−1})}$$

The capacitance of a capacitor, $\mathrm{C=\frac{K \varepsilon_0 A}{d}}$

$$\mathrm{C=\frac{1\times 8.85\times 10^{−12}\times 6}{3}}$$

$$\mathrm{C=17.7\times 10^{−12}F}$$

Q6. Define the loss tangent of a dielectric material.

Ans. Due to several physical processes like electrical conduction, dielectric resonance and relaxation there is a dissipation of energy in the material which is known as dielectric loss tangent, denoted by $\mathrm{tan \delta}$