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Dielectric constant

From Academic Kids

The dielectric constant εr (represented as <math>\kappa<math> or K in some cases) is defined as the ratio:

<math> \epsilon_{r} = \frac{\epsilon_{s}}{\epsilon_{0}} <math>

where εs is the static permittivity of the material in question, and ε0 is the vacuum permittivity. This permittivity of free space is derived from Maxwell's Equations by relating the electric field intensity E to the electric flux density D. In vacuum (free space), the permittivity ε is just ε0, so the dielectric constant is unity.

Overview

Dielectrics are usually insulators. Examples include porcelain (ceramic), mica, glass, plastics, and the oxides of various metals. Some liquids and gases can serve as good dielectric materials. Dry air is an excellent dielectric, and is used in variable capacitors and some types of transmission lines. Distilled water is a fair dielectric.

Dielectrics have the property of making space seem bigger or smaller than it is dimensionally. For example, when you put a dielectric between two electric charges it reduces the force acting between them, just as if you had moved them apart. When an electromagnetic wave travels through a dielectric, the velocity of the wave will be slowed down and behave as if it had a shorter wavelength.

Electrically, the dielectric constant is a measure of the extent to which a substance concentrates the electrostatic lines of flux. More specifically it is the ratio of the amount of electrical energy stored in an insulator, when a static electric field is imposed across it, relative to vacuum (which has a dielectric constant of 1). Thus, the dielectric constant is also known as the static permittivity.

Measurement

The relative dielectric constant εr can be measured for static electric fields as follows: first the capacitance of a test capacitor C0 is measured with air between its plates. Then, using the same capacitor and distance between its plates the capacitance Cx with a dielectric between the plates is measured. The relative dielectric constant can be then calculated as:

<math> \epsilon_{r} = \frac{C_{x}} {C_{0}}<math>

For time-varying electromagnetic fields, the dielectric constant of materials becomes frequency dependant and in general is called permittivity.

Applications

The dielectric constant is an essential piece of information when designing capacitors, and in other circumstances where a material might be expected to introduce capacitance into a circuit. If a material with a high dielectric constant is placed in an electric field, the magnitude of that field will be measurably reduced within the volume of the dielectric. This fact is commonly exploited to increase the rating of capacitors.

Dielectrics are used in RF transmission lines. In a coax, polyethylene can be used between the center conductor and outside shield. It can also be placed inside of waveguides to form dielectric waveguides. Dielectric waveguides are seldomly used, because the dielectric losses for all known dielectric materials are too great to transfer electric and magnetic fields efficiently, however they can have special applications, for instance in filters.

Optical fibers are purposely doped with impurities so as to control the precise value of εr within the cross-section. This will control the refractive index of the material and therefore also the optical modes of transmission. Doped fiber can also be configured to form an optical amplifier.

Dielectrics are also used in Printed Wiring Boards (PWBs), in the layers beneath etched conductors.de:Dielektrizitätszahl sl:influenčna konstanta

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