Definitions

# Dielectric

[dahy-i-lek-trik]
A dielectric is a nonconducting substance, i.e. an insulator. The term was coined by William Whewell in response to a request from Michael Faraday. Although "dielectric" and "insulator" are generally considered synonymous, the term "dielectric" is more often used when considering the effect of alternating electric fields on the substance while "insulator" is more often used when the material is being used to withstand a high electric field . Von Hippel, in his seminal book takes this definition further. He states,
"Dielectrics... are not a narrow class of so-called insulators, but the broad expanse of nonmetals considered from the standpoint of their interaction with electric, magnetic, of electromagnetic fields. Thus we are concerned with gases as well as with liquids and solids, and with the storage of electric and magnetic energy as well as its dissipation."

Dielectrics is the study of dielectric materials and involves physical models to describe how an electric field behaves inside a material. It is characterised by how an electric field interacts with an atom and is therefore possible to approach from either a classical interpretation or a quantum one.

Many phenomena in electronics, solid state and optical physics can be described using the underlying assumptions of the dielectric model. This can mean that the same mathematical objects can go by many different names.

## Definitions

### Classical

In the classical approach to the dielectric model, a material is made up of atoms. Each atom consists of a cloud of negative charge bound to and surrounding a positive point charge at its centre. Because of the comparatively huge distance between them, none of the atoms in the dielectric material interact with one another . Note: Remember that the model is not attempting to say anything about the structure of matter. It is only trying to describe the interaction between an electric field and matter.

In the presence of an electric field the charge cloud is distorted, as shown in the top right of the figure.

This can be reduced to a simple dipole using the superposition principle. A dipole is characterized by its dipole moment, a vector quantity shown in the figure as the blue arrow labeled M. It is the relationship between the electric field and the dipole moment that gives rise to the behavior of the dielectric. Note: The dipole moment is shown to be pointing in the same direction as the electric field. This isn't always correct, and it is a major simplification, but it is suitable for many materials.

When the electric field is removed the atom returns to its original state.

### Behavior

This is the essence of the model. The behavior of the dielectric now depends on the situation. The more complicated the situation the more rich the model has to be in order to accurately describe the behavior. Important questions are:

• Is the electric field constant or does it vary with time?
• If the electric field does vary, does it vary quickly or slowly?
• What are the characteristics of the material?
• Is the direction of the field important (isotropy)?
• Is the material the same all the way through (homogeneous)?
• Are there any boundaries/interfaces that have to be taken into account?
• Is the system linear or do nonlinearities have to be taken into account?

The relationship between the electric field E and the dipole moment M gives rise to the behavior of the dielectric, which, for a given material, can be characterized by the function F defined by the equation: $mathbf\left\{M\right\} = mathbf\left\{F\right\}\left(mathbf\left\{E\right\}\right)$.

When both the type of electric field and the type of material have been defined, one then chooses the simplest function F that correctly predicts the phenomena of interest. Examples of possible phenomena:

May be modeled by choosing a suitable function F.

## Dielectric model applied to vacuum

From the definition it might seem strange to apply the dielectric model to a vacuum, however, it is both the simplest and the most accurate example of a dielectric.

Recall that the property which defines how a dieletric behaves is the relationship between the applied electric field and the induced dipole moment. For a vacuum the relationship is a real constant number. This constant is called the permittivity of free space, ε0.

## Applications

### Capacitors

Commercially manufactured capacitors typically use a solid dielectric material with high permittivity as the intervening medium between the stored positive and negative charges. This material is often referred to in technical contexts as the "capacitor dielectric" . The most obvious advantage to using such a dielectric material is that it prevents the conducting plates on which the charges are stored from coming into direct electrical contact. More significantly however, a high permittivity allows a greater charge to be stored at a given voltage. This can be seen by treating the case of a linear dielectric with permittivity ε and thickness d between two conducting plates with uniform charge density $sigma_\left\{epsilon\right\}$. In this case, the charge density is given by

$sigma_\left\{epsilon\right\}=epsilonfrac\left\{V\right\}\left\{d\right\}$

and the capacitance per unit area by

$c=frac\left\{sigma_\left\{epsilon\right\}\right\}\left\{V\right\}=frac\left\{epsilon\right\}\left\{d\right\}$

From this, it can easily be seen that a larger $epsilon$ leads to greater charge stored and thus greater capacitance.

Dielectric materials used for capacitors are also chosen such that they are resistant to ionization. This allows the capacitor to operate at higher voltages before the insulating dielectric ionizes and begins to allow undesirable current flow.

### Cable insulation

The term "dielectric" may also refer to the insulation used in power and RF cables.

## Some practical dielectrics

Dielectric materials can be solids, liquids, or gases. In addition, a high vacuum can also be a useful, lossless dielectric even though its relative dielectric constant is only unity.

Solid dielectrics are perhaps the most commonly used dielectrics in electrical engineering, and many solids are very good insulators. Some examples include porcelain, glass, and most plastics. Air, nitrogen and sulfur hexafluoride are the three most commonly used gaseous dielectrics.

• Industrial coatings such as parylene provide a dielectric barrier between the substrate and its environment.
• Mineral oil is used extensively inside electrical transformers as a fluid dielectric and to assist in cooling. Dielectric fluids with higher dielectric constants, such as electrical grade castor oil, are often used in high voltage capacitors to help prevent corona discharge and increase capacitance.
• Because dielectrics resist the flow of electricity, the surface of a dielectric may retain stranded excess electrical charges. This may occur accidentally when the dielectric is rubbed (the triboelectric effect). This can be useful, as in a Van de Graaff generator or electrophorus, or it can be potentially destructive as in the case of electrostatic discharge.
• Specially processed dielectrics, called electrets (also known as ferroelectrics), may retain excess internal charge or "frozen in" polarization. Electrets have a semipermanent external electric field, and are the electrostatic equivalent to magnets. Electrets have numerous practical applications in the home and industry.
• Some dielectrics can generate a potential difference when subjected to mechanical stress, or change physical shape if an external voltage is applied across the material. This property is called piezoelectricity. Piezoelectric materials are another class of very useful dielectrics.
• Some ionic crystals and polymer dielectrics exhibit a spontaneous dipole moment which can be reversed by an externally applied electric field. This behavior is called the ferroelectric effect. These materials are analogous to the way ferromagnetic materials behave within an externally applied magnetic field. Ferroelectric materials often have very high dielectric constants, making them quite useful for capacitors.