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Dimensions of Permittivity

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Last updated date: 20th May 2024
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Learn What is Permittivity on Vedantu

Permittivity is an important topic in electricity. It is often represented by the symbol \[ \varepsilon _{0}\] and the ratio of \[\frac{\varepsilon}{\varepsilon _{0}}\] is referred to as the dielectric constant. In the SI system unit of permittivity is meter - kilogram-second   Permittivity gives a relation between the electric field and the electric displacement it undergoes due to the field. It basically means the tendency of the atomic charge to get distorted by the electric field. Permittivity can be of a medium or it can be even in a vacuum space. When a medium is there the medium shows its ability to restrict the electric field generated between two charges and this force with which it restricts is inversely proportional to the strength of the electric field. However in the case of permittivity in a vacuum where permittivity is minimum due to maximum electric field lines in between the two charges without a medium in between them. 

 

Permittivity is the ability of a material to oppose the passing of electric field lines through it. It can be better understood by Coulomb’s law.

 

Let’s understand permittivity from Coulomb’s law.

 

Coulomb’s law states that when two charges are kept at a distance from each other. The distance between their centers is ‘r’. Then, the electrostatic force between them is given by  \[F = \frac{kq_{1}q_{2}}{r^2}\].

 

Where k depends upon the medium, and its value is \[\frac{1}{4\pi \varepsilon }\].

 

So, the above formula becomes:

 

\[ F = \frac{1}{4πε}.\frac{q_{1}q_{2}}{r^{2}}\]…(1)

 

Here, ε is the permittivity, and it is inversely proportional to the force. This means more is the permittivity, less is the electrostatic force between the two charges.

 

So, permittivity is a property of a medium that permits its field to decrease the interaction field between the two charges.

 

In this article, we are going to derive the dimensional formula of permittivity. Before, starting with our derivation, let’s understand why we study the dimension of a physical quantity.

 

Dimensions of a Physical Quantity

The dimensions of a physical object are the powers to which the base (or the fundamental) units are based to represent the physical quantities.

FAQs on Dimensions of Permittivity

1. What is the importance of permittivity in Physics syllabus?

Permittivity in physics is important to know the variation in the force experienced by a charge in the medium compared to the force it experiences in a vacuum space. It helps to determine the capacitance of the capacitor. It gives the concept of Gauss’s law which is very important in physics. It has innumerable uses in the field of electricity in day-to-day physics. Its applications in daily life cannot be ignored easily and hence this topic is rightly included in school level physics.

2. Who invented Permittivity?

Count Alessandro Volta, an Italian physicist, born in the town of Como in Duchy of Milan is credited with the discovery of permittivity. He is also credited with the invention of the electric cell and core conceptual physical concept of voltage named after him. Voltameter was again his creation. Through these contributions to physics, the SI unit of electric potential difference is named after him, Volts. Not only physics, but Volta the prodigy is also credited with the discovery of Methane gas.    

3. What is the unit of permittivity? What is the significance of permittivity?

Farad per meter is the unit of permittivity. Farad is the SI unit of electric capacitance and metre being the SI unit of length. Farad is named after the famous English physicist, Michael Faraday who is credited with the discovery of principles of electromagnetic induction, diamagnetism and electrolysis. The use of permittivity is felt in calculation of electric field by knowing the value of electric displacement field and dividing the latter by the absolute permittivity constant.

4. What are the Differences Between Permeability and Permittivity?

The main differences between permeability and permittivity are as follows

  • Permeability is actually the measure of the capability of a certain body to allow the magnetic lines of force to pass through it while permittivity only determines how much resistance a material can impose in the form of electric field. 

  • Permeability is represented by 𝛍. and Permittivity is represented by the symbol 𝛜 

  • Unit of permeability is Henry/meter while that of permittivity is Farad/meter.

  • The physical basis of permeability is Magnetization while that of permittivity is Polarization.

  • Field used in permeability is magnetic field but that in permittivity is electric field.

  • Application of permeability is seen in the transformer core while that of permittivity is seen in capacitor.

  • Permeability determines the ratio of density of magnetic field to strength of magnetic field while permittivity determines the ratio of displacement to the strength of the electric field.

5. What is the importance of this topic in JEE?

The topic of permittivity is quite important both for JEE Mains and JEE Advanced. At Least 1-2 questions are sure to come from this topic. The topic is not very hard to understand. A little effort in this topic can bring sure marks. The topic should be read conceptually. The formula and derivations of this topic should be practiced to get a fluency in the numerical problems of this topic. Practicing different types of problems from sample papers on this topic will bring confidence to score good marks in this section. The weightage of this topic is quite significant in all other competitive exams, especially the ones for engineering admission. Vedantu is constantly giving support in all topics including this topic with resourceful study material and sample questions prepared by physics teachers who have a lot of experience in framing questions for competitive exams.

6. What is the Formula for Relative Permittivity?

We know that εr is the ratio of the capacitance of a capacitor filled with the dielectric in between the plates to the capacitance of the same capacitor with vacuum or air between the plates, i.e., without the dielectric material.


So, \[\varepsilon_{r} = \frac{C_{m}}{C_{o}}\]


Where \[C_{m} = KC_{o} = \frac{\varepsilon_{0}A}{d} = \frac{\varepsilon A}{d}\]

7. The Capacity of a Capacitor Becomes 20 μF When the Air Between the Two Plates is Removed by a Dielectric slab of K = 4. What is the Capacity of a Condenser with Air in Between the Plates?

Here, \[C_{m}\] = 20 μF, K = 4,  \[C_{0}\] = ?


As \[K= \frac{C_{m}}{C_{0}}\]


\[ \therefore C_{m} = \frac{C_{0}}{K} = \frac{20}{4}\] = \[5 \mu F\]

8. What is the Value of Absolute Permittivity of Water?

Absolute permittivity is the value of the permittivity of free space. Its value is \[8.85 \times 10^{-12}C^{2}N^{-1}m^{-2}\]