# Permittivity and Permeability

PhysicsElectricity

#### Class 11th Physics - Elasticity

6 Lectures 1 hours

#### Class 11th Physics - Oscillations

12 Lectures 2 hours

#### Class 11th Physics - Waves

14 Lectures 3 hours

## Introduction

Permittivity and permeability are two of the properties of every material that is placed within an electric field or a magnetic field. Although both the properties are related to each other to some extent, the differences between them are too vibrant. Permittivity mostly operates in the formation of an electric field whereas permeability operates in the formation of a magnetic field. In simple words, both are quantities to measure electromagnetism, where permittivity relates to the polarization and permeability relates to the magnetization of materials.

## What is Permittivity?

Permittivity is an electric quantity that decides if a material placed within an electric field is going to pass it or not. It measures a material's ability to store energy within itself to pass the electric field it is placed within. It also analyses if the material is capable enough of supporting the formation of an external electric field.

Figure 1: Permittivity

Permittivity can also be defined as a vacuum or electric constant of free space. It also outlines the number of charges required for generating a unit of electric flux within a medium. It can also be explained as the electric displacement ratio to the intensity of the electric field that is completely polarized by an electric field (Circuitglobe.com, 2022). Permittivity is denoted by the symbol ε

## What is Permeability?

Permeability is a magnetic quantity that decides if a material placed within the magnetic field is going to pass it or not. It supports the formation of a magnetic field by measuring it within a material. It is commonly related to the magnetization of materials if placed within a magnetic field.

Figure 2: Permeability

Permeability depends on some of the predominant factors like frequency, humidity, temperature and the strength of the magnetic field. The relation between the conduction of the magnetic line of force and the material placed within a magnetic field is directly proportional (Circuitglobe.com, 2022). Permeability is commonly defined by μ.

## Types of Permeability

Permeability can be categorized into three different types, relative permeability, magnetic permeability, permeability of free space and permeability of free space.

## Relative Permeability

Relative permeability is commonly represented as the material's ratio to the permeability of a vacuum (free space). For example, if the common permeability of air is $1.257 \times 10^{−6}$, then the relative permeability of the material appears as 1.000. Similarly, if a vacuum has a permeability of $4\pi\times10^{−7}$, then the relative permeability of the vacuum appears as 1. Relative permeability is denoted as μr.

## Magnetic Permeability

Magnetic permeability is the exhibition of material where it allows the magnetic line of force to pass through the magnetic force. Henry per meter is commonly used as the Sl unit of magnetic permeability and it is officially used to measure magnetic permeability. It can commonly be defined as the ratio of flux density of a magnetic force (Alhassoon, Malallah & Daryoush, 2021). Factors like the temperature, humidity and frequency of materials affect the magnetic permeability the most and decided whether a material can pass through the magnetic field it is placed into. Magnetic permeability is commonly denoted as $\mu = B/H$.

## Permeability of Free Space

The permeability of free space is mostly known as the permeability of a vacuum or air. Here, the ratio of the magnetic intensity of a vacuum or air is magnetised with the magnetic field. The permeability of the free space is represented with $\mu_{0} = B_{0}/H_{0}$.

## Permeability of Medium

The permeability of the medium is measured by analysing the intensity of the medium and the magnetising field. It is expressed with $\mu = B/H$ while presenting the permeability of a medium.

## Difference between Permittivity and Permeability

Permittivity and Permeability have multiple differences based on their physical meaning, value for free space, Sl unit, importance and many more. The first difference appears in the operational area of permittivity and permeability. Permittivity operates on the electric field whereas permeability operates on the magnetic field. In terms of physical meaning, permittivity can enable the material to polarize itself while responding to an external electric field (McLachlan, 2021).

Permeability, on the other hand, enables a material to magnetize itself while responding to external magnetic fields. Another difference between these two appears in their representation in electromagnetism.

Permittivity is denoted by $\epsilon$ whereas permeability is represented by μ. Permittivity and permeability have different SI units as well as different values in terms of free spaces. In the case of permittivity, Henry/metre is commonly used as its unit but in the case of permeability, Faraday/metre is commonly used while calculating. For permittivity, the Sl unit is $Fm^{−1}$ whereas, for permeability, the Sl unit value appears as

$$Hm^{−1} (kgms^{−2}A^{−2})$$

Similarly, the value in the free space in terms of permittivity is 8.85 $Fm^{−1}$ and for permeability, the value in the free space is 1.26$Hm^{−1}$. The values of permittivity are related to the electric fields whereas permeability is related to the magnetic fields (Han, 2020).

Permittivity and permeability both have real-life applications and importance based on their quantity. Permittivity is commonly used in the capacitors as the dielectric materials and permeability is used in the inductors and transformer cores. In addition, permittivity is not commonly affected by external factors whereas permeability is affected by the strength of the field, humidity, frequency and temperature of the external environment (Scirp.org, 2022). Based on the displacement and density of the electric field, permittivity and permeability can also be explained. Here, permittivity occurs due to high polarization, whereas permeability occurs due to magnetism.

## Conclusion

Permittivity and Permeability are two of the core concepts related to electromagnetic theory. Permittivity is related to an electric field formation which measures how a material can allow electromagnetic force to pass through it. Permeability, on the other hand, is related to the formation of a magnetic field where it measures how magnetic force can pass through the material placed into the magnetic force line. Though the permittivity and permeability are related, they have sheer differences in terms of physical meaning, Sl unit and the value in the free space. So, with these differences permittivity and permeability appear as important for real-life application. With their application in making capacitors and transformer cores, both these units have become an integral part of human day-to-day lives.

## FAQs

Q1. Does the speed of light depend on permittivity and permeability in real-time?

Yes, light in the space depends on permittivity and permeability, as their values are different for different materials. Due to their different values, the speed of light appears different for different materials in space.

Q2. How permittivity and permeability can be applied in daily lives?

High permittivity is used in the formation of dielectric materials in capacitors and permeability is used for making inductors and transformer cores.

Q3. What is the main difference between permittivity and permeability?

The main difference between permittivity and permeability is in their operating fields. Permittivity operates in the electric fields whereas permeability operates in the magnetic fields.

Q4. What are the values of free space permittivity and permeability?

The value of free space permittivity is 8.85F/m and for permeability, the value is 1.26 H/m.

## References

### Journals

Alhassoon, K. A., Malallah, Y., & Daryoush, A. S. (2021). Complex Permittivity and Permeability Extraction of Ferromagnetic Materials For Magnetically Tuned Microwave Circuits. IEEE Journal of Microwaves, 1(2), 639-645. Retrieved from: https://ieeexplore.ieee.org/iel7/9171629/9398231/09398245.pdf

McLachlan, D. S. (2021). The percolation exponents for electrical and thermal conductivities and the permittivity and permeability of binary composites. Physica B: Condensed Matter, 606, 412658. Retrieved from: https://www.sciencedirect.com/science/article/pii/S0921452620306475