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Dielectric Constant - Permittivity

In Electromagnetics, permittivity is one of the fundamental material parameters, which affects the propagation of Electric Fields. Permittivity is typically denoted by the symbol .

To understand permittivity, consider Figure 1, in which two charged plates are separated, with equal and opposite charges on either side. Assume for the moment that between the plates, there is no material (vacuum).

two plates with nothing between them

Figure 1. Two Plates with Equal Charge Separated by a Distance d.

As you can imagine, there will exist an Electric Field in Figure 1, directed downward (from the positive charge to the negative charge). Now, imagine that some material is placed between the plates. This material is no doubt made up of atoms which often form molecules. And as in the case of water, these molecules often look (electrically) like small dipoles (with a positive charge on one end and negative charge on the other end). This is illustrated in Figure 2 for a water molecule.

example of an H20 molecule (water) displaying a dipole moment

Figure 2. Illustration of an H20 Molecule (water) exhibiting an Electric Dipole Moment.

In general, a material will be made up of some lattice or composition of molecules or atoms. These molecules will often have some sort of dipole moment. In the absence of an external electric field, these molecules will align randomly, as shown in Figure 3:

without an externally applied field, the molecules of a substance have random orientations

Figure 3. In the absence of an externally applied electric field, the molecules of a material have random orientations.

Now, suppose this material is placed between the charged plates of Figure 1. The result is that the molecules will align themselves as shown in Figure 4:

the dipoles moment opposes the externally applied field - this is permittivity

Figure 4. The Molecules are aligned by their Dipole Moment and the external Electric Field.

As you can see, the molecules are aligned by their dipole moment and the external electric field. The picture shows something very important - the electric field due to the dipole moment of the materials molecules opposes the external electric field E in Figure 4. The result is that the net electric field is reduced within the material. Generally, permittivity will vary with frequency, temperature, and humidity. For many common materials this variation will be negligible.

The permittivity is a measure of how much the molecules oppose the external E-field. If you recall the E-field due to a single point charge of value q [C] at a distance R:

The Electric Field from a point charge at a distance R depends on the permittivity
[Equation 1]

In Equation [1], permittivity of free space is the permittivity of Free Space, which is measured in Farads/meter. This is the permittivity of a vacuum (no atoms present). In general, the Electric Field due to a point charge will be reduced due to the molecules within a material. The effect on the Electric Field is written in Equation [2]:

The Electric Field from a point charge at a distance R is reduced by the permittivity
[Equation 2]

In Equation [2], we have added a term relative permittivity or dielectric constant. This term is known as the relative permittivity or dielectric constant. The permittivity of a medium is expressed as the product of the dielectric constant and the free space permittivity:

permittivity is the product of the dielectric constant and the free space permittivity
[Equation 3]

The dielectric constant is always greater than or equal to 1.0. This means the E-field in Equation [2] is always reduced relative to what the E-field would be in free space [Equation 1]. The permittivity is a measure of this reduction.

The permittivity of common materials is given in Table 1.

TABLE I. Common Values for the Dielectric Constant.

Water (200 deg C)
Water (20 deg C)
Water (0 deg C)
Calcium Copper Titanate

A material that has low conductivity but a dielectric constant greater than 1 is known as a dielectric.

Properties of the Permittivity in Relation to Maxwell's Equations

The permittivity is the multiplier that relates the Electric Flux Density and the Electric Field:

[Equation 5]

In addition, it is known that the speed of light in free space is related to the permittivity and permeability of a medium:

[Equation 6]

As you can see, the speed of light slows down in a dielectric relative to the speed in a vacuum. Another consequence of this is that the wavelength for an electromagnetic wave of a given frequency is smaller in a dielectric than it is in a vacuum:

permittivity reduces wavelength
[Equation 7]

Equation [7] is very important to the subject of Antenna Theory. Since antennas often need to be about a half-wavelength long for good radiation, surrounding them in a dielectric can reduce the required size (since the wavelength reduces as well, per [7]).

Maxwell's Equations

This page on permittivity or dielectric constant is copyrighted, particularly the application to Maxwell's Equations. Copyright, 2012. All rights reserved.