Permittivity

Charged bodies have Coulomb forces acting upon them. We often refer to these charges as point-like and placed in a vacuum, however, in real life that's usually not the case. They are almost always surrounded by a medium that is a nonconductor of electricity - a dielectric, such as air. It's intuitive to conclude that in a dielectric medium, the forces involved decrease in comparison to those in a vacuum. To describe this relation, a coefficient that describes the extent of polarization of a material in an electric field is introduced. This coefficient is called electric permittivity, and it shows how many times the Coulomb force in a dielectric medium is smaller than in a vacuum. In this article, we'll discuss this property of matter in greater detail. 

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      Permittivity Meaning

      First, let's define what exactly is electric permittivity.

      Electric permittivity is a measurement of the degree to which a material or medium is polarized in the presence of an electric field.

      To better understand it, let's imagine the following situation. Two plates are placed in a medium with a distance \(d\) separating them.


      Permittivity Diagram showing the polarized and non-polarized dipoles StudySmarterFig. 1 - Non-polarized dipoles outside an electric field are chaotically distributed. In the presence of an electric field \(\vec{E}\) these dipoles become polarized.

      First, let's consider the case where this medium is air, made up of various molecules. These molecules are made up of sub-atomic positive nuclei and negative electrons and so in the presence of an electric field, these air molecules rotate in a way to create an electric dipole moment. The electric field created by the polarized dielectric is opposite to the direction of the external field.

      The direction of this dipole moment is in the direction of the intensity of the electric field.

      The medium, which in this case is air, resists the electric field, and this resistance is known as relative permittivity. If we remove all the air molecules leaving the electric field in a vacuum, it would experience no resistance, also known as absolute permittivity. Let's look at each of these two types of permittivity separately in the next sections of this article.

      Permittivity of Free Space

      The first kind of permittivity is known as the absolute permittivity of free space. Permittivity of free space, or vacuum, (\(\varepsilon_0\)) is a constant value equal to \(8.85\times10^{-12}\,\frac{\mathrm{C}}{\mathrm{N}\,\mathrm{m}^2}\). Mathematically, it can be obtained using the following equation:

      \[\varepsilon_0=\frac{1}{\mu_0c^2},\]

      where \(\mu_0\) is vacuum permeability equal to \(4\pi\times10^{-7} \, \frac{\mathrm{T} \, \mathrm{m}}{\mathrm{A}}\), and \(c\) is the speed of light \(3.00\times10^8\,\frac{\mathrm{m}}{\mathrm{s}}\).

      Relative Permittivity

      As soon as we're dealing with a medium other than free space, the permittivity becomes different from \(\varepsilon_0\). The extent to which this permittivity differs depends on the specific matter's atomic composition and arrangement. This value is obtained by determining how easily the electrons can change their arrangement within the material.

      Relative permittivity \(\varepsilon_\mathrm{r}\) is found using by combining the permittivity of a specific material \(\varepsilon\) and the absolute permittivity \(\varepsilon_0\), described earlier. Mathematically, they combine into the following expression:

      \[\varepsilon_\mathrm{r}=\frac{\varepsilon}{\varepsilon_0}.\]

      Relative permittivity is always greater than one and dimensionless due to the equation above!

      We can distinguish two types of materials, conductors and insulators. In conductors, the charge carriers can easily move through them. The best conductors of electricity are metals, such as copper and aluminum.

      Permittivity Inside of an Electric wire StudySmarterFig. 2 - The permittivity of all metals, including those used in electric wires, is infinite.

      The opposite occurs in insulators, where the charge carriers cannot easily move through. Another commonly used name for insulators is dielectrics, which we'll discuss in greater detail in the next section.

      Dielectric Permittivity

      First, let's define what exactly is a dielectric material.

      Dielectrics are a type of insulator, substances that have very few free-charge carriers, meaning they are not free to move as in a conductor. However, dielectrics have the additional property that they can be polarized by an electric field.

      Instead, the material itself becomes polarized in the presence of an external electric field.

      A common example of a dielectric medium is air, which has an electric permittivity of \(1.00059\). Many other non-ionized gases and liquids are also dielectrics. In a dielectric, the Coulomb force acting between charges becomes \(\varepsilon\) times weaker than if the charges were in a vacuum. This relation was mathematically defined earlier by using relative permittivity.

      Relative permittivity is also known as the dielectric constant \(\kappa\), meaning \(\kappa = \varepsilon_\mathrm{r}\).

      So all the dielectric mediums, air, paper, and oil,—weaken the electric field created by the conductors. Some of the most commonly used dielectrics and their dielectric constants are combined in the table below.

      Table 1 - Common dielectric materials and their dielectric constants.

      Medium/materialDielectric constant \(\kappa\)
      Vacuum1
      Air1.00059
      Paper3.85
      Glass5
      Rubber6.7
      Mica7
      Silicon11.7
      Isopropanol19.7
      Glycol40.6
      Water81

      Capacitance and Permittivity

      Before we can look at the expression that combines capacitance and permittivity, we must explain the concept of parallel-plate capacitors.

      A parallel-plate capacitor is made up of two separated parallel conducting surfaces that can hold equal amounts of opposite charges when placed in a circuit.

      Permittivity Parallel plate capacitor real life diagram StudySmarterFig. 3 - Parallel plate capacitor.

      Keeping that in mind, capacitance is then used to connect the amount of the charge stored on each plate and the electric potential difference created by separating those charges. Capacitance depends solely on the physical properties of the capacitor, such as its shape and material.

      Mathematically, capacitance \(C\) can be expressed as

      \[C=\kappa \varepsilon_0 \frac{A}{d}.\]

      In other words, the capacitance of a parallel plate capacitor is proportional to the area \(A\) of one of its plates and inversely proportional to the separation \(d\) between its plates. Here, the constant of proportionality (\(\kappa \varepsilon_0\)) is what relates capacitance to permittivity.

      Permittivity - Key takeaways

      • Electric permittivity is a measurement of the degree to which a material or medium is polarized in the presence of an electric field.
      • Permittivity of free space \(\varepsilon_0\) is a constant value equal to \(8.85\times10^{-12}\,\frac{\mathrm{C}}{\mathrm{N}\,\mathrm{m}^2}\).
      • The permittivity of matter differs from that of vacuum, which stems from its atomic composition and arrangement.
      • In conductors, the charge carriers can easily move through them, while in insulators or dielectrics, the charge carriers cannot easily move through.
      • Relative permittivity, also known as the dielectric constant, can be found using \( \varepsilon_\mathrm{r}=\kappa =\frac{\varepsilon}{\varepsilon_0}\).
      • A parallel-plate capacitor is made up of two separated parallel conducting surfaces that can hold equal amounts of opposite charges when placed in a circuit.
      • Capacitance of a capacitor can be calculated using the following equation: \(C=\kappa \varepsilon_0 \frac{A}{d}\).

      References

      1. Fig. 1 - Polarized and non-polarized dipols, StudySmarter Originals.
      2. Fig. 2 -Electric guide (electric wire) 3×2.5 mm (diameter) (https://commons.wikimedia.org/wiki/File:Electric_guide_3%C3%972.5_mm.jpg) by Petar Milošević (https://commons.wikimedia.org/wiki/User:PetarM) is licensed by CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/deed.en).
      3. Fig. 3 - Parallel-plate capacitor with field overlay (https://commons.wikimedia.org/wiki/File:Parallel-plate-capacitor-with-field-overlay.jpg) by MikeRun (https://commons.wikimedia.org/w/index.php?title=User:MikeRun&action=edit&redlink=1) is licensed by CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/deed.en).
      Frequently Asked Questions about Permittivity

      What is permittivity?

      Electric permittivity is a measurement of the degree to which a material or medium is polarized in the presence of an electric field.

      What is the permittivity of free space?

      The permittivity of free space is equal to 8.85x10-12 CN/m2.

      What is absolute permittivity?

      Absolute permittivity is the permittivity of free space. 

      What is relative permittivity?

      Relative permittivity is the ratio of the permittivity of a specific material and the absolute permittivity of free space. 

      How to measure permittivity?

      Permittivity can be measured using transition line method. 

      What is dielectric permittivity?

      Dielectric permittivity is another name for relative permittivity, which quantifies a material's ability to pass charges. 

      What is the permittivity of water?

      The permittivity of water is 81. 

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      Test your knowledge with multiple choice flashcards

      What is the value of the absolute permittivity of free space?

      What equation can be used to find the absolute permittivity of free space?

      In the presence of an electric field, dipoles rotate in a way to create an electric dipole moment. What is the direction of this dipole moment? 

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