Permittivity (Absolute Permittivity and Relative Permittivity)

We know that two similarly charged bodies repeal each other. On the other hand two oppositely charged bodies attract each other. The Coulomb’s law gives the expression for the force acting between two charged bodies (either similarly or oppositely charged).

Coulomb’s Law

Suppose, F is the force acting between two electrically charged bodies. Furthermore, as per Coulomb’s law the expression of F will be,

coulomb's law

Where ‘Q1’ and ‘Q2’ are the charges of the bodies. Whereas ‘d’ is the distance between the center of these charged bodies.

Permittivity of The Medium

The term ε0εr in the expression of the Coulombic force (F) is the permittivity. In fact it is the permittivity of the medium in which the charged bodies are placed.

Absolute Permittivity

In the term of the permittivity that is in ε0εr, ε0 is the absolute permittivity of a vacuum space. Hence, it will have a specific value. And the value of this ε0 is 8.85×10-12 F/m.

Likewise other mediums have different absolute permittivity values. For different scientific calculation we need to recall those values as per requirement. Obviously it is difficult to remember all those values individually. But there is a solution from where the concept of relative permittivity comes.

Relative Permittivity

We consider the absolute permittivity of a vacuum space as a unity. Considering this as a unit we compare the actual permittivity of other mediums. In this way it becomes easy to remember those numerical values. When we need to have the actual value of the permittivity of a certain medium, we just multiply the absolute permittivity of the vacuum space with that numerical value.

For example the actual or absolute permittivity of mica is 44.27×10-12 F/m. So, if we divide this value with the absolute permittivity of vacuum we get 5 as numerical value. It is needless to say that 5 is easier to remember than 44.27×10-12. So whenever we need to have the absolute permittivity of mica we just multiply the absolute permittivity of vacuum with 5. We refer to this 5 as the relative permittivity of mica.

Formula of Relative Permittivity

Suppose, the absolute permittivity of a certain medium is ε. Then the relative permittivity of the same medium is ε/ε0. This ε0 is absolute permittivity of vacuum.

formula of relative permittivity

Significance of Permittivity

To understand the significance of permittivity we need to recall the expression of force acting between two charged bodies as per Coulomb’s law.

coulomb's law

This expression shows that the force is directly proportional to the product of the charges.

significance of permittivity 1

Also, this expression shows that the force is inversely proportional to the square of the distance between the charged bodies.

significance of permittivity 2

Again 4π is a constant term. So, we can finally write,

significance of permittivity 3

Where ε is the permittivity of medium. So, finally we can say the force acting between two electrically charged bodies depends on the permittivity of the medium in which the bodies are placed.

Permittivity of Water

The relative permittivity of water is 80. Hence, the absolute permittivity of water is 80 times of that of a vacuum space.

Relative Permittivity of Air

The relative permittivity of the air is 1.0006. Besides this, we have considered relative permittivity of a vacuum space as 1. Since, 1.0006 very nearly equals to 1. We can say the permittivity of air is the same as that of a vacuum space.

Example

For example, let us consider a molecule sodium chloride. The sodium chloride molecule has an ionic bond between positive Na+ ion and negative Cl ion. Obviously we can consider the Na+ ion as a positively charged body. On the other hand, we can consider the Cl ion as a negatively charged body. Due to the coulombic force acting between these two oppositely charged bodies the Na+ ion and Cl ion are attached together in the air. But when we dissolve sodium chloride salt in water, this coulombic force becomes 80 times weaker. Because the relative permittivity of water is 80. So, this weak attraction force no longer can attach the Na+ and Cl ions together. As a result they de-touch from each other and stay in the water in the form of individual Na+ and Cl ions.

This is how the permittivity of a medium acts.

Unit of Permittivity

We can determine the unit of permittivity from the expression of columbic force.

unit of permittivity

Unit of Relative Permittivity

The relative permittivity is nothing but the ratio of the absolute permittivity of medium to absolute permittivity of vacuum.

unit of relative permittivity

Since, εr is the ratio of two absolute permittivity having the unit of F/m; the relative permittivity is a unit less quantity.

Relative Permittivity of Different Mediums

SL. No. Material Permittivity (εr)

(Approx)

1 Air 1.0
2 Paper 1.4
3 Teflon 2.1
4 Polypropylene 2.4
5 Polyethylene 2.5
6 Carbon-di-sulfide 2.6
7 Mylar 3.1
8 Polyimide 3.4
9 Silicon-di-oxide 3.9
10 Mica 5.0
11 Neoprene 6.5
12 Rubber 7.0
13 Diamond 9.8
14 Silicon 11.6
15 Ammonia 26.4
16 Methanol 30.1
17 Ethylene glycol 37.4
18 Glycerol 42.5
19 Water 87.9
20 Sulfuric acid 96.8

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