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Dielectric Constant

Dielectric constant

The relative dielectric constant ε_r (represented as

\kappa

or K in some cases) is defined as the ratio: :

\varepsilon_ = \frac

where ε_s 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 good dielectric if kept free from impurities and has a relative dielectric constant of about 80. Dielectrics have the property of making space seem bigger or smaller than it is dimensionally. For example, when a dielectric material is placed between two electric charges it reduces the force acting between them, just as if they had moved apart. When an electromagnetic wave travels through a dielectric, the velocity of the wave will be reduced and it will 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 ε_r 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 C_x with a dielectric between the plates is measured. The relative dielectric constant can be then calculated as: :

\varepsilon_ = \frac

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

Practical relevance

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 used to increase the capacitance of a particular capacitor design. The layers beneath etched conductors in Printed Wiring Boards (PWBs) also act as dielectrics. Dielectrics are used in RF transmission lines. In a coaxial cable, polyethylene can be used between the center conductor and outside shield. It can also be placed inside waveguides to form filters. Optical fibers are examples of dielectric waveguides. They consist of dielectric materials that are purposely doped with impurities so as to control the precise value of ε_r within the cross-section. This controls 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.

Permittivity

The permittivity of a medium is an intensive physical quantity that describes how an electric field affects and is affected by the medium.

Explanation

Permittivity can be looked at as the quality of a material that allows it to store electrical charge. A given amount of material with high permittivity can store more charge than a material with lower permittivity. A high permittivity tends to reduce any electric field present. Therefore the capacitance of a capacitor can be increased by increasing the permittivity of the dielectric material inside it. In electromagnetism one can define an electric displacement field D, which represents how an applied electric field E will influence the organization of electrical charges in the medium, including charge migration and electric dipole reorientation. Its relation to permittivity is given by :

\mathbf=\varepsilon \cdot \mathbf

where ε is a scalar if the medium is isotropic or a 3 by 3 matrix otherwise. Permittivity can take a real or complex value. In general, it is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In SI units, permittivity is measured in farads per metre (F/m). The displacement field D is measured in units of coulombs per square metre (C/m²), while the electric field E is measured in volts per metre (V/m). D and E represent the same phenomenon in that they are the results of a charge. D is useful for specifying the electric flux of a charge. E is useful for measuring the force on a unit charge within the electric flux. The permittivity of free space,

\varepsilon_0

, is the scale factor that relates the values of D and E in a vacuum.

\varepsilon_0

is equal to 8.8541878176...×10^-12 F/m. The units of

\varepsilon_0

in the International System of Units are farads per meter (F/m). In the International System of Units, force is in newtons (N), charge is in coulombs (C), distance is in meters (m), and energy is in joules (J). As in all equations that describe physical phenomena, using a consistent set of units is essential.

Vacuum permittivity

The permittivity of a material is usually given relative to that of vacuum, as a relative permittivity,

\varepsilon_

(also called dielectric constant in some cases). The actual permittivity is then calculated by multiplying the relative permittivity by

\varepsilon_

: :

\varepsilon = \varepsilon_r \varepsilon_0  = (1+\chi_e)\varepsilon_0

where

\,\chi_e

is the electric susceptibility of the material. Vacuum permittivity

\varepsilon_

("the permittivity of free space") is the ratio D/E in vacuum. It also appears in Coulomb's law as a part of the Coulomb force constant,

\frac

, which expresses the attraction between two unit charges in vacuum. :

\varepsilon_0 = \frac = 8.8541878176\ldots \times 10^ \ \mathrm

, where

c

is the speed of light and

\mu_0

is the permeability of vacuum. All three of these constants are exactly defined in SI units.

Permittivity in media

In the common case of isotropic media, D and E are parallel vectors and

\varepsilon

is a scalar, but in general anisotropic media this is not the case and

\varepsilon

is a rank-2 tensor (causing birefringence). The permittivity

\varepsilon

and magnetic permeability

\mu

of a medium together determine the phase velocity v of electromagnetic radiation through that medium: :

\varepsilon \mu = \frac

When an electric field is applied to a medium, a current flows. The total current flowing in a real medium is in general made of two parts: a conduction and a displacement current. The displacement current can be thought of as the elastic response of the material to the applied electric field. As the magnitude of the electric field is increased, the displacement current is stored in the material, and when the electric field is decreased the material releases the displacement current. The electric displacement can be separated into a vacuum contribution and one arising from the material by :

\mathbf = \varepsilon_ \mathbf + \mathbf = \varepsilon_ \mathbf + \varepsilon_\chi\mathbf = \varepsilon_ \mathbf \left( 1 + \chi \right)

, where P is the polarization of the medium and

\chi

its electric susceptibility. It follows that the relative permittivity and susceptibility of a sample are related,

\varepsilon_ = \chi + 1

Complex permittivity

electric susceptibility Opposed to vacuum, the response of real materials to external fields generally depends on the frequency of the field. This frequency dependence reflects the fact that a material's polarization does not respond instantaneously to an applied field. The response must always be causal (arising after the applied field). For this reason permittivity is often treated as a complex function of the frequency of the applied field

\omega

\varepsilon \rightarrow \hat(\omega)

. The definition of permittivity therefore becomes :

D_e^ = \hat(\omega) E_ e^,

where

D_

and

E_

are the amplitudes of the displacement and electrical fields, respectively,

i=\sqrt

is the imaginary unit. The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity or dielectric constant

\varepsilon_

(also

\varepsilon_

): :

\varepsilon_ = \lim_ \hat(\omega)

At the high-frequency limit, the complex permittivity is commonly referred to as ε_∞. At the plasma frequency and above, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity is a good approximation for altering fields of low frequencies, and as the frequency increases a measureable phase difference

\delta

emerges between D and E. The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate fields strength (

E_

), D and E remain proportional, and :

\hat = \frace^ = |\varepsilon|e^

. Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way: :

\hat(\omega) = \varepsilon'(\omega) - i\varepsilon

(\omega) = \frac \left( cos\delta - i\sin\delta \right) . In the equation above, $\varepsilon$ is the imaginary part of the permittivity. The real part of the permittivity,

\varepsilon'

, is related to the fraction of the energy dispersed by the medium. The complex permittivity is usually a complicated function of frequency ω, since it is a sumperimposed description of dispersion phenomena occurring at multiple frequencies. The dielectric function

\varepsilon(\omega)

must have poles only for frequencies with positive imaginary parts, and therefore satisfies the Kramers-Kronig relations. However, in the narrow frequency ranges that are often studied in practice, the permittivity can be approximated as frequency-independent or by model functions. At a given frequency, the imaginary part of

\hat

leads to absorption loss if it is positive (in the above sign convention) and gain if it is negative. More generally, the imaginary parts of the eigenvalues of the anisotropic dielectric tensor should be considered.

Classification of materials

Materials can be classified according to their permittivity. Those with a permittivity that has a negative real part

\varepsilon'

are considered to be metals, in which no propagating electromagnetic waves exists. Those with a positive real part are dielectrics. A perfect dielectric is a material that exhibits a displacement current only, therefore it stores and returns electrical energy as if it were an ideal battery. In the case of lossy medium, i.e. when the conduction current is not negligible, the total current density flowing is: :

J_ = J_c + J_d = \sigma E + i \omega \varepsilon_0 \varepsilon_r  E = i  \omega \varepsilon_0 \hat E

:σ is the conductivity of the medium :ε_r is the relative permittivity The size of the displacement current is dependent on the frequency ω of the applied field E; there is no displacement current in a constant field. In this formalism, the complex permittivity

\hat

is defined as: :

\hat = \varepsilon_r - i \frac

Dielectric absorption processes

In general, the absorption of electromagnetic energy by dielectrics is covered by a few different mechanisms that influence the shape of the permittivity as a function of frequency:
- Relaxation effects associated with permanent and induced molecular dipoles. At low frequencies the field changes slowly enough to allow dipoles to reach equilibrium before the field has measurably changed. For frequencies at which dipole orientations cannot follow the applied field due to the viscosity of the medium, absorption of the field's energy leads to energy dissipation. The mechanism of dipoles relaxing is called dielectric relaxation and for ideal dipoles is described by classic Debye relaxation
- Resonance effects, which arise from the rotations or vibrations of atoms, ions, or electrons. These processes are observed in the neighborhood of their characteristic absorption frequencies.

Quantum-mechanical interpretation

Quantum-mechanically speaking, there are distinct regions of atomic and molecular interactions, microscopically, that account for the macroscopic behavior we label as permittivity. At low frequencies in polar dielectrics, molecules are polarized by an applied electric field, which induces periodic rotations. For example, at the microwave frequency, the microwave field causes the periodic rotation of water molecules, sufficient to break hydrogen bonds. The field does work against the bonds and the energy is absorbed by the material in terms of heat, which is why microwave ovens work very well for materials containing water. There are two maximums of the imaginary component (the absorptive index) of water, one at the microwave frequency, and the other at far ultraviolet (UV) wavelengths. At UV and above, and at high frequencies in general, the frequencies are too high for molecules to relax in, and thus the energy is purely absorbed by atoms, exciting electron energy levels. At the plasma frequency, the electrons are fully ionized, and will conduct electricity. At moderate frequencies, where the energy content is not high enough to affect electrons directly, yet too high for rotational aspects, the energy is absorbed in terms of resonant molecular vibrations. In water, this is where the absorptive index starts to drop sharply, and the minimum of the imaginary permittivity is at the frequency of blue light (optical regime). This is why water is blue, and also why sunlight does not damage water-containing organs such as the eye. While carrying out a complete ab initio or first-principles modelling is now computationally possible, it has not been widely applied yet. Thus, a phenomological model is accepted as being an adequate method of capturing experimental behaviors. The Debye model and the Lorentz model use a 1st order and 2nd order (respectively) lumped system parameter linear representation (such as an RC and an LRC resonant circuit).

Permittivity measurements

The dielectric constant of a material can be found by a variety of static electrical measurements. The complex permittivity is evaluated over a wide range of frequencies by using different variants of dielectric spectroscopy, covering nearly 21 decades from 10^-6 to 10¹⁵ Hz. Also, by using cryostats and ovens, the dielectric properties of a medium can be characterized over an array of temperatures. In order to study systems for such diverse exciting fields, a number of measurement setups are used, each adequate for a special frequency range.
- low-frequency time domain measurements (10^-6-10³ Hz)
- low frequency frequency domain measurements (10^-5-10⁶ Hz)
- reflective coaxial methods (10⁶-10¹⁰ Hz)
- transmission coaxial method (10⁸-10¹¹ Hz)
- quasi-optical methods (10⁹-10¹⁰ Hz)
- Fourier-transform methods (10¹¹-10¹⁵ Hz)

External links

- [http://www.newton.dep.anl.gov/newton/askasci/1993/physics/PHY48.HTM What is the significance of permittivity of free space?] Category:Electric and magnetic fields in matter Category:Physical quantity ko:유전율 ja:誘電率

Free space

In physics, free space is a concept of electromagnetic theory, corresponding to a theoretical "perfect vacuum".

Theory and mathematics

Free space simply means no material present. Free space is considered the baseline state of the electromagnetic field. Radiant energy propagates through free space in the form of electromagnetic waves, such as radio waves and visible light (among other electromagnetic spectrum frequencies). According to relativity, radiant energy in free space propagates at the speed of light, independent of the speed of the observer or of the source of the waves. Quantum field theory suggests the presence of virtual particles which would prevent any region of space from being completely empty. The constant value

\mu_0 \,

is known as the permeability of free space. The permittivity of free space,

\varepsilon_0

, is the ratio of the electric displacement field to the electric field in free space. This permittivity is used in the construction of the fine-structure constant.

Ideal states and real world applications

Free space conveys that the region is absolutely devoid of matter and has no external fields or forces other than those considered in the problem at hand. In reality, no such state exists except as an idealization. Even in the "vacuum" of outer space, there are small quantities of matter (mostly hydrogen), and noise sources. The density of the interplanetary medium and interstellar medium is to a large degree low, and so for many applications (especially when there are weak external fields or forces) interplanetary and interstellar regions are "free space". The United States Patent Office defines "free space" for radio and radar applications as "space where the movement of energy in any direction is substantially unimpeded, such as the atmosphere, the ocean, or the earth". (US Patent Class 342, Class Notes ) This is slightly different from the technical physics definition of free space as there exists considerable material in all of the USPTO's examples (though this is not exclusionary of other situations). As per this defintion, at various electromagnetic frequencies some density conditions are reasonable approximations to free space.

Electromagnetic field propagation

An active antenna directly couples to free space and transmits energy into, or receives energy from "free space". Wave propagation in multi-dimensional free space differs from propagation in one-dimensional systems (such as waveguides and cable). In one dimensional systems, loss is mainly to absorption or scattering. In two or three-dimensional isotropic systems, the wave extends spherically and the surface area of the wavefront increases with distance. As energy is conserved, the energy per unit surface area decreases. For radio and radar applications in frequencies ranging up to millimetre-wave frequencies, this free space loss is an important source of loss as electromagnetic waves are transmitted to the receiver (and, at times, requires greater power than other systems). When obstructions in "free-space" are hit by waves traveling, new waves result from the influence of the object via reflection, refraction, diffraction, or scattering.

Patents

- X.-C. Zhang, L. Libelo, and Q. Wu, - "Electro-Optic Sensing Apparatus and Method for Characterizing Free-Space Electromagnetic Radiation".

External articles and references

- U.S. Patent Classification System - [http://www.uspto.gov/web/offices/ac/ido/oeip/taf/def/342.htm Classification Definitions] as of June 30, 2000
- Saleem Bhatti, "[http://www.cs.ucl.ac.uk/staff/S.Bhatti/D51-notes/node22.html The electromagnetic spectrum; propagation in free-space and the atmosphere; noise in free-space]". 1995.
- Davida, "[http://www.newton.dep.anl.gov/newton/askasci/1993/physics/PHY48.HTM What is the significance of permittivity of free space?]". Ask A Scientist, Physics Archive.
- Susan Lea, "[http://www.physics.sfsu.edu/~lea/courses/grad/waveguid.PDF Electromagnetic waves in free space]". (PDF)
- Eric W. Weisstein, "[http://scienceworld.wolfram.com/physics/PermittivityofFreeSpace.html Permittivity of Free Space]".
- Wei Ye, "Chapter 17: [http://www.isi.edu/~weiye/pub/propagation_ns.pdf Radio Propagation Models]" 17.1 Free space model. USC Information Sciences Institute.
- Eric W. Weisstein, "[http://scienceworld.wolfram.com/physics/PermeabilityofFreeSpace.html Permeability of Free Space]".
- "[http://whatis.techtarget.com/definition/0,,sid9_gci845268,00.html Characteristic impedance of free space]". TechTarget, 2005.
- Steven J. Smith, "[http://www.geocities.com/electrogravitics/eds1.html Electrodynamic Structure of Space - Part 1]; The complexity of nothing,.
- Mike Willis, "[http://www.mike-willis.com/Tutorial/free_space.htm Propagation in free space]". January, 2005.
- E. J. N. Wilson, "[http://wlap.physics.lsa.umich.edu/cern/lectures/academ/2000/wilson/01/real/sld012.htm Slide 012 - Free space electromagnetic wave]". Physics of Accelerators, Lecture (CERN, AC-division)
- Clark Vitek, "[http://www.evaluationengineering.com/archive/articles/0597deal.htm Free-Space Chambers for Radiated Emissions Measurements]". Dealing with EMI/RFI, CKC Laboratories.
- Jani Tervo, "[http://physics.joensuu.fi/publications/data/thesis_tervo.pdf On electromagnetic treatment of free-space propagation and paraxial diffractive optics]". University of Joensus, Dept. of Physics, Dessiertation 29. (PDF) Category:Electromagnetism Category:Quantum field theory

Electric field intensity

Electric Field :Electric field intensity is known as the space surrounding a charge particle in which any other particle feels a force of attraction or repulsion.

Dielectric

Definition

A dielectric, or electrical insulator, is a substance that is highly resistant to flow of electric current.

Applications

The use of a dielectric in a capacitor presents several advantages. The simplest of these is that the conducting plates can be placed very close to one another without risk of contact. Also, if subjected to a very high electric field, any substance will ionize and become a conductor. Dielectrics are more resistant to ionization than air, so a capacitor containing a dielectric can be subjected to a higher voltage. Layers of dielectric are commonly incorporated in manufactured capacitors to improve their performance above that of capacitors with only air or a vacuum between their plates, and the term dielectric refers to this application as well as the insulation used in power and RF cables.

Dielectrics in Parallel-Plate Capacitors

Putting a dielectric material between the plates in a parallel plate capacitor causes an increase in the capacitance in proportion to k, the dielectric constant of the material: ::

C = \frac

:where

\epsilon_0

is the permittivity of free space, A is the area covered by the capacitors, and d is the distance between the plates. This happens because an electric field polarizes the molecules of the dielectric, producing concentrations of charge on its surfaces that create an electric field opposed (antiparallel) to that of the capacitor. Thus, a given amount of charge produces a weaker field between the plates than it would without the dielectric, which reduces the electric potential. Considered in reverse, this argument means that, with a dielectric, a given electric potential causes the capacitor to accumulate a larger charge.

Some practical dielectrics

Dielectric materials can be solid, liquid, or gaseous. Solid dielectrics are perhaps the most commonly used in electrical engineering and very many solids are very good insulators. Some examples include porcelain, glass, and plastics. Air and sulfur hexafluoride are the two most commonly used gaseous dielectrics.
- Industrial coatings provide a dieltric barrier between the substrate and its environment.
- Mineral oil is used extensively inside electrical transformers as a fluid dielectric and to assist in cooling, and various dielectric fluids are also used in high voltage capacitors.

Insulator

:This page refers to electrical insulation. For thermal insulation see insulation, and for sound insulation see sound proofing. Insulator is also a DNA-sequence that prevents eucariotic gene regulatory proteins from influencing distant genes, see Insulator (DNA)

Definition

An Insulator is a material or object which resists the flow of electric charge.

Electrical insulator

electric charge wire]] The term electrical insulator has the same meaning as the term dielectric, but the two terms are used in different contexts.The opposite of electrical insulators are conductors and semiconductors, which permit the flow of charge. Semiconductors are strictly speaking also insulators, since they prevent the flow of electric charge at low temperatures, unless doped with atoms that release extra charges to carry the current. However, some materials (such as silicon dioxide) are very nearly perfect electrical insulators, which allows flash memory technology. A much larger class of materials, (for example rubber and many plastics) are "good enough" insulators to be used for home and office wiring (into the hundreds of volts) without noticeable loss of safety or efficiency.

High voltage insulators

High voltage insulators used for high voltage power transmission are either porcelain insulators or composite insulators. Porcelain insulators are made from clay, quartz or alumina and feldspar. Alumina insulators are used where high mechanical strength is a criterion. In recent times there is a shift towards composite insulators which have a central rod made of fibre reinforced plastic and outer weathersheds made of silicone rubber or EPDM. Glass insulators were, and in some places are still used to mount electrical power lines. Most insulator manufacturers stopped making glass insulators in the late 1960's, switching to ceramic materials. Composite insulators are less costly, light weight and have excellent hydrophobic capability and hence can be used in polluted areas.

Low voltage insulators

Insulating materials such as PVC (polyvinyl chloride) are used to minimise the possibility of a person coming into contact with a 'live' wire. Some appliances such as electric shavers and hair dryers are doubly insulated to protect the user. They can be recognised because their leads have two pins, or on 3 pin plugs the third (earth) pin is made of plastic rather than metal. In the EU, double insulated appliances all are marked with a symbol of 2 squares, one inside the other. Double insulation requires that cables have basic and supplementary insulation, each of which is sufficient to prevent electric shock. Usually, the internal electrical components are totally enclosed in an insulated packaging which prevents any contact with live parts.

External links

- http://www.myinsulators.com/downtownseattle/ — one person's obsession with telephone pole insulators
- [http://CPRR.org/Museum/Ephemera/Brooks_Insulator.html Transcontinental Telegraph Insulators, 1867]
- [http://www.insulators.com www.insulators.com]
- [http://www.insulatorscanada.com www.insulatorscanada.com]
- http://www.nia.org — National Insulator Association Category:Insulators ja:絶縁体

Capacitor

:See Capacitor (component) for a discussion of specific types. A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. A capacitor is occasionally referred to using the older term condenser. condenser condenser

History

In circa 600 BC, Thales of Miletus recorded that the Ancient Greeks could generate sparks by rubbing balls of amber on spindles. This is the triboelectric effect, the mechanical separation of charge in a dielectric. This effect is the basis of the capacitor. In October 1745, Ewald Georg von Kleist of Pomerania invented the first recorded capacitor: a glass jar coated inside and out with metal. The inner coating was connected to a rod that passed through the lid and ended in a metal sphere. By layering the insulator between two metal plates, von Kleist dramatically increased charge density. Before Kleist's discovery became widely known, a Dutch physicist Pieter van Musschenbroek independently invented a very similar capacitor in January 1746. It was named the Leyden jar, after the University of Leyden where van Musschenbroek worked. Benjamin Franklin investigated the Leyden jar, and proved that the charge was stored on the glass, not in the water as others had assumed. Originally, the units of capacitance were in 'jars'. A jar is equivalent to about 1 nF. Early capacitors were also known as condensers, a term that is still occasionally used today. It was coined by Volta in 1782 (derived from the Italian condensatore), with reference to the device's ability to store a higher density of electric charge than a normal isolated conductor. Most non-English languages still use a word derived from "condensatore", like the French condensateur or the German kondensator. 1782

Physics

Overview

A capacitor consists of two electrodes or plates, each of which stores an opposite charge. These two plates are conductive and are separated by an insulator or dielectric. The charge is stored at the surface of the plates, at the boundary with the dielectric. Because each plate stores an equal but opposite charge, the total charge in the capacitor is always zero. dielectric dielectric

Capacitance

The capacitor's capacitance (C) is a measure of the amount of charge (Q) stored on each plate for a given potential difference or voltage (V) which appears between the plates: :

C = \frac

In SI units, a capacitor has a capacitance of one farad when one coulomb of charge causes a potential difference of one volt across the plates. Since the farad is a very large unit, values of capacitors are usually expressed in microfarads (µF), nanofarads (nF) or picofarads (pF). The capacitance is proportional to the surface area of the conducting plate and inversely proportional to the distance between the plates. It is also proportional to the permittivity of the dielectric (that is, non-conducting) substance that separates the plates. The capacitance of a parallel-plate capacitor is given by: :

C \approx \frac; A >> d^2

[http://www.ttc-cmc.net/~fme/captance.html] where ε is the permittivity of the dielectric, A is the area of the plates and d is the spacing between them.

Stored energy

As opposite charges accumulate on the plates of a capacitor due to the separation of charge, a voltage develops across the capacitor owing to the electric field of these charges. Ever increasing work must be done against this ever increasing electric field as more charge is separated. The energy (measured in joules, in SI) stored in a capacitor is equal to the amount of work required to establish the voltage across the capacitor, and therefore the electric field. The energy stored is given by: :

E_\mathrm =  C V^2

where V is the voltage across the capacitor.

Hydraulic model

As electrical circuitry can be modeled by fluid flow, a capacitor can be modeled as a chamber with a flexible diaphragm separating the input from the output. As can be determined intuitively as well as mathematically, this provides the correct characteristics: the pressure across the unit is proportional to the integral of the current, a steady-state current cannot pass through it but a pulse or alternating current can be transmitted, the capacitance of units connected in parallel is equivalent to the sum of their individual capacitances; etc.

In electric circuits

Circuits with DC sources

Electrons cannot directly pass across the dielectric from one plate of the capacitor to the other. When there is a current through a capacitor, electrons accumulate on one plate and electrons are removed from the other plate. This process is commonly called 'charging' the capacitor even though the capacitor is at all times electrically neutral. In fact, the current through the capacitor results in the separation rather than the accumulation of electric charge. This separation of charge causes an electric field to develop between the plates of the capacitor giving rise to voltage across the plates. This voltage V is directly proportional to the amount of charge separated Q. But Q is just the time integral of the current I through the capacitor. This is expressed mathematically as: :

I = \frac = C\frac

where :I is the current flowing in the conventional direction, measured in amperes :dV/dt is the time derivative of voltage, measured in volts / second. :C is the capacitance in farads For circuits with a constant (DC) voltage source, the voltage across the capacitor cannot exceed the voltage of the source. Thus, an equilibrium is reached where the voltage across the capacitor is constant and the current through the capacitor is zero. For this reason, it is commonly said that capacitors block DC current.

Circuits with AC sources

The capacitor current due to an AC voltage or current source reverses direction periodically. That is, the AC current alternately charges the plates in one direction and then the other. With the exception of the instant that the current changes direction, the capacitor current is non-zero at all times during a cycle. For this reason, it is commonly said that capacitors 'pass' AC current. However, at no time do electrons actually cross between the plates. Since the voltage across a capacitor is the integral of the current, as shown above, with sine waves in AC or signal circuits this results in a phase difference of 90 degrees, the current leading the voltage phase angle. It can be shown that the AC voltage across the capacitor is in quadrature with the AC current through the capacitor. That is, the voltage and current are 'out-of-phase' by a quarter cycle. The amplitude of the voltage depends on the amplitude of the current divided by the product of the frequency of the current with the capacitance, C. The ratio of the voltage amplitude to the current amplitude is called the reactance of the capacitor. This capacitive reactance is given by: :

X_C = -\frac = -\frac

where : $\omega = 2 \pi f$ , the angular frequency measured in radians per second :X_C = capacitive reactance, measured in ohms :f = frequency of AC in hertz :C = capacitance in farads and is analogous to the resistance of a resistor. Clearly, the reactance is inversely proportional to the frequency. That is, for very high-frequency alternating currents the reactance approaches zero so that a capacitor is nearly a short circuit to a very high frequency AC source. Conversely, for very low frequency alternating currents, the reactance increases without bound so that a capacitor is nearly an open circuit to a very low frequency AC source. Reactance is so called because the capacitor doesn't dissipate power, but merely stores energy. In electrical circuits, as in mechanics, there are two types of load, resistive and reactive. Resistive loads (analogous to an object sliding on a rough surface) dissipate energy that enters them, ultimately by electromagnetic emission (see Black body radiation), while reactive loads (analogous to a spring or frictionless moving object) retain the energy. The impedance of a capacitor is given by: :

Z_C = \frac = \frac

Hence, capacitive reactance is the negative imaginary component of impedance. The negative sign indicates that the current leads the voltage by 90° for a sinusoidal signal, as opposed to the inductor, where the current lags the voltage by 90°. Also significant is that the impedance is inversely proportional to the capacitance, unlike resistors and inductors for which impedances are linearly proportional to resistance and inductance respectively. This is why the series and shunt impedance formulae (given below) are the inverse of the resistive case. In series, impedances sum. In shunt, conductances sum. In a tuned circuit such as a radio receiver, the frequency selected is a function of the inductance (L) and the capacitance (C) in series, and is given by: :

f = \frac

This is the frequency at which resonance occurs in an RLC series circuit. For an ideal capacitor, the capacitor current is proportional to the time rate of change of the voltage across the capacitor where the constant of proportionality is the capacitance, C: :

i(t) = C \frac

The impedance in the frequency domain can be written as :

Z = \frac = - j X_C

. This shows that a capacitor has a high impedance to low-frequency signals (when ω is small) and a low impedance to high-frequency signals (when ω is large). This frequency dependent behaviour accounts for most uses of the capacitor (see "Applications", below). When using the Laplace transform in circuit analysis, the capacitive impedance is represented in the s domain by: :

Z(s)=\frac

Capacitors and displacement current

The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampere's law consistent with conservation of charge in cases where charge is accumulating as in a capacitor. He interpreted this as a real motion of charges, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the ether. Although this interpretation has been abandoned, Maxwell's correction to Ampere's law remains valid.

Capacitor networks

A capacitor can be used to block the DC Current flowing within the circuit and therefore have important applications in coupling of ac signals between amplifier stages, whilst preventing dc from passing.

Series or parallel arrangements

Capacitors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent capacitance (C_eq): :A diagram of several capacitors, side by side, both leads of each connected to the same wires :

C_ = C_1  + C_2 + \cdots + C_n  \,

The current through capacitors in series stays the same, but the voltage across each capacitor can be different. The sum of the potential differences (voltage) is equal to the total voltage. To find their total capacitance: :A diagram of several capacitors, connected end to end, with the same amount of current going through each :

\frac = \frac + \frac + \cdots +  \frac

In parallel, the total charge stored is the sum of the charge in each capacitor. While in series, the charge on each capacitor is the same. One possible reason to connect capacitors in series is to increase the overall voltage rating. In practice, a very large resistor might be connected across each capacitor to ensure that the total voltage is divided appropriately for the individual ratings, rather than by minute differences in the capacitance values. Another application is for use of polarized capacitors in alternating current circuits; the capacitors are connected in series, in reverse polarity, so that at any given time one of the capacitors is not conducting.

Capacitor/inductor duality

In mathematical terms, the ideal capacitor can be considered as an inverse of the ideal inductor, because the voltage-current equations of the two devices can be transformed into one another by exchanging the voltage and current terms. Just as two or more inductors can be magnetically coupled to make a transformer, two or more charged conductors can be electrostatically coupled to make a capacitor. The mutual capacitance of two conductors is defined as the current that flows in one when the voltage across the other changes by unit voltage in unit time.

Applications

Energy storage

A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary battery. The recent commercial availability of very large value capacitors, close to one farad in size, has enabled such components to allow batteries to be changed in electronic devices without the memory being lost, for instance, or for energy storage for delivery during extreme peak demands, as often found in the enormously powerful car audio systems now seen.

Signal processing

The energy stored in a capacitor can be used to represent information, either in binary form, as in computers, or in analogue form, as in switched-capacitor circuits and bucket-brigade delay lines. Capacitors can be used in analog circuits as components of integrators or more complex filters and in negative feedback loop stabilization. Signal processing circuits also use capacitors to integrate a current signal.

Power supply applications

Capacitors are commonly used in power supplies where they smooth the output of a full or half wave rectifier. They can also be used in charge pump circuits as the energy storage element in the generation of higher voltages than the input voltage. Capacitors are connected in parallel with the power circuits of most electronic devices and larger systems (such as factories) to shunt away and conceal current fluctuations from the primary power source to provide a "clean" power supply for signal or control circuits. Audio equipment, for example, uses several capacitors in this way, to shunt away power line hum before it gets into the signal circuitry. The capacitors act as a local reserve for the DC power source, and bypass AC currents from the power supply. Capacitors are used in power factor correction. Such capacitors often come as three capacitors connected as a three phase load. Usually, the values of these capacitors are given not in farads but rather as a reactive power in Volt-Amperes reactive (VAr). The purpose is to match the inductive loading of machinery which contains motors, to make the load appear to be mostly resistive. Capacitors are also used in parallel to interrupt units of a high-voltage circuit breaker in order to distribute the voltage between these units. In this case they are called grading capacitors. In schematic diagrams, a capacitor used primarily for DC charge storage is often drawn vertically in circuit diagrams with the lower, more negative, plate drawn as an arc. The straight plate indicates the positive terminal of the device, if it is polarized (see electrolytic capacitor). Non-polarized electrolytic capacitors used for signal filtering are typically drawn with two curved plates. Other non-polarized capacitors are drawn with two straight plates.

Tuned circuits

Capacitors and inductors are applied together in tuned circuits to select information in particular frequency bands. For example, radio receivers rely on variable capacitors to tune the station frequency. Speakers use passive analog crossovers, and analog equalizers use capacitors to select different audio bands.

Signal coupling

Because capacitors pass AC but block DC signals (when charged up to the applied dc voltage), they are often used to separate the AC and DC components of a signal. This method is known as AC coupling. (Sometimes transformers are used for the same effect.) Here, a large value of capacitance, whose value need not be accurately controlled, but whose reactance is small at the signal frequency, is employed. Capacitors for this purpose designed to be fitted through a metal panel are called feed-through capacitors, and have a slightly different schematic symbol.

Transducer applications

Although capacitors usually maintian a fixed physical structure and utilization varies the electrical voltage and current, the effects of varying the physical and/or electrical characteristics of the dielectric with a fixed electrical supply can also be of use. Capacitors with an exposed and porous dielectric can be used to measure humidity in air. Capacitors with a flexible plate can be used to measure strain or pressure. Capacitors are used as the transducer in condenser microphones, where one plate is moved by air pressure, relative to the fixed position fo the other plate.

Noise filters, motor starters, and snubbers

When an inductive circuit is opened, the energy stored in the magnetic field of the inductance collapses quickly, creating a large voltage across the open circuit of the switch or relay. If the inductance is large enough, the energy will generate a spark, causing the contact points to oxidize, deteriorate, or sometimes weld together, or destroying a solid-state switch. A snubber capacitor across the newly opened circuit creates a path for this impulse to bypass the contact points, thereby preserving their life; these were commonly found in contact breaker ignition systems, for instance. Similarly, in smaller scale circuits, the spark may not be enough to damage the switch but will still radiate undesirable radio frequency interference (RFI), which a filter capacitor absorbs. Snubber capacitors are usually employed with a low-value resistor in series, to dissipate energy more slowly and minimize RFI. Such resistor-capacitor combinations are available in a single package. In an inverse fashion, to initiate current quickly through an inductive circuit requires a greater voltage than required to maintain it; in uses such as large motors, this can cause undesirable startup characteristics, and a motor starting capacitor is used to store enough energy to give the current the initial push required to start the motor up.

Weapons applications

An obscure military application of the capacitor is in an EMP weapon. A plastic explosive is used for the dielectric. The capacitor is charged up and the explosive is detonated. The capacitance becomes smaller, but the charge on the plates stays the same. This creates a high-energy electromagnetic shock wave capable of destroying unprotected electronics for miles around. These devices are rumored to have been employed by the US in the 2003 invasion of Iraq, though this is highly unlikely. See Explosively pumped flux compression generator. Large high-voltage low-inductance capacitors are used as energy sources for the exploding-bridgewire detonators or slapper detonators in nuclear weapons and other specialty weapons, and are also used as power supplies for electromagnetic guns such as railguns or coilguns.

Ideal and nonideal capacitors

In practice, this ideal model of the capacitor often has to be modified to reflect real world capacitor construction and operation. The most obvious example is electrolytic capacitors, where the capacitor is polarized such that when the voltage is connected in reversed fashion, the capacitor acts as a resistor. Similar problems of dielectric leakage are a constant complication of all capacitor design however, and have led to constant improvements in capacitor design, as the material used for dielectrics has changed from oiled paper to mylar and from ceramic to Teflon. This also addresses the related problem of dielectric stability; oiled or electrolyte soaked paper dries out over time, reducing the capacitance and increasing leakage, a problem reduced in modern components. On the other hand, the requirements of large plate area for reasonably useful capacitor values as well as reasonable packaging resulted in the universal practice of rolling the plate/dielectric sandwich into a cylinder, which was then encapsulated. However, this process also creates an inductance in series with the capacitance, just as introducing a coiled wire of similar characteristics in series with the flat capacitor would; in sensitive circuits, this inductance must be taken into account, either by using a capacitor designed to have lower inductance, or by bypassing a large capacitor with a smaller, noninductive one. This practice has become more common in audiophile-oriented products recently, as inductive problems in low-cost capacitors were demonstrated to degrade high-frequency fidelity. Dielectric materials can produce unwanted side effects. For example, the dielectric constant of barium titanate used in ceramic capacitors changes with temperature and pressure. Such capacitors are sensitive to vibration and flexing, and can cause a type of signal modulation in electronic circuits call microphonics.

Capacitor hazards and safety

Capacitors may retain a charge long after power is removed from a circuit; this charge can cause shocks (up to and including electrocution) or damage to connected equipment. Since capacitors have such low ESRs, they have the capacity to deliver large currents into short circuits; this can be dangerous. Care must be taken to ensure that any large or high-voltage capacitor is properly discharged before servicing the containing equipment. For safety purposes, all large capacitors should be discharged before handling. For board-level capacitors, this is done by placing a bleeder resistor across the terminals, whose resistance is large enough that the leakage current will not affect the circuit, but small enough to discharge the capacitor shortly after power is removed. High voltage capacitors should be stored with the terminals shorted to dissipate any stored charge. Large oil-filled old capacitors must be disposed of properly as some contain polychlorinated biphenyls (PCBs). It is known that waste PCBs can leak into groundwater under landfills. If consumed by drinking contaminated water, PCBs are carcinogenic, even in very tiny amounts. If the capacitor is physically large it is more likely to be dangerous and may require precautions in addition to those described above. New electrical components are no longer produced with PCBs.

External links

- [http://leonardo.eeug.caltech.edu/~ee14/lab1cds.html Caltech: Practical capacitor properties]
- [http://www.faradnet.com/ FaradNet: The Capacitor Resource]
- [http://www.nesscap.com NessCap, maker of 5000 farad capacitors]
- [http://www.ga-esi.com/ General Atomics Electronic Systems, inc. High Voltage Pulsed Power Capacitors and Systems.]
- [http://www.skeletonnanolab.com Skeleton NanoLab, Research & Development of advanced capacitors]
- [http://electronics.howstuffworks.com/capacitor.htm/printable Howstuffworks.com: How Capacitors Work]
- [http://my.execpc.com/~endlr/ CapSite 2005]

References

- Glenn Zorpette "Super Charged: A Tiny South Korean Company is Out to Make Capacitors Powerful enough to Propel the Next Generation of Hybrid-Electric Cars", "IEEE Spectrum", January, 2005 Vol 42, No. 1, North American Edition.
- "The ARRL Handbook for Radio Amateurs, 68th ed", The Amateur Radio Relay League, Newington CT USA, 1991
- "Basic Circuit Theory with Digital Computations", Lawrence P. Huelsman, Prentice-Hall, 1972
- Philosophical Transactions of the Royal Society LXXII, Appendix 8, 1782 (Volta coins the word condenser)
- A. K. Maini "Electronic Projects for Beginners", "Pustak Mahal", 2nd Edition: March, 1998 (INDIA)
- [http://www.sparkmuseum.com/BOOK_LEYDEN.HTM Spark Museum] (von Kleist and Musschenbroek)
- [http://www.acmi.net.au/AIC/VON_KLEIST_BIO.html Biography of von Kleist] Category:Capacitors Category:Electronics ja:コンデンサ th:ตัวเก็บประจุ

Electromagnetic

Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess a property known as electric charge, and is in turn affected by the presence and motion of such particles. The term electrodynamics is sometimes used to refer to the combination of electromagnetism with mechanics, and deals with the effects of the electromagnetic field on the dynamic behavior of electrically-charged particles.

Electric and magnetic fields

It is often convenient to understand the electromagnetic field in terms of two separate fields: the electric field and the magnetic field. A non-zero electric field is produced by the presence of electrically charged particles, and gives rise to the electric force; this is the force that causes static electricity and drives the flow of electric charge (electric current) in electrical conductors. The magnetic field, on the other hand, can be produced by the motion of electric charges, or electric current, and gives rise to the magnetic force associated with magnets. The term "electromagnetism" comes from the fact that the electric and magnetic fields generally cannot be described independently of one another. A changing magnetic field produces an electric field (this is the phenomenon of electromagnetic induction, which underlies the operation of electrical generators, induction motors, and transformers). Similarly, a changing electric field generates a magnetic field. Because of this inter-dependence between the electric and magnetic fields, it makes sense to consider them as a single, theoretically coherent entity — the electromagnetic field. This unification, which was completed by James Clerk Maxwell, is one of the triumphs of 19th century physics. It had far-reaching consequences, one of which was the elucidation of the nature of light: as it turns out, what we think of as "light" is actually a propagating oscillatory disturbance in the electromagnetic field, i.e., an electromagnetic wave. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies. The theoretical implications of electromagnetism led to the development of special relativity by Albert Einstein in 1905.

The electromagnetic force

The force that the electromagnetic field exerts on electrically charged particles, called the electromagnetic force, is one of the four fundamental forces. The other fundamental forces are the strong nuclear force (which holds atomic nuclei together), the weak nuclear force (which causes certain forms of radioactive decay), and the gravitational force. All other forces are ultimately derived from these fundamental forces. As it turns out, the electromagnetic force is the one responsible for practically all the phenomena one encounters in daily life, with the exception of gravity. Roughly speaking, all the forces involved in interactions between atoms can be traced to the electromagnetic force acting on the electrically charged protons and electrons inside the atoms. This includes the forces we experience in "pushing" or "pulling" ordinary material objects, which come from the intermolecular forces between the individual molecules in our bodies and those in the objects. It also includes all forms of chemical phenomena, which arise from interactions between electron orbitals.

Origins of electromagnetic theory

The scientist William Gilbert proposed, in his De Magnete (1600), that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had the ability to disturb a compass needle, but the link between lightning and electricity was not confirmed until Franklin's proposed experiments (performed initially by others) in 1752. One of the first to discover and publish a link between man-made electric current and magnetism was Romagnosi, who in 1802 noticed that connecting a wire across a Voltaic pile deflected a nearby compass needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment. Ørsted's work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation. An accurate theory of electromagnetism, known as classical electromagnetism, was developed by various physicists over the course of the 19th century, culminating in the work of James Clerk Maxwell, who unified the preceding developments into a single theory and discovered the electromagnetic nature of light. In classical electromagnetism, the electromagnetic field obeys a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law. One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity. According to Maxwell's equations, the speed of light is a universal constant, dependent only on the electrical permittivity and magnetic permeability of the vacuum. This violates Galilean invariance, a long-standing cornerstone of classical mechanics. One way to reconcile the two theories is to assume the existence of a luminiferous aether through which the light propagates. However, subsequent experiments efforts failed to detect the presence of the aether. In 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaces classical kinematics with a new theory of kinematics that is compatible with classical electromagnetism. In addition, Relativity theory shows that in moving frames of reference a magnetic field becomes an electrostatic field and vice versa; thus firmly showing that they are two sides of the same coin, and thus the term Electromagnetism.

Failures of classical electromagnetism

In another paper published in that same year, Einstein undermined the very foundations of classical electromagnetism. His theory of the photoelectric effect (for which he won the Nobel prize for physics) posited that light could exist in discrete particle-like quantities, which later came to be known as photons. Einstein's theory of the photoelectric effect extended the insights that appeared in the solution of the ultraviolet catastrophe presented by Max Planck in 1900. In his work, Planck showed that hot objects emit electromagnetic radiation in discrete packets, which leads to a finite total energy emitted as black body radiation. Both of these results were in direct contradiction with the classical view of light as a continuous wave. Planck's and Einstein's theories were progenitors of quantum mechanics, which, when formulated in 1925, necessitated the invention of a quantum theory of electromagnetism. This theory, completed in the 1940s, is known as quantum electrodynamics (or "QED"), and is one of the most accurate theories known to physics.

SI electricity units

References

-
-
-
-

External links

- [http://www.rmcybernetics.com/science/physics/electromagnetism_intro_electric_force.htm Introduction to Electromagnetism] From the basics to advanced level science
- [http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-and-MagnetismSpring2002/VideoLectures/index.htm MIT Video Lectures - Electricity and Magnetism] from Spring 2002. Taught by Professor Walter Lewin.
- [http://www.lightandmatter.com/area1book4.html Electricity and Magnetism] - an online textbook (uses algebra, with optional calculus-based sections)
- [http://www.plasma.uu.se/CED/Book/ Electromagnetic Field Theory] - an online textbook (uses calculus)
- [http://farside.ph.utexas.edu/teaching/em/em.html Classical Electromagnetism: An intermediate level course] - an online intermediate level texbook downloadable as PDF file ko:전자기학 ja:電磁気学

Velocity

This article is about velocity in physics. For other meanings, see velocity (disambiguation). The velocity of an object is simply its speed in a particular direction. Note that both speed and direction are required to define a velocity.

Explanation

The velocity (v) is an physical quantity of the motion. A change in an object's velocity can therefore arise from either a change in its speed or in its direction. For example an aeroplane that is circling at a constant speed of 200km/h is changing its velocity because it is continously changing its direction. A aeroplane that is taking-off may go from zero to 200km/h in a straight line and so would also be changing its velocity. A change in velocity is called an acceleration. Objects are only accelerated if a force is applied to them. (The amount of acceleration depends the size of the force and the mass of the object being shifted, see Newton's Second Law of Motion.) In the case of the circling aeroplane, the pilot banks to use the force of lift from the wings to change direction. In another example the Space Shuttle orbits the earth at a constant speed but is constantly changing its velocity because of the circular orbit. In this case the force causing the acceleration is provided by the earth's gravity acting on the shuttle. The average speed v of an object moving a distance d during a time interval t is described by the formula: :

v = \frac

Acceleration is the rate of change of an object's velocity over time. The average acceleration of a of an object whose speed changes from v_i to v_f during a time interval t is given by: :

a = \frac

Where

v_i

= an object's initial velocity and

v_f

= the object's final velocity over a period of time t

Formal description

Velocity (symbol: v) is a vector measurement of the rate and direction of motion. The scalar absolute value (magnitude) of velocity is speed. Velocity can also be defined as rate of change of displacement or just as the rate of displacement, depending on how the term displacement is used. It is thus a vector quantity with dimension length/time. In the SI (metric) system it is measured in metre per second The instantaneous velocity vector v of an object that has position at time t is given by x(t) can be computed as the derivative :

v= = \lim_

The instantaneous acceleration vector a of an object that has position at time t is given by x(t) is :

\mathbf = \frac   = \frac

The equation for an object's velocity can be obtained mathematically by taking the integral of the equation for its acceleration beginning from some initial period time $t_0$ to some point in time later $t_n$ . The final velocity v_f of an object which starts with velocity v_i and then accelerates at constant acceleration a for a period of time t is: :

v_f = v_i + a t

The average velocity of an object undergoing constant acceleration is (v_i + v_f)/2. To find the displacement d of such an accelerating object during a time interval t, substitute this expression into the first formula to get: :

d = t \times \frac

When only the object's initial velocity is known, the expression :

d = v_i t + \frac

can be used. These basic equations for final velocity and displacement can be combined to form an equation that is independent of time, also known as Torricelli's Equation: :

v_f^2 = v_i^2 + 2 a d

The above equations are valid for both classical mechanics and special relativity. Where classical mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in classical mechanics, all observers agree on the value of t and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. The kinetic energy (energy of motion) of a moving object is linear with both its mass and the square of its velocity: :

E_ = \begin \frac \end mv^2

The kinetic energy is a scalar quantity.

Polar coordinates

In polar coordinates, a two-dimensional velocity can be decomposed into a radial velocity, defined as the component of velocity away from or toward the origin, and transverse velocity, the component of velocity along a circle centred at the origin, and equal to the distance to the origin times the angular velocity. Angular momentum in scalar form is the distance to the origin times the transverse speed, or equivalently, the distance squared times the angular speed, with a plus or minus to distinguish clockwise and anti-clockwise direction. If forces are in the radial direction only, as in the case of a gravitational orbit, angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as Kepler's laws of planetary motion.

Wavelength

:For the album by Van Morrison, see Wavelength (album). The wavelength is the distance between repeating units of a wave pattern. It is commonly designated by the Greek letter lambda (λ). In a sine wave, the wavelength is the distance between the midpoints of the wave: Image:Wavelength.png The x axis represents distance, and I would be some varying quantity at a given point in time as a function of x, for instance air pressure for a sound wave or strength of the electric or magnetic field for light. Wavelength λ has an inverse relationship to frequency f, the number of peaks to pass a point in a given time. The wavelength is equal to the speed of the wave type divided by the frequency of the wave. When dealing with electromagnetic radiation in a vacuum, this speed is the speed of light c, for signals (waves) in air, this is the speed of sound in air. The relationship is given by: :

\lambda = \frac

where: :λ = wavelength of a sound wave or electromagnetic wave :c = speed of light in vacuum = 299,792.458 km/s ~ 300,000 km/s = 300,000,000 m/s or :c = speed of sound in air = 343 m/s at 20 °C (68 °F) :f = frequency of the wave in 1/s = Hz For radio waves this relationship is approximated with the formula: wavelength λ (in metres) = 300 / frequency (in megahertz).
For sound waves this relationship is approximated with the formula: wavelength λ (in metres) = 333 / frequency (in hertz). When light waves (and other electromagnetic waves) enter a medium, their wavelength is reduced by a factor equal to the refractive index n of the medium but the frequency of the wave is unchanged. The wavelength of the wave in the medium, λ' is given by: :

\lambda^\prime = \frac

where: :λ₀ is the vacuum wavelength of the wave Wavelengths of electromagnetic radiation, no matter what medium they are travelling through, are usually quoted in terms of the vacuum wavelength, although this is not always explicitly stated. Louis de Broglie discovered that all particles with momentum have a wavelength associated with their quantum mechanical wavefunction, called the de Broglie wavelength.

External link

- [http://www.sengpielaudio.com/calculator-wavelength.htm Conversion: Wavelength to frequency and vice versa - The calculator] Category:Length Category:Wave mechanics ko:파장 ja:波長 th:ความยาวคลื่น

Permittivity

The permittivity of a medium is an intensive physical quantity that describes how an electric field affects and is affected by the medium.

Explanation

\mathbf=\varepsilon \cdot \mathbf

\varepsilon_0

, is the scale factor that relates the values of D and E in a vacuum.

\varepsilon_0

is equal to 8.8541878176...×10^-12 F/m. The units of

\varepsilon_0

Vacuum permittivity

The permittivity of a material is usually given relative to that of vacuum, as a relative permittivity,

\varepsilon_

(also called dielectric constant in some cases). The actual permittivity is then calculated by multiplying the relative permittivity by

\varepsilon_

: :

\varepsilon = \varepsilon_r \varepsilon_0  = (1+\chi_e)\varepsilon_0

where

\,\chi_e

is the electric susceptibility of the material. Vacuum permittivity

\varepsilon_

("the permittivity of free space") is the ratio D/E in vacuum. It also appears in Coulomb's law as a part of the Coulomb force constant,

\frac

, which expresses the attraction between two unit charges in vacuum. :

\varepsilon_0 = \frac = 8.8541878176\ldots \times 10^ \ \mathrm

, where

c

is the speed of light and

\mu_0

is the permeability of vacuum. All three of these constants are exactly defined in SI units.

Permittivity in media

In the common case of isotropic media, D and E are parallel vectors and

\varepsilon

is a scalar, but in general anisotropic media this is not the case and

\varepsilon

is a rank-2 tensor (causing birefringence). The permittivity

\varepsilon

and magnetic permeability

\mu

of a medium together determine the phase velocity v of electromagnetic radiation through that medium: :

\varepsilon \mu = \frac

\mathbf = \varepsilon_ \mathbf + \mathbf = \varepsilon_ \mathbf + \varepsilon_\chi\mathbf = \varepsilon_ \mathbf \left( 1 + \chi \right)

, where P is the polarization of the medium and

\chi

its electric susceptibility. It follows that the relative permittivity and susceptibility of a sample are related,

\varepsilon_ = \chi + 1

Complex permittivity

\omega

\varepsilon \rightarrow \hat(\omega)

. The definition of permittivity therefore becomes :

D_e^ = \hat(\omega) E_ e^,

where

D_

and

E_

are the amplitudes of the displacement and electrical fields, respectively,

i=\sqrt

is the imaginary unit. The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity or dielectric constant

\varepsilon_

(also

\varepsilon_

): :

\varepsilon_ = \lim_ \hat(\omega)

\delta

emerges between D and E. The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate fields strength (

E_

), D and E remain proportional, and :

\hat = \frace^ = |\varepsilon|e^

\hat(\omega) = \varepsilon'(\omega) - i\varepsilon

(\omega) = \frac \left( cos\delta - i\sin\delta \right) . In the equation above, $\varepsilon$ is the imaginary part of the permittivity. The real part of the permittivity,

\varepsilon'

\varepsilon(\omega)

\hat

Classification of materials

Materials can be classified according to their permittivity. Those with a permittivity that has a negative real part

\varepsilon'

J_ = J_c + J_d = \sigma E + i \omega \varepsilon_0 \varepsilon_r  E = i  \omega \varepsilon_0 \hat E

\hat

is defined as: :

\hat = \varepsilon_r - i \frac

Dielectric absorption processes

Quantum-mechanical interpretation

Permittivity measurements

External links

Capacitance

Definition

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The capacitance is usually defined as the total electric charge placed on the object divided by the potential of the object: ::

C = \frac

or, according to Gauss's law, the capacitance can be expressed as the electric flux per volt ::

C = \frac

where :C is the capacitance in farads :Q is the charge in coulombs :V is the potential in volts :

\Phi

is the electric flux associated with the charge Q in coulombs Compare this form with the definition of inductance.

Introduction

Capacitance exists between any two conductors insulated from one another. The formula defining capacitance above is valid if it is understood that the conductors have equal but opposite charge Q, and the voltage V is the potential difference between the two conductors. The SI unit of capacitance is the farad (F). A capacitance of one farad results in a potential of one volt for one coulomb of charge. The capacitance of the majority of capacitors used in electronic circuits is several orders of magnitude smaller than the farad. The most common units of capacitance in use today are the microfarad (µF), the nanofarad (nF) and the picofarad (pF). It should be noted that the above equation (C=Q/V) is only applicable for values of Q which are much larger than the electron charge e = 1.602×10^-19 C. For example, if a capacitance of 1 pF is charged to a voltage of 100 nV, the equation would predict a charge Q = 10^-19 C, which is smaller than the charge on a single electron. The capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. For example, the capacitance of a parallel-plate capacitor constructed of two identical plane electrodes of area A at constant spacing d is approximately equal to the following: :

C = \epsilon_0 \epsilon_r \frac

where :C is the capacitance in farads :ε₀ is the permittivity of free space, measured in farad per meter :ε_r is the dielectric constant or relative permittivity of the insulator used :A is the area of each plane electrode, measured in square metres :d is the separation between the electrodes, measured in metres

Energy

The energy (measured in joules) stored in a capacitance is equal to the work done to charge it. Consider a capacitance C, holding a charge +q on one plate and -q on the other. Moving a small element of charge dq from one plate to the other against the potential difference V = q/C requires the work dW: :

dW = \fracdq

where :W is the work measured in joules :q is the charge measured in coulombs :C is the capacitance, measured in farads We can find the energy stored in a capacitance by integrating this equation. Starting with an uncharged capacitance (q=0) and moving charge from one plate to the other until the plates have charge +Q and -Q requires the work W: :

W_ = \int_^ \frac dq = \frac\frac = \fracCV^2 = W_

Combining this with the above equation for the capacitance of a flat-plate capacitor, we get: :

W_ = \frac \epsilon_0 \epsilon_r \frac V^2

Capacitance and 'displacement current'

The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampere's law consistent with conservation of charge in cases where charge is accumulating, for example in a capacitor. He interpreted this as a real motion of charges, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the ether. Although this interpretation has been abandoned, Maxwell's correction to Ampere's law remains valid (a changing electric field produces a magnetic field).

Capacitance/inductance duality

In mathematical terms, the ideal capacitance can be considered as an inverse of the ideal inductance, because the voltage-current equations of the two phenomena can be transformed into one another by exchanging the voltage and current terms.

Self-capacitance

In electrical circuits, the term capacitance is usually a shorthand for the mutual capacitance between two adjacent conductors, such as the two plates of a capacitor. There also exists a property called self-capacitance, which is the amount of electrical charge that must be added to an isolated conductor to raise its electrical potential by one volt. The reference point for this potential is a theoretical hollow conducting sphere, of infinite radius, centred on the conductor. Using this method, the self-capacitance of a conducting sphere of radius R is given by: :

C=4\pi\epsilon_0R

[http://www.phys.unsw.edu.au/COURSES/FIRST_YEAR/pdf%20files/5Capacitanceanddielectr.pdf] Typical values of self-capacitance are:
- for the top electrode of a van de Graaf generator, typically a sphere 20 cm in diameter: 20 pF
- the planet Earth: about 710 μF

References

- Tipler, Paul (1998). Physics for Scientists and Engineers: Vol. 2: Electricity and Magnetism, Light (4th ed.). W. H. Freeman. ISBN 1572594926
- Serway, Raymond; Jewett, John (2003). Physics for Scientists and Engineers (6 ed.). Brooks Cole. ISBN 0534408427

Frequency

: Frequency is the measurement of the number of times that a repeated event occurs per unit time. It is also defined as the rate of change of phase of a sinusoidal waveform.

Measurement

To calculate the frequency of an event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval. In

Dielectric constant

Overview

Measurement

Practical relevance

See also

Permittivity

Explanation

Vacuum permittivity

Permittivity in media

Complex permittivity

Classification of materials

Dielectric absorption processes

Quantum-mechanical interpretation

Permittivity measurements

See also

Suggested readings

External links

Free space

Theory and mathematics

Ideal states and real world applications

Electromagnetic field propagation

See also

Patents

External articles and references

Electric field intensity

Dielectric

Definition

Applications

Dielectrics in Parallel-Plate Capacitors

Some practical dielectrics

See also

Insulator

Definition

Electrical insulator

High voltage insulators

Low voltage insulators

See also

External links

Capacitor

History

Physics

Overview

Capacitance

Stored energy

Hydraulic model

In electric circuits

Circuits with DC sources

Circuits with AC sources

Capacitors and displacement current

Capacitor networks

Series or parallel arrangements

Capacitor/inductor duality

Applications

Energy storage

Signal processing

Power supply applications

Tuned circuits

Signal coupling

Transducer applications

Noise filters, motor starters, and snubbers

Weapons applications

Ideal and nonideal capacitors

Capacitor hazards and safety

See also

External links

References

Electromagnetic

Electric and magnetic fields

The electromagnetic force

Origins of electromagnetic theory

Failures of classical electromagnetism

SI electricity units

References

External links

Velocity

Explanation

Formal description

Polar coordinates

See also

Wavelength