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# permittivity (electric permittivity)

## What is permittivity (electric permittivity)?

Permittivity (electric permittivity) is the ratio of electric displacement to the electric field intensity. It is a constant of proportionality between these two parameters.

In the meter-kilogram-second and International System of Units (SI) frameworks, the permittivity of free space in a vacuum is symbolized as εo. Its value is approximately equal to 8.85 x 10-12 farads per meter (F/m). In other materials, the permittivity constant can have a different value and is often substantially greater than the free space value.

## Permittivity explained

Permittivity is a property of a material that measures the opposition it offers against an electric field. It affects how electric fields propagate and is a fundamental parameter in electromagnetics and materials science.

Another way of looking at permittivity is as the tendency of a material's atomic charge to distort when the material is placed in an electric field. This tendency is also called charge distortion or electric polarization. The larger the electric polarization, the larger the value of the material's permittivity.

### Permittivity and dielectric constant

The permittivity of an insulating or dielectric material is symbolized as ε. In electrical engineering applications, permittivity is often expressed in relative rather than absolute terms. Simply put, relative permittivity is the ratio of the permittivity of a substance or material to the permittivity of free space or vacuum.

If εo represents the permittivity of free space and ε represents the permittivity of a particular substance, relative permittivity is symbolized as εr. Relative permittivity is also called the dielectric constant. It is expressed as the following:

εr=ε/εo

εr=ε/(8.85⋅10-12)=ε⋅(1.13⋅1011)

Both εo and ε are expressed in farads per meter. However, εr is a dimensionless constant. Sometimes, the dielectric constant may also be symbolized by κ.

In the centimeter-gram-second system, the value of the permittivity of free space, εo, is arbitrarily chosen as 1.

### Dielectric constant of various materials

The permittivity of free space, εo, represents the smallest possible value of permittivity. The relative permittivity of all other substances or materials is greater than 1. These substances are called dielectric materials or simply dielectrics. A dielectric is a material that has low conductivity but a dielectric constant greater than 1.

Some common dielectrics are glass, paper, mica, various ceramics, polyethylene and certain metal oxides. Dielectrics are used in capacitors and transmission lines in alternating current, audio frequency, and radio frequency (RF) applications.

The relative permittivity of some common dielectrics are given below.

 Substance Dielectric Constant (εr) Air 1.0006 Hydrogen (0° C) 1.000265 Nitrogen (25° C) 1.000538 Helium (25° C) 1.000067 Rubber 2.0-2.3 Paper 3.85 Mica 5.6-8.0 Glass 5-10 Graphite 10-15 Silicon 11.68 Water (0° C) 88

The higher the value of the dielectric constant, the greater the opposition the material offers against the formation of an electric field.

## Types of permittivity

Although permittivity is a general term represented by ε, there are various types of permittivity. Which term or definition is used depends on the application and environment in which it is being measured.

Absolute permittivity is the measure of permittivity in a vacuum or free space. It measures the resistance encountered when forming an electric field in a vacuum. εo is the smallest possible value of permittivity.

Relative permittivity is the permittivity of a material in relation to the permittivity of a vacuum. It is symbolized as εr and is always greater than εo.

Static permittivity is the permittivity of a material when exposed to a static electric field. The value is usually measured to assess the material's response to the frequency of some applied voltage.

## Factors affecting permittivity

At low frequencies or specific temperatures, the permittivity of materials remains constant or static. However, several factors can affect it, causing it to change. In particular, permittivity almost always varies with the frequency of applied voltage. As the frequency increases, permittivity decreases. Humidity and the strength of the electric field applied also affect permittivity. Finally, when temperatures increase, permittivity falls.

Permittivity variations often are small and even negligible. Nonetheless, these characteristics must be taken into account when designing a capacitor because they can affect its performance.

## Applications of permittivity

Permittivity plays an important role in capacitor design because the value determines how much electrostatic energy a dielectric material can store per unit of volume. The two plates of a capacitor are separated by an insulator, which is a dielectric material that governs many of the capacitor's properties.

The type of insulating material chosen is important because capacitors are becoming smaller and extremely close separation is required between their plates to achieve the required level of capacitance. The right dielectric material with the right permittivity makes it possible to achieve high levels of capacitance in a small volume.

Permittivity and dielectric constant are also important for applications involving RF transmission lines and the propagation of radio waves.

In RF transmission lines, the dielectric material placed between conductors and between a conductor and ground affects important characteristics like impedance and velocity factor. In radio wave propagation, changes to the relative permittivity of the atmosphere can affect the path, traversal and transmission of radio signals.

## Permittivity vs. permeability

Permeability is a property of a material that measures its ability to support the formation of a magnetic field. It refers to the material's ability for magnetization for an applied magnetic field and plays a role in classifying materials based on their magnetization property. Permeability is the ratio of magnetic flux density, or magnetic induction, to the magnetic field strength of the material, or the intensity of a magnetic field. It is directly proportional to the conduction of magnetic lines of force. It is denoted by μ.

Mathematically, permeability is expressed as the following:

μ=magnitude of magnetic induction/intensity of magnetic field

μ=B/H

In SI units, μ is expressed as henries per meter (H/m).

The permeability of free space, expressed as μo, is known as the absolute permeability or the permeability constant. Its value is 4π⋅10-7 H/m.

The absolute permeability of other materials is expressed relative to μo as the following:

μ = μo⋅μr

Here, μr is the relative permeability of a a dimensionless quantity.

For diamagnetic materials, magnetic permeability is less than μo, and for paramagnetic materials, magnetic permeability is greater than μo.

Permittivity and permeability are important but different parameters of any given material. Whereas permittivity measures the material's ability to store energy, permeability measures its ability to support a magnetic field. Here is a summary of additional differences between permittivity and permeability.

 Permittivity Permeability Measures the opposition offered by the material against the formation of an electric fields Measures the ability of the material to allow magnetic lines to enter it Caused by polarization Caused by magnetism Represented as ε Represented as μ SI unit = farads per meter (F/m) SI unit = henries per meter (H/m) Permittivity of free space=8.85⋅10-12 F/m Permeability of free space=4π⋅10-7 H/m Main application: capacitors Main application: inductors and transformer cores

This was last updated in September 2022

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