Permittivity and Relative Permittivity or Dielectric Constant

Contents

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Key learnings:

Permittivity Definition: Permittivity is defined as a measure of how an electric field affects and is affected by a dielectric medium.
Relative Permittivity: Relative permittivity is the ratio of a medium’s permittivity to the permittivity of a vacuum.
Coulomb’s Law and Medium: The force between charged bodies changes based on the permittivity of the medium they are in.
Capacitance and Permittivity: The capacitance of a capacitor increases with higher permittivity of the dielectric medium between its plates.
Energy Storage: The energy stored in a capacitor is directly proportional to the permittivity of the dielectric medium.

When two electrically charged bodies are placed nearby, they experience a force. This force can be either attractive or repulsive depending on their charges. Like charges repel each other, while unlike charges attract. Coulomb’s Law can be used to calculate the force between these bodies.

The force acting between nearby electrically charged bodies depends on mainly three factors.

Charge of the bodies Q₁ and Q₂ coulombs that is the product of charges of the bodies.
Distance between the center of the charges i.e. d meters. The force is inversely proportional to the square of the distance d.
The medium in which the bodies are placed.

The role of permittivity comes in this third point. It is found that force acting between nearby same charged bodies separated by the same distance is different in different mediums. From the equation of Coulomb’s law, we find that the force acting between nearby electrically charged bodies is inversely proportional to the term ε_oε_r. This term is called permittivity of the medium. Here, ε_o is known as the absolute permittivity of the vacuum and ε_r is the relative permittivity of the medium in which the bodies are placed.

Relative Permittivity or Dielectric Constant

Relative Permittivity is defined as the ratio of the actual or absolute permittivity of a medium to the absolute permittivity of vacuum. If the permittivity of a medium is ε then
This ratio is 1.0006 for air. That means relative permittivity of air is 1.0006.The electrostatic force acting between nearby electrically charged bodies is inversely proportional to the permittivity of the medium. Hence, the relative permittivity of any medium is defined as the ratio of force acting between nearby electrically charged bodies in the vacuum to the force acting between the same bodies separated by the same distance in the medium.

We know that electric field intensity at any point in a field is defined as,

From that relationship, we can establish the expression of electrical flux density (D) at that point as,

From the expression of electrical field intensity and flux density we can write,

It is clear that the ratio of the electric flux density to the electric field intensity at a point in the field can be defined as the permittivity of the medium at that point.

Let us take a parallel plates capacitor with effective plate area A and distance between the plates is d and the dielectric between the plates has permittivity ε. The charge accumulated in the capacitor is Q due to an applied voltage across the capacitor is V.

The electric field intensity is
The flux density is
The relation between flux density and electric field intensity is

Here, in the expression of capacitance, it is found that capacitance of a capacitor is directly proportional to the electric permittivity of the dielectric medium between the plates.
Again, the expression of energy stored in the capacitor is

From that expression, it can be concluded that the energy stored in the capacitor is directly proportional to permittivity of the medium in between the plates.

So capacitance and the energy stored in the capacitor both are directly proportional to permittivity of the dielectric medium.

Hence permittivity of the medium used for making a capacitor is an essential parameter which determines the dimensions of the capacitor during designing of the capacitor.

Absolute Permittivity

Absolute permittivity, or simply permittivity, is defined as a medium’s property that determines how much flux density an electric field intensity creates at a point. It can be represented as the product of the absolute permittivity of a vacuum and the medium’s relative permittivity. This simplifies calculations, using the permittivity of a vacuum as a base value. Relative permittivity shows how much greater a medium’s permittivity is compared to a vacuum.

Unit of Permittivity

Unit of Absolute Permittivity

From the equation of Coulomb’s law, we can write the expression of permittivity as,
From the expression of permittivity, as shown above, we can determine the unit of permittivity as

Another Unit of Absolute Permittivity

The relationship between capacitance and the permittivity of the dielectric medium in a capacitor can be expressed as

From this expression, the unit of permittivity comes as