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Coulomb

Coulomb

The coulomb (symbol: C) is the SI unit of electric charge. It is named after Charles-Augustin de Coulomb (1736 to 1806).

Definition

1 coulomb is the amount of electric charge carried by a current of 1 ampere flowing for 1 second. :

C = A \cdot s

Explanation

The coulomb is also the unit of electric flux. (See Gauss Law). The coulomb could in principle be defined in terms of the charge of an electron or elementary charge. Since the values of the Josephson (CIPM (1988) Recommendation 1, PV 56; 19) and von Klitzing (CIPM (1988), Recommendation 2, PV 56; 20) constants have been given conventional values (K_J ≡ 4.835 979 Hz/V and R_K ≡ 2.5812807 Ω), it is possible to combine these values to form an alternative (not yet official) definition of the coulomb. A coulomb is then equal to exactly 6.24150962915265 elementary charges. Combined with the current definition of the ampere, this proposed definition would make the kilogram a derived unit.

SI multiples

Conversions

- One mole of electrons (approximately 6.022, or Avogadro's number) is known as a faraday (actually -1 faraday, since electrons are negatively charged). One faraday equals 96.4853415 kC (the Faraday constant). In terms of Avogadro's number (N_A), one coulomb is equal to approximately 1.036 × N_A elementary charges.
- one ampere-hour = 3600 C
- The elementary charge is approximately 160.2176 zC.
- One statcoulomb (statC), the CGS electrostatic unit of charge (esu), is approximately 3.3356 C or about 1/3 nC.

SI

The International System of Units (abbreviated SI from the French language name Système International d'Unités) is the modern form of the metric system. It is the world's most widely used system of units, both in everyday commerce and in science. The older metric system included several groupings of units. The SI was developed in 1960 from one of these, the metre-kilogram-second (MKS) system, rather than the centimetre-gram-second (CGS) system, which, in turn, had many variants. The SI introduced several newly named units. The SI is not static; it is a living set of standards where units are created and definitions are modified with international agreement as measurement technology progresses. With few exceptions (such as draught beer sales in the United Kingdom), the system is legally being used in every country in the world, and many countries do not maintain official definitions of other units. In the United States, industrial use of SI is increasing, but popular use is still limited. In the United Kingdom, conversion to metric units is official policy but not yet complete. Those countries that still recognize non-SI units (e.g. the US and UK) have redefined most of their traditional, non-SI units in terms of SI units.

History

:See main articles: metre, kilogram, second, ampere, Kelvin, and candela. The metric system was officially adopted in France after the French Revolution. During the history of the metric system a number of variations have evolved and their use spread around the world replacing many traditional measurement systems. By the end of World War II a number of different systems of measurement were still in use throughout the world. Some of these systems were metric system variations whilst others were based on the Imperial and American systems. It was recognised that additional steps were needed to promote a worldwide measurement system. As a result the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities. Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units recommended were the metre, kilogram, second, ampere, Kelvin degree (later renamed the kelvin), and the candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name: Le Système International d'Unités. The seventh base unit, the mole, was added in 1970 by the 14th CGPM. The International System is now either obligatory or permissible throughout the world. It is administered by the standards organisation: the Bureau International des Poids et Mesures (International Bureau of Weights and Measures).
Units
:Main articles: SI base unit, SI derived unit, SI prefix The international system of units consists of a set of units together with a set of prefixes. The units of SI can be divided into two subsets. There are the seven base units. Each of these base units are dimensionally independent. From these seven base units several other units are derived. In addition to the SI units there are also a set of non-SI units accepted for use with SI. A prefix may be added to units to produce a multiple of the original unit. All multiples are integer powers of ten. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a kilogram is a milligram not a microkilogram.
SI writing style

- Symbols are written in lower case, except for symbols derived from the name of a person. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa" whereas the unit itself is written "pascal". The one exception is the litre, whose original abbreviation "l" is dangerously similar to "1". The NIST recommends that "L" be used instead, a usage which is common in the U.S., Canada and Australia, and has been accepted as an alternative by the CGPM. The cursive "ℓ" is occasionally seen, especially in Japan, but this is not currently recommended by any standards body. For more information, see Litre.
- Symbols are written without grammatical markers when used with singular numerals: i.e. "25 kg", not "25 kgs". Pluralization would be language dependent; "s" plurals (as in French and English) are particularly undesirable since "s" is the symbol of the second. Other cases may be marked in a language-dependent manner, e.g. Finnish 25 kg:lla = 25 kilogrammalla "with 25 kg".
- Symbols do not have an appended period (.).
- It is preferable to write symbols in upright Roman type (m for metres, L for litres), so as to differentiate from the italic type used for mathematical variables (m for mass, l for length).
- A space should separate the number and the symbol, e.g. "2.21 kg", "7.3×10² m²", "22 °C" [http://physics.nist.gov/Pubs/SP811/sec07.html]. Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
- Spaces should be used to group decimal digits in threes, e.g. 1 000 000 or 342 142 (in contrast to the commas or dots used in other systems, e.g. 1,000,000 or 1.000.000).
- The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line". In practice, the full stop is used in English, and the comma in most other European languages.
- Symbols for derived units formed from multiple units by multiplication are joined with a space or centre dot (·), e.g. N m or N·m.
- Symbols formed by division of two units are joined with a solidus (/), or given as a negative exponent. For example, the "metre per second" can be written "m/s", "m s^-1", "m·s^-1" or $\frac$ . A solidus should not be used if the result is ambiguous, i.e. "kg·m^-1·s^-2" is preferable to "kg/m/s²".
Spelling variations

- Several nations, notably the United States, typically use the spellings 'meter' and 'liter' instead of 'metre' and 'litre' in keeping with standard American English spelling. In addition, the official US spelling for the SI prefix 'deca' is 'deka'.
- The unit 'gram' is also sometimes spelled 'gramme' in English-speaking countries other than the United States, though that is an older spelling and its use is declining.
Cultural issues
The swift worldwide adoption of the metric system as a tool of economy and everyday commerce was based mainly on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardize the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. Scientifically, it provides ease when dealing with very large and small quantities because it lines up so well with our decimal numeral system. Cultural differences can be represented in the local everyday uses of metric units. For example, bread is sold in one-half, one or two kilogram sizes in many countries, but you buy them by multiples of one hundred grams in the former USSR. In some countries, the informal cup measurement has become 250 mL, and prices for items are sometimes given per 100 g rather than per kilogram. A profound cultural difference between physicists and engineers, especially radio engineers, existed prior to the adoption of the metre-kilogram-second (MKS) system and hence its descendent, SI. Engineers work with volts, amperes, ohms, farads, and coulombs, which are of great practical utility, while the centimetre-gram-second (CGS) units, which, though appropriate for theoretical physics, can be inconvenient for electrical engineering usage and are largely unfamiliar to householders using appliances rated in volts and watts. People with diabetes test their plasma glucose level regularly. In the U.S., measurement are recorded in milligrams per deciliter (mg/dL); in Europe, the standard is millimole/liter (mmol/L). The fine-tuning that has happened to the metric base units over the past 200 years, as experts have tried periodically to refine the metric system to fit the best scientific research do not affect the everyday use of metric units. Since most non-SI units, such as the U.S. customary units, are nowadays defined in terms of SI units, any change in the definition of the SI units results in a change of the definition of the older units as well.
See also

- Units of measurement
- Weights and measures
- Mesures usuelles
- Metrified English unit
- History of measurement
- Other systems of measurement:
- Imperial units
- U.S. customary units
- Metre-tonne-second system of units
- Chinese system of units
- Planck units
- Atomic units
- Geometrized units
- CODATA
- Metrication
- Metric system in the United States
- Metrology
- UTC (Coordinated Universal Time)
- Binary prefixes - used to quantify large amounts of computer data
- Orders of magnitude
- ISO 31
External links
Official
- [http://www.bipm.fr/en/si/ BIPM (SI maintenance agency)] (home page)
- [http://www.bipm.org/en/si/si_brochure/ BIPM brochure] (SI reference)
- [http://www.iso.ch/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=5448&ICS1=1 ISO 1000:1992 SI units and recommendations for the use of their multiples and of certain other units], with its price tag of 99 Swiss francs for a 22 page, coverless pamphlet showing why the public is sometimes a little slow to pick up on their recommendations. Information
- [http://physics.nist.gov/cuu/Units/index.html US NIST reference on SI]
- [http://ts.nist.gov/ts/htdocs/200/202/pub814.htm#chart chart]
- [http://www.aticourses.com/international_system_units.htm SI - Its history and use in science and industry]
- [http://www.unc.edu/~rowlett/units/ A Dictionary of Units of Measurement]
- [http://www.unics.uni-hannover.de/ntr/russisch/si-einheiten.html5 Cyrillic transcription of SI symbols]
- Judson, Lewis B., Weights and Measures Standards of the United States: A brief history, NBS Special Publication 447, orig. iss. October 1963, updated March 1976 ([http://ts.nist.gov/ts/htdocs/200/202/SP%20447.pdf 46 page PDF file])
- [http://www.france-property-and-information.com/metric_conversion_table.htm Metric system and conversion tables (courtesy French property advice)]
- [http://www.metre.info metre-info - an encyclopaedia of all metric units] Pro-metric pressure groups
- [http://www.ukma.org.uk/ The UK Metric Association]
- [http://www.metric.org/ The US Metric Association] Pro-customary measures pressure groups
- [http://www.bwmaonline.com/ The British Weights and Measures Association]
Further reading

- I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC: Quantities, Units and Symbols in Physical Chemistry, 2nd ed., Blackwell Science Inc 1993, ISBN 0632035838. Category:SI units Category:Systems of units Category:International standards Category:Dimensional analysis ko:SI 단위계 ja:国際単位系 simple:SI th:หน่วยเอสไอ

Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between charge and field is the source of one of the four fundamental forces, the electromagnetic force.

Overview

Electric charge is a characteristic of subatomic particles, and is quantized. For example, electrons have a charge, by convention, of −1. Protons have the opposite charge of +1. Quarks have a fractional charge of −1/3 or +2/3. The antiparticle equivalents of these have the opposite charge. There are other charged particles. The SI unit of electric charge is the coulomb, which represents approximately 6.24 x 10¹⁸ elementary charges (the charge on a single electron or proton). The coulomb is defined as the quantity of charge that has passed through the cross-section of a conductor carrying one ampere within one second. The symbol Q is used to denote a quantity of electric charge. Electric charge can be directly measured with an electrometer. The discrete nature of electric charge was demonstrated by Robert Millikan in his oil-drop experiment. Formally, a measure of charge should be a multiple of the elementary charge e (charge is quantized), but since it is an average, macroscopic quantity, many orders of magnitude larger than a single elementary charge, it can effectively take on any real value.

History

As reported by the Ancient Greek philosopher Thales of Miletus around 600 BC, charge (or electricity) could be accumulated by rubbing fur on various substances, such as amber. The Greeks noted that the charged amber buttons could attract light objects such as hair. They also noted that if they rubbed the amber for long enough, they could even get a spark to jump. This property derives from the triboelectric effect. The word electricity derives from ηλεκτρον (electron), the Greek word for amber. C. F. Du Fay proposed in 1733 [http://www.sparkmuseum.com/BOOK_DUFAY.HTM] that electricity came in two varieties which cancelled each other, and expressed this in terms of a two-fluid theory. When glass was rubbed with silk, DuFay said that the glass was charged with vitreous electricity, and when amber was rubbed with fur, the amber was said to be charged with resinous electricity. By the 18th century, the study of electricity had become popular. One of the foremost experts was Benjamin Franklin, who argued in favor of a one-fluid theory of electricity. Franklin imagined electricity as being a type of invisible fluid present in all matter; for example he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was "negatively" charged, and when it had an excess it was "positively" charged. Arbitrarily (or for a reason that was not recorded) he identified the term "positive" with vitreous electricity and "negative" with resinous electricity. William Watson arrived at the same explanation at about the same time. We now know that the Franklin/Watson model was close, but too simple. Matter is actually composed of several kinds of electrically charged particles, the most common being the positively charged proton and the negatively charged electron. Rather than one possible electric current there are many: a flow of electrons, a flow of electron "holes" which act like positive particles, or in electrolytic solutions, a flow of both negative and positive particles called ions moving in opposite directions. To reduce this complexity, electrical workers still use Franklin's convention and they imagine that electric current (known as conventional current) is a flow of exclusively positive particles. The conventional current simplifies electrical concepts and calculations, but it ignores the fact that within some conductors (electrolytes, semiconductors, and plasma), two or more species of electric charges flow in opposite directions. The flow direction for conventional current is also backwards compared to the actual electron drift taking place during electric currents in metals, the typical conductor of electricity, which is a source of confusion for beginners in electronics.

Properties

Aside from the properties described in articles about electromagnetism, charge is a relativistic invariant. This means that any particle that has charge q, no matter how fast it goes, always has charge q. This property has been experimentally verified by showing that the charge of one helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at incredible speeds) is the same as two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus).

Conservation of charge

The total electric charge of isolated systems remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from Maxwell's equation as a continuity equation. More generally, the net change in charge density

\rho

within a volume of integration

V

is equal to the area integral over the current density

J

on the surface of the volume

S

, which is in turn equal to the net current

I

: :

- \frac \int_V \rho dV = \int_S \mathbf \cdot \mathbf = I

External links

- [http://www.unitconversion.org/unit_converter/charge.html Online Charge Converter] - convert between various units of charge, such as coulomb, EMU of charge, franklin, ampere-hour, faraday, and so on
- [http://www.unitconversion.org/unit_converter/charge-v.html Interactive Charge Conversion Table] - convert selected unit to all other units of charge
- [http://www.ce-mag.com/archive/2000/marapril/mrstatic.html How fast does a charge decay?]
- Category:Electricity Category:Physical quantity Category:Chemical properties Category:Introductory physics Category:Fundamental physics concepts ko:전하 ja:電荷

Charles-Augustin de Coulomb

Charles Augustin Coulomb (June 14, 1736 – August 23, 1806) was a French physicist. Coulomb was born in Angoulême, France. He chose the profession of military engineer, and spent three years, to the decided injury of his health, at Fort Bourbon, Martinique. Upon his return, he was employed at La Rochelle, the Isle of Aix and Cherbourg. In 1781, he was stationed permanently at Paris. On the outbreak of the Revolution in 1789, he resigned his appointment as intendant des eaux et fontaines, and retired to a small estate which he possessed at Blois. He was recalled to Paris for a time in order to take part in the new determination of weights and measures, which had been decreed by the Revolutionary government. Of the National Institute he was one of the first members; and he was appointed inspector of public instruction in 1802. But his health was already very feeble, and four years later he died in Paris. Coulomb is distinguished in the history of mechanics and of electricity and magnetism. In 1779 he published an important investigation of the laws of friction (Théorie des machines simples, en ayant égard au frottement de leurs parties et à la roideur des cordages), which was followed twenty years later by a memoir on viscosity. In 1785 his Recherches théoriques et expérimentales sur la force de torsion et sur l'élasticité des fils de metal appeared. This memoir contained a description of different forms of his torsion balance. He used the instrument with great success for the experimental investigation of the distribution of charge on surfaces, of the laws of electrical and magnetic force, and of the mathematical theory of which he may also be regarded as the founder. The unit of charge, the coulomb, and Coulomb's law are named after him. ---- Coulomb, Charles-Augustin de Coulomb, Charles-Augustin de Coulomb Coulomb, Charles-Augustin de Coulomb, Charles-Augustin de ja:シャルル・ド・クーロン

Current (electricity)

In electricity, current refers to electric current, which is the flow of electric charge. Lightning is an example of an electric current, as is the solar wind, the source of the polar aurora. Probably the most familiar form of electric current is the flow of conduction electrons in a metallic wire. This is how utility companies deliver electricity. In electronics, electric current is most often the flow of electrons through conductors and devices such as resistors, but it is also the flow of ions inside a battery or the flow of holes within a semiconductor.

Relation between current and charge

The symbol typically used for the amount of current (the amount of charge Q flowing per unit of time t) is I, from the German word Intensität, which means 'intensity'. :

I =

Formally this is written as :

i(t) =

or inversely as

q(t) = \int_^ i(x)\, dx

Conventional current

Conventional current was defined early in the history of electrical science as a flow of positive charge. In solid metals, like wires, the positive charges are immobile, and only the negatively charged electrons flow in the direction opposite conventional current, but this is not the case in most non-metallic conductors. In other materials, charged particles flow in both directions at the same time. Electric currents in electrolytes are flows of electrically charged atoms (ions), which exist in both positive and negative varieties. For example, an electrochemical cell may be constructed with salt water (a solution of sodium chloride) on one side of a membrane and pure water on the other. The membrane lets the positive sodium ions pass, but not the negative chlorine ions, so a net current results. Electric currents in plasma are flows of electrons as well as positive and negative ions. In ice and in certain solid electrolytes, flowing protons constitute the electric current. To simplify this situation, the original definition of conventional current still stands. There are also instances where the electrons are the charge that is physically moving, but where it makes more sense to think of the current as the movement of positive "holes" (the spots that should have an electron to make the conductor neutral). This is the case in a p-type semiconductor. The SI unit of electrical current is the ampere. Electric current is therefore sometimes informally referred to as amperage or ampage, by analogy with the term voltage. Though this is a valid term, some engineers frown on it.

The speed of an electric current

The charged particles whose movement causes an electric current do not always move in straight lines. In metals, for example, they follow an erratic path, bouncing from atom to atom, but generally drifting in the direction of the electric field. The speed at which they drift can be calculated from the equation: :

I=nAvQ \!\

where :I is the current :n is number of charged particles per unit volume :A is the cross-sectional area of the conductor :v is the drift velocity, and :Q is the charge on each particle. For example, in a copper wire of cross-section 0.5 mm², carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode ray tube, the electrons travel in near-straight lines ("ballistically") at about a tenth of the speed of light. However, we know that an electric signal travels much faster than this; usually close to the speed of light. These results show that the speed of the charged particles is not necessarily related to the speed of the electric signal. To understand how signals travel faster than the particles that carry them, it is necessary to understand the properties of electromagnetic waves (see article).

Current density

Current density is the current per unit (cross-sectional) area. Mathematically, current is defined as the net flux through an area. Thus: :

I = j \cdot A

where, in the MKS or SI system of measurement, :I is the current, measured in amperes :j is the "current density" measured in amperes per square metre :A is the area through which the current is flowing, measured in square metres The current density is defined as: :

j=\int_i n_i \cdot x_i \cdot \mathbf

where :n is the particle density (number of particles per unit volume) :x is the mass, charge, or any other characteristic whose flow one would like to measure. :u is the average velocity of the particles in each volume Current density is an important consideration in the design of electrical and electronic systems. Most electrical conductors have a finite, positive resistance, making them dissipate power in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up, or the insulating material failing. In superconductors, excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property.

Electromagnetism

Every electric current produces a magnetic field. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire. Electric current can be directly measured with a galvanometer, but this method involves breaking the circuit, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field it creates. Devices used for this include Hall effect sensors, current clamps and Rogowski coils.

Ohm's law

Ohm's law predicts the current in an (ideal) resistor (or other ohmic device) to be the quotient of applied voltage over electrical resistance: :

I = \frac

where :I is the current, measured in amperes :V is the potential difference measured in volts :R is the resistance measured in ohms

Electrical safety

The danger of an electric shock depends on the current (in milliamperes), duration and the current's path in the body:
- 1 mA causes a tingle
- 5 mA causes a slight shock
- 50 to 150 mA may result in death, e.g. through rhabdomyolysis (muscle breakdown) and resultant acute renal failure
- 1-4 A causes ventricular fibrillation
- 10 A causes cardiac arrest (only at this current will a typical home fuse break the circuit) Currents through the heart and the nervous system are the most dangerous. As most dangerous sources are voltage sources, the current present depends on the resistance of the body between the points of contact and any current limiting built into the source. The comparison between the dangers of alternating current and direct current has been a subject of debate ever since the War of Currents in the 1880s. DC tends to cause continuous muscular contractions that make the victim hold on to a live conductor, thereby increasing the risk of deep tissue burns. On the other hand, mains-frequency AC tends to interfere more with the heart's electrical pacemaker, leading to an increased risk of fibrillation. AC at higher frequencies holds a different mixture of hazards, such as RF burns and the possibility of tissue damage with no immediate sensation of pain.

External links

- [http://www.unitconversion.org/unit_converter/current.html Online Current Converter] - convert between various units of current, such as ampere, biot, abampere, statampere, and so on
- [http://www.unitconversion.org/unit_converter/current-v.html Interactive Current Conversion Table] - convert selected unit to all other units of current
- [http://amasci.com/amateur/elecdir.html Which direction does electricity really flow?] Category:Electromagnetism Category:Magnetism ko:전류 ja:電流 th:กระแสไฟฟ้า

Second

:This article is about the unit of time. For other uses, see second (disambiguation). The second (symbol: s) is the SI base unit of time.

Definition

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

Origin

Originally, the second was known as a "second minute", meaning the second minute (i.e. small) division of an hour. The first division was known as a "prime minute" and is equivalent to the minute we know today.

Conversions

- 60 seconds = 1 minute
- 3 600 seconds = 1 hour
- 86.4 kiloseconds (86 400 seconds) = 1 day (in the SI sense)

Explanation

The factor of 60 may have been influenced by the Babylonians who used factors of 60 in their counting system. The hour had previously been defined by the Egyptians in terms of the rotation of the Earth as 1/24 of a mean solar day. This made the second 1/86,400 of a mean solar day. In 1956 the second was defined in terms of the period of revolution of the Earth around the Sun for a particular epoch, because by then it had become recognized that the Earth's rotation on its own axis was not sufficiently uniform as a standard of time. The Earth's motion was described in Newcomb's Tables of the Sun, which provides a formula for the motion of the Sun at the epoch 1900 based on astronomical observations made during the eighteenth and nineteenth centuries. The second thus defined is :the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time. This definition was ratified by the Eleventh General Conference on Weights and Measures in 1960. Reference to the year 1900 does not mean that this is the epoch of a mean solar day of 86,400 seconds. Rather, it is the epoch of the tropical year of 31,556,925.9747 seconds of ephemeris time. Ephemeris Time (ET) was defined as the measure of time that brings the observed positions of the celestial bodies into accord with the Newtonian dynamical theory of motion. With the development of the atomic clock, it was decided to use atomic clocks as the basis of the definition of the second, rather than the rotation of the earth. Following several years of work, two astronomers at the United States Naval Observatory (USNO) and two astronomers at the National Physical Laboratory (Teddington, England) determined the relationship between the hyperfine transition frequency of the caesium atom and the ephemeris second. Using a common-view measurement method based on the received signals from radio station WWV, they determined the orbital motion of the Moon about the Earth, from which the apparent motion of the Sun could be inferred, in terms of time as measured by an atomic clock. As a result, in 1967 the Thirteenth General Conference on Weights and Measures defined the second of atomic time in the International System of Units (SI) as :the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. The ground state is defined at zero magnetic field. The second thus defined is equivalent to the ephemeris second. The definition of the second was later refined at the 1997 meeting of the BIPM to include the statement :This definition refers to a caesium atom at rest at a temperature of 0 K. In practice, this means that high-precision realizations of the second should compensate for the effects of ambient radiation to try to extrapolate to the value of the second as defined above.

External links

- [http://www.bipm.fr/en/si/si_brochure/chapter2/2-1/second.html Official BIPM definition of the second]
- [http://tycho.usno.navy.mil/leapsec.html Public domain article about definition of seconds and leap seconds] Category:SI base units Category:Units of time Category:CGS units ja:秒 simple:Second

Electric flux

:This article is about the concept of flux in science and mathematics. For other uses of the word, see flux (disambiguation). In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.
- In the fields of heat transport and mass transport (fluid dynamics, hydrogeology, chemical engineering), flux is defined as the amount of a given quantity that flows through a unit area per unit time (Bird, Stewart, and Lightfoot, Transport Phenomenon, 1960). Flux in this definition is a vector.
- In the field of electromagnetism, flux is usually the integral of a vector quantity over a finite surface. The result of this integration is a scalar quantity (Lorrain and Corson, Electromagnetic Fields and Waves, 1962). The magnetic flux is thus the integral of the magnetic vector field over a surface, and the electric flux is defined similarly. Using this definition, the flux of the Poynting vector over a specified surface is the rate at which electromagnetic energy flows through that surface. Confusingly, the Poynting vector is sometimes called the power flux, which is an example of the first usage of flux, above. It has units of watts/(meter)² (R.K. Wangsness, Electromagnetic Fields, 2nd ed., Wiley (1986), p.357) One could argue, based on the work of James Clerk Maxwell (1892 Treatise on Electricity and Magnetism) that the transport definition precedes the more recent way the term is used in electromagnetism. The specific quote from Maxwell is "In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. The result of this operation is called the surface integral of the flux. It represents the quantity which passes through the surface." In addition to these common mathematically defined definitions, there are many more loose usages found in fields such as biology. =Transport phenomenon=

Flux definition and theorems

There are many fluxes used in the study of transport phenomena. Each type of flux has its own distinct unit of measurement along with distinct physical constants. Five of the most common forms of flux from the transport literature are defined as: # Momentum flux, the rate of momentum moving across a unit area (N/m2). (Newtonian fluid, viscous flow) # Heat flux, the rate of heat flow across a unit area (J/(m2 s)). (Fourier's Law) # Chemical flux, the rate of movement of moles across a unit area (moles/(m2 s). (Fick's first law) # Mass flux, the rate of mass flow across a unit area (kg/(m2 s). (An alternate form of Fick's law that includes the grams per mole term to convert moles to mass) # Volumetric flux, the rate of volume flow across a unit area (m3/(m2 s). (Darcy's law) These fluxes are vectors at each point in space, and have a definite magnitude and direction. Also, one can take the divergence of any of these fluxes to determine the accumulation rate of the quantity in a control volume around a given point in space. For incompressible flow, the divergence of the volume flux is zero. The fundamental laws that govern this process include:
- Newton's law of viscosity
- Fourier's law of convection
- Fick's law of diffusion.
- Darcy's law of groundwater flow

Thermal systems

In thermal systems, the flux is the rate of heat flow per area per time (J/(m2 s)) (Carslaw and Jaeger, Conduction of Heat in Solids, Second Edition, 1959). This definition of heat flux fits the original definition of Maxwell (1892).

Chemical diffusion

Flux, or diffusion, for gaseous molecules can be related to the function: :

\Phi = 4\pi\sigma_^2\sqrt

where N is the total number of gaseous particles, k is Boltzmann's constant, T is the relative temperature in kelvins, and

\sigma_

is the mean free path between the molecules a and b. Chemical flux is also defined in Ficks's first law as: J = -D grad(C) where D is the molecular diffusion coefficient (m2/s) and C is the concentration ( moles/m3) (Bird, Stewart, and Lightfoot, Transport Phenomenon, 1960). This flux has units of moles/(m2 s) and fits the original definition of flux (Maxwell, 1892). =Electromagnetism =

Flux definition and theorems

An example of the second definition of flux is the magnitude of a river's current, that is, the amount of water that flows through a cross-section of the river each second. The amount of sunlight that lands on a patch of ground each second is also a kind of flux. To better understand the concept of flux in Electromagnetism, imagine a butterfly net. The amount of air moving through the net at any given instant in time is the flux. If the wind speed is high, then the flux through the net is large. If the net is made bigger, then the flux would be larger even though the wind speed is the same. For the most air to move through the net, the opening of the net must be facing the direction the wind is blowing. If the net opening is parallel to the wind, then no wind will be moving through the net. (These examples are not very good because they rely on a transport process and as stated in the introduction, transport flux is defined differently than E+M flux.) function As a mathematical concept, flux is represented by the surface integral of a vector field, :

\Phi_f = \int_S \mathbf \cdot \mathbf

where F is a vector field, dA is the area element of the surface S, directed as the surface normal, and

\Phi_f

is the resulting flux. The surface has to be orientable, i.e. two sides can be distinguished: the surface does not fold back onto itself. Also, the surface has to be actually oriented, i.e. we use a convention as to flowing which way is counted positive; flowing backward is then counted negative. The surface normal is directed accordingly, usually by the right-hand rule. Conversely, one can consider the flux the more fundamental quantity, and call the vector field the flux density. Often a vector field is drawn by curves (field lines) following the "flow"; the magnitude of the vector field is then the line density, and the flux through a surface is the number of lines. Lines originate from areas of positive divergence (sources) and end at areas of negative divergence (sinks). See also the image at right: the number of red arrows passing through a unit area is the flux density, the curve encircling the red arrows denotes the boundary of the surface, and the orientation of the arrows with respect to the surface denotes the sign of the inner product of the vector field with the surface normals. If the surface encloses a 3D region, usually the surface is oriented such that the outflux is counted positive; the opposite is the influx. The divergence theorem states that the net outflux through a closed surface, in other words the net outflux from a 3D region, is found by adding the local net outflow from each point in the region (which is expressed by the divergence). If the surface is not closed, it has an oriented curve as boundary. Stokes theorem states that the flux of the curl of a vector field is the path integral of the vector field over this boundary. This path integral is also called circulation, especially in fluid dynamics. Thus the curl is the circulation density. We can apply the flux and these theorems to many disciplines in which we see currents, forces, etc., applied through areas.

Maxwell's equations

The flux of electric and magnetic field lines is frequently discussed in electrostatics. This is because in Maxwell's equations in integral form involve integrals like above for electric and magnetic fields. For instance, Gauss's law states that the flux of the electric field out of a closed surface is proportional to the electric charge enclosed in the surface (regardless of how that charge is distributed). The constant of proportionality is the reciprocal of the permittivity of free space. Its integral form is: :

\oint_A \epsilon_0 \mathbf \cdot d\mathbf = Q_A

where

\mathbf

is the electric field,

d\mathbf

is the area of a differential square on the surface A with an outward facing surface normal defining its direction,

Q_\mbox \

is the charge enclosed by the surface,

\epsilon_0 \

is the permittivity of free space and

\oint_A

is the integral over the surface A. Either

\oint_A \epsilon_0 \mathbf \cdot d\mathbf

\oint_A \mathbf \cdot d\mathbf

is called the electric flux. Faraday's law of induction in integral form is: :

\oint_C \mathbf \cdot d\mathbf = -\int_ \  \cdot d\mathbf = - \frac

The magnetic field density, also called magnetic flux density, is denoted by

\mathbf

. Its flux is called the magnetic flux. The time-rate of change of the magnetic flux through a loop of wire is minus the electromotive force created in that wire. The direction is such that if current is allowed to pass through the wire, the electromotive force will cause a current which "opposes" the change in magnetic field by itself producing a magnetic field opposite to the change. This is the basis for inductors and many electric generators.

Poynting vector

The flux of the Poynting vector through a surface is the electromagnetic power, or energy per unit time, passing through that surface. This is commonly used in analysis of electromagnetic radiation, but has application to other electromagnetic systems as well. =Flux in biology=

General biology usage

In general, 'flux' in biology relates to movement of a substance between compartments. There are several cases where the concept of 'flux' is important.
- The movement of molecules across a membrane: in this case, flux is defined by the rate of diffusion or transport of a substance across a permeable membrane. Except in the case of active transport, net flux is directly proportional to the concentration difference across the membrane, the surface area of the membrane, and the membrane permeability constant.
- In ecology, flux is often considered at the ecosystem level - for instance, accurate determination of carbon fluxes (at a regional and global level) is essential for modeling the causes and consequences of global warming.
- Metabolic flux refers to the rate of flow of metabolites along a metabolic pathway, or even through a single enzyme. A calculation may also be made of carbon (or other elements, e.g. nitrogen) flux. It is dependent on a number of factors, including: enzyme concentration; the concentration of precursor, product, and intermediate metabolites; post-translational modification of enzymes; and the presence of metabolic activators or repressors. Metabolic control analysis provides a framework for understanding metabolic fluxes and their constraints.

An archaic use in biology

Flux is also an archaic term for dysentery, but also seems to cover any extensive flow of fluid from the body, so there's bloody flux, etc. =See also=
- Carbon flux
- Electron flux
- Energy flux
- Explosively pumped flux compression generator
- Fast Flux Test Facility
- Fluid dynamics
- Flux quantization
- Flux pinning
- Gauss's law
- Heat flux
- Latent heat flux
- Luminous flux
- Magnetic flux
- Magnetic flux quantum
- Neutron flux
- Poynting flux
- Poynting theorem
- Radiant flux
- Rapid single flux quantum
- Sound energy flux Category:Physical quantity Category:Vector calculus

Electron

The electron is a fundamental subatomic particle which carries a negative electric charge.

Overview

Within an atom the electrons surround the nucleus of protons and neutrons in an electron configuration. The word electron was coined in 1894 and is derived from the term electric, whose ultimate origin is the Greek word 'ηλεκτρον, meaning amber. Electrons in motion constitute electric current which may be used by scientists and engineers to measure many physical properties. Electric current existing for a finite time gives rise to a movement of charge (electricity) that may be harnessed as a practical means to perform work. The variations in electric field generated by differing numbers of electrons and their configurations in atoms determine the chemical properties of the elements. These fields play a fundamental role in chemical bonds and chemistry.

Electrons in practice

Classification of electrons

The electron is one of a class of subatomic particles called leptons which are believed to be fundamental particles (that is, they cannot be broken down into smaller constituent parts). The word "particle" is somewhat misleading however, because quantum mechanics shows that electrons also behave like a wave, e.g. in the double-slit experiment; this is called wave-particle duality. The antiparticle of an electron is the positron, which has the same mass but positive rather than negative charge. The term negatron is sometimes used to refer to standard electrons so that the term electron may be used to describe both positrons and negatrons, as proposed by Carl D. Anderson. Under ordinary circumstances, however, electron refers to the negatively charged particle alone.

Properties and behavior of electrons

Electrons have a negative electric charge of −1.6 × 10⁻¹⁹ coulombs, and a mass of about 9.11 × 10⁻³¹ kg (0.51 MeV/c²), which is approximately ¹⁄₁₈₃₆ of the mass of the proton. These are commonly represented as e⁻. According to quantum mechanics, electrons can be represented by wavefunctions, from which the electron density can be determined. The exact momentum and position of an electron cannot be simultaneously determined. This is a limitation described by the Heisenberg uncertainty principle, which, in this instance, simply states that the more accurately we know a particle's position, the less accurately we can know its momentum and vice versa. The electron has spin ½, which implies it is a fermion, i.e., it follows the Fermi-Dirac statistics. While most electrons are found in atoms, others move independently in matter, or together as an electron beam in a vacuum. In some superconductors, electrons move in Cooper pairs, in which their motion is coupled to nearby matter via lattice vibrations called phonons. When electrons move, free of the nuclei of atoms, and there is a net flow, this flow is called electricity, or an electric current. A body has a static charge when the body has more or fewer electrons than are required to balance the positive charge of the nuclei. When there is an excess of electrons, the object is said to be negatively charged. When there are fewer electrons than protons, the object is said to be positively charged. When the number of electrons and the number of protons are equal, their charges cancel out and the object is said to be electrically neutral. A macroscopic body can acquire charge through rubbing, i.e. the phenomena of triboelectricity. Electrons and positrons can annihilate each other and produce a pair of photons. Conversely, high-energy photons may transform into an electron and a positron by a process called pair production. The electron is an elementary particle — that means that it has no substructure (at least, experiments have not found any so far, and there is good reason to believe that there is not any). Hence, it is usually described as point-like, i.e. with no spatial extension. However, if one gets very near an electron, one notices that its properties (charge and mass) seem to change. This is an effect common to all elementary particles: the particle influences the vacuum fluctuations in its vicinity, so that the properties one observes from far away are the sum of the bare properties and the vacuum effects (see renormalization). There is a physical constant called the classical electron radius, with a value of 2.8179 × 10⁻¹⁵ m. Note that this is the radius that one could infer from its charge if the physics were only described by the classical theory of electrodynamics and there were no quantum mechanics (hence, it is an outdated concept that nevertheless sometimes still proves useful in calculations). The speed of an electron in a vacuum can approach, but never reach c, the speed of light in a vacuum. This is due to an effect of special relativity. The effects of special relativity are based on a quantity known as gamma or the Lorentz factor. Gamma is a function of v, the velocity of the particle, and c. The following is the formula for gamma: :

\gamma = 1 / \sqrt

The energy necessary to accelerate a particle is gamma minus one times the rest mass. For example, the linear accelerator at Stanford can [http://www2.slac.stanford.edu/vvc/theory/relativity.html accelerate] an electron to roughly 51 GeV. This gives you a gamma of 100,000 given that the rest mass of an electron is 0.51 MeV/c² (the relativistic mass of this fast electron is 100 000 times its rest mass). Solving the equation above for the speed of the electron gives a speed of: :

(1-\frac   \gamma ^)c

= 0.999 999 999 95 c. (The formula applies for large γ.)

Electrons in the universe

It is believed that the number of electrons existing in the known universe is at least 10⁷⁹. This number amounts to a density of about one electron per cubic metre of space. Based on the classical electron radius and assuming a dense sphere packing, it can be calculated that the number of electrons that would fit in the observable universe is on the order of 10¹³⁰. Of course, this number is even less meaningful than the classical electron radius itself.

Electrons in industry

Electron beams are used in welding as well as lithography.

Electrons in the laboratory

Early experiments

The quantum or discrete nature of electron's charge was observed by Robert Millikan in the Oil-drop experiment of 1909.

Use of electrons in the laboratory

Electron microscopes are used to magnify details up to 500,000 times. Quantum effects of electrons are used in Scanning tunneling microscope to study features at the atomic scale.

Electrons in theory

In relativistic quantum mechanics, the electron is described by the Dirac Equation. Quantum electrodynamics (QED) models an electron as a charged particle surrounded a sea of interacting virtual particles, modifying the sea of virtual particles which makes up a vacuum. Although this theory involves difficult theoretical problems where calculations produce infinite terms, a practical (although mathematically dubious) method called renormalization was discovered whereby infinite terms can be cancelled to produce finite predictions about the electron. The correction of just over 0.1% to the predicted value of the electron's gyromagnetic ratio from exactly 2 (as predicted by Dirac's single particle model), and its extraordinarily precise agreement with the experimentally determined value, is viewed as one of the pinnacles of modern physics. There are now indications that string theory and its descendants may provide a model of the electron and other fundamental particles where the infinities in calculations do not appear, because the electron is no longer seen as a dimensionless point. At present, string theory is very much a 'work in progress' and lacks predictions analogous to those made by QED that can be experimentally verified. In the Standard Model of particle physics, it forms a doublet in SU(2) with the electron neutrino, as they interact through the weak interaction. The electron has two more massive partners, with the same charge but different masses: the muon and the tau lepton. The antimatter counterpart of the electron is its antiparticle, the positron. The positron has the same amount of electrical charge as the electron, except that the charge is positive. It has the same mass and spin as the electron. When an electron and a positron meet, they may annihilate each other, giving rise to two gamma-ray photons, each having an energy of 0.511 MeV (511 keV). See also Electron-positron annihilation. Electrons are also a key element in electromagnetism, an approximate theory that is adequate for macroscopic systems, and for classical modelling of microscopic systems.

History

The electron as a unit of charge in electrochemistry had been posited by G. Johnstone Stoney in 1874. In 1894, he also invented the word itself. The discovery that the electron was a subatomic particle was made in 1897 by J.J. Thomson at the Cavendish Laboratory at Cambridge University, while he was studying "cathode rays". Influenced by the work of James Clerk Maxwell, and the discovery of the X-ray, he deduced that cathode rays existed and were negatively charged "particles", which he called "corpuscles". He published his discovery in 1897. The periodic law states that the chemical properties of elements largely repeat themselves periodically and is the foundation of the periodic table of elements. The law itself was initially explained by the atomic mass of the elements. However, as there were anomalies in the periodic table, efforts were made to find a better explanation for it. In 1913, Henry Moseley introduced the concept of the atomic number and explained the periodic law with the number of protons each element has. In the same year, Niels Bohr showed that electrons are the actual foundation of the table. In 1916, Gilbert Newton Lewis and Irving Langmuir explained the chemical bonding of elements by electronic interactions.

External links

- [http://www.aip.org/history/electron/ The Discovery of the Electron] from the American Institute of Physics History Center
- [http://pdg.lbl.gov/ Particle Data Group]
- Stoney, G. Johnstone, "[http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Stoney-1894.html Of the 'Electron,' or Atom of Electricity]". Philosophical Magazine. Series 5, Volume 38, p. 418-420 October 1894.
- Eric Weisstein's World of Physics: [http://scienceworld.wolfram.com/physics/Electron.html Electron]

References

-
-
- Brumfiel, G. (6 January 2005). Can electrons do the splits? In Nature, 433, 11. ko:전자 ja:電子 simple:Electron th:อิเล็กตรอน

Elementary charge

The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. This is a fundamental physical constant and the unit of electric charge in the system of atomic units. It has a value of 1.602 176 53(14) × 10^-19 C, according to the 2002 CODATA list of physical constants. In the Centimetre gram second system of units, the value is approximately 4.803 × 10^-10 statcoulombs. Since it was first measured in Robert Millikan's famous oil-drop experiment in 1909, the elementary charge has been considered indivisible. Quarks, first posited in the 1960s, are believed to have fractional electric charges (in units of e/3), but only to exist in particles with an integer charge. They have never been detected singly. In 1982 Robert Laughlin tried to explain the fractional quantum Hall (FQH) effect by predicting the existence of fractionally charged quasiparticles. In 1995 fractional charge of Laughlin quasiparticles has been measured directly in a quantum antidot electrometer at Stony Brook University (New York). In 1997, two groups of physicists at the Weizmann Institute of Science in Rehovot, Israel, and at the CEA laboratory near Paris, claimed to have detected such quasiparticles carrying an electric current.

External links

- [http://www.jstor.org/view/00368075/di002303/00p0036t/0?currentResult=00368075%2bdi002303%2b00p0036t%2b0%2c01%2b19950217%2b9993%2b80049782&searchID=8dd55340.10818876572&frame=noframe&sortOrder=SCORE&userID=81313876@sunysb.edu/018dd55340005010fc7d6&dpi=3&viewContent=Article&config=jstor "Measurement of fractional charge" (Science Report) 1995]
- [http://quantum.physics.sunysb.edu/index.html "Quantum antidot electrometer"]
- [http://physicsweb.org/article/news/1/10/7/1 "Fractional charge carriers discovered" - Physics Web article 1997-10-24]
- [http://www.nature.com/cgi-taf/google_referrer.taf?article_product_code=NATURE&fulltext_filename=/nature/journal/v389/n6647/full/389162a0_fs.html&_UserReference=C0A804F846B4FE09B530543FD0523FA3D356 "Direct observation of a fractional charge" (letter to Nature) 1997] Category:Physical constants ja:電気素量

Josephson constant

The magnetic flux quantum Φ₀ is the quantum of magnetic flux passing through a superconductor. The inverse of the flux quantum, 1/Φ₀, is called the Josephson constant, and is denoted K_J. The quantization of magnetic flux is closely related to the Aharonov-Bohm effect, but was predicted earlier by F. London in 1948 using a phenomenological model.

Introduction

It is a property of a supercurrent (superconducting electrical current) that the magnetic flux passing through any area bounded by such a current is quantized. The quantum of magnetic flux is a physical constant, as it is independent of the underlying material as long as it is a superconductor. Its value is :

\Phi_0 = \frac = 2.067833636 \times 10^\,\mathrm

If the area under consideration consists entirely of superconducting material, the magnetic flux through it will be zero, for supercurrents always flow in such a way as to expel magnetic fields from the interior of a superconductor, a phenomenon known as the Meissner effect. A non-zero magnetic flux may be obtained by embedding a ring of superconducting material in a normal (non-superconducting) medium. There are no supercurrents present at the center of the ring, so magnetic fields can pass through. However, the supercurrents at the boundary will arrange themselves so that the total magnetic flux through the ring is quantized in units of Φ₀. This is the idea behind SQUIDs, which are the most accurate type of magnetometer available. A similar effect occurs when a superconductor is placed in a magnetic field. At sufficiently high field strengths, some of the magnetic field may penetrate the superconductor in the form of thin threads of material that have turned normal. These threads, which are sometimes called fluxons because they carry magnetic flux, are in fact the central regions ("cores") of vortices in the supercurrent. Each fluxon carries an integer number of magnetic flux quanta.

Measuring the magnetic flux

The magnetic flux quantum may be measured with great precision by exploiting the Josephson effect. In fact, when coupled with the measurement of the quantum Hall resistance quantum R_H = h / e², this provides the most precise values of Planck's constant h obtained to date. This is remarkable since h is generally associated with the behavior of microscopically small systems, whereas the quantization of magnetic flux in a superconductor and the quantum Hall effect are both collective phenomena associated with thermodynamically large numbers of particles. Category:Superconductivity Category:Magnetism

Von Klitzing constant

The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional systems of electrons subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ takes on the quantized values :

\sigma = \nu \; \frac,

where e is the elementary charge and h is Planck's constant. In the "ordinary" quantum Hall effect, known as the integer quantum Hall effect, ν takes on integer values (ν = 1, 2, 3, etc.). There is another type of quantum Hall effect, known as the fractional quantum Hall effect, in which ν can occur as a vulgar fraction with an odd denominator (ν = 2/7, 1/3, 2/5, 3/5, etc.) The quantization of the Hall conductance has the important property of being incredibly precise. Actual measurements of the Hall conductance have been found to be integer or fractional multiples of e²/h to nearly one part in a billion. This phenomenon, referred to as "exact quantization", has been shown to be a subtle manifestation of the principle of gauge invariance. It has allowed for the definition of a new practical standard for electrical resistance: the resistance unit h/e², roughly equal to 25 812.8 ohms, is referred to as the von Klitzing constant [http://physics.nist.gov/cgi-bin/cuu/Value?rk|search_for=RK R_K] (after Klaus von Klitzing, the discoverer of exact quantization) and since 1990, a fixed conventional value [http://physics.nist.gov/cgi-bin/cuu/Value?rk90|search_for=RK R_K-90] is used in resistance calibrations worldwide. The quantum Hall effect also provides an extremely precise independent determination of the fine structure constant, a quantity of fundamental importance in quantum electrodynamics. The integer quantization of the Hall conductance was originally predicted by Ando, Matsumoto, and Uemura in 1975, on the basis of an approximate calculation. Several workers subsequently observed the effect in experiments carried out on the inversion layer of MOSFETs. It was only in 1980 that von Klitzing, working with samples developed by Michael Pepper and Gerhard Dorda, made the totally unexpected discovery that the Hall conductivity was exactly quantized. For this finding, von Klitzing was awarded the 1985 Nobel Prize in Physics. The link between exact quantization and gauge invariance was subsequently found by Robert Laughlin. The fractional effect is due to completely different physics, and was experimentally discovered in 1982 by Daniel Tsui and Horst Störmer, in experiments performed on gallium arsenide heterostructures developed by Arthur Gossard. The effect was explained by Robert_B._Laughlin in 1983, using a novel quantum liquid phase that accounts for the effects of interactions between electrons. Tsui, Störmer, and Laughlin were awarded the 1998 Nobel Prize for their work. Although it was generally assumed that the discrete resistivity jumps found in the Tsui experiment were due to the presence of fractional charges, it was not until 1997 that R. de-Picciotto, et. al., directly observed fractional charges through measurements of quantum shot noise. The fractional quantum hall effect continues to be influential in theories about topological order.

References

- T. Ando, Y. Matsumoto, and Y. Uemura, J. Phys. Soc. Jpn. 39, 279 (1975)
- K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980)
- R.B. Laughlin, Phys. Rev. B. 23, 5632 (1981).
- D.C. Tsui, H.L. Stormer, and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)
- R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
- R. de-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu, Nature 389, 162-164 (1997) Category:Condensed matter physics Category:Quantum mechanics ja:量子ホール効果

Mole unit

The mole (symbol: mol) is the SI term identifying the number of particles in a given amount of matter. It is a dimensionless quantity (meaning a number without units) numerically equal to Avogadro's number.

Definition

The formal definition of the mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 12 grams of carbon 12, where the carbon 12 atoms are unbound, at rest and in their ground state. The number of atoms in 0.012 kilogram of carbon 12 is known as Avogadro's number. It is approximately 6.0221415 (2002 CODATA value). A mole is a dimensionless name for an integer, much like dozen or googol. Although the exact value of the mole is not known at present, it is equal to Avogadro's number, which is known to 1 part in 10 million. Because of the relationship of the atomic mass unit to Avogadro's number, a practical way of stating this for atoms or molecules is: That amount of the substance containing exactly the same number of grams as the number of the atomic weight of the substance. Since iron, for example, has an atomic weight of 55.845, there are 55.845 grams in a mole of iron.

Elementary entities

When the mole is used to specify the amount of a substance, the kind of elementary entities (particles) in the substance must be identified. The particles can be atoms, molecules, ions, formula units, electrons, or other particles. For example, one mole of water is equivalent to about 18 grams of water and contains one mole of H₂O molecules, but three moles of atoms (two moles H and one mole O). When the substance of interest is a gas, the particles are usually molecules. However, the noble gases (He, Ar, Ne, Kr, Xe, Rn) are all monoatomic, that is each particle of gas is a single atom. All gases have the same molar volume of 22.4 litres per mole at STP (see Avogadro's Law). A mole of atoms or molecules is also called a "gram atom" or "gram molecule".

History

The name mole is attributed to Wilhelm Ostwald who introduced the concept in the year 1902. He used it to express the gram molecular weight of a substance. So, for example, 1 mole of hydrochloric acid (HCl) has a mass of 36.5 grams (atomic weights Cl: 35.5 u, H: 1.0 u). Prior to 1959 both the IUPAP and IUPAC used oxygen to define the mole, the chemists defining the mole as the number of atoms of oxygen which had mass 16 g, the physicists using a similar definition but with the oxygen-16 isotope only. The two organizations agreed in 1959/1960 to define the mole as such: The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol." This was adopted by the CIPM (International Committee for Weights and Measures) in 1967, and in 1971 it was adopted by the 14th CGPM (General Conference on Weights and Measures) In 1980 the CIPM clarified the above definition, defining that the carbon-12 atoms are unbound and in their ground state.

Utility of moles

The mole is useful in chemistry because it allows different substances to be measured in a comparable way. Using the same number of moles of two substances, both amounts have the same number of molecules or atoms. The mole makes it easier to interpret chemical equations in practical terms. Thus the equation: :2H₂ + O₂ = 2H₂O can be understood as "two moles of hydrogen plus one mole of oxygen yields two moles of water." Moles are useful in chemical calculations, because they enable the calculation of yields and other values when dealing with particles of different mass. Number of particles is a more useful unit in chemistry than mass or weight, because reactions take place between atoms (for example, two hydrogen atoms and one oxygen atom make one molecule of water) that have very different weights (one oxygen atom weighs almost 16 times as much as a hydrogen atom). However, the raw numbers of atoms in a reaction are not convenient, because they are very large; for example, just one mL of water contains over 3 × 10²² (or 30,000,000,000,000,000,000,000) molecules.

Example calculation

In this example, moles are used to calculate the mass of CO₂ given off when 1 g of ethane is burnt. The equation for this chemical reaction is: :7 O₂ + 2 C₂H₆ → 4 CO₂ + 6 H₂O Here, 7 moles of oxygen react with 2 moles of ethane to give 4 moles of carbon dioxide and 6 moles of water. Notice that the number of moles does not need to balance on either side of the equation. This is because a mole does not count mass or the number of atoms involved, simply the number of individual particles. In our calculation it is first necessary to work out the number of moles of ethane that has been burnt. The mass in grams of one mole of a substance is by definition its atomic or molecular mass. The atomic mass of hydrogen is 1, and the atomic mass of carbon is 12, so the molecular mass of C₂H₆ is (2 × 12) + (6 × 1) = 30. One mole of ethane is 30 g. The amount burnt was 1 g, or 1/30th of a mole. The molecular mass of CO₂ (the atomic mass of carbon is 12 and that of oxygen is 16) is 2 × 16 + 12 = 44, so one mole of carbon dioxide is 44 g. From the formula we know that :1 mole of ethane gives off 2 moles of carbon dioxide (because 2 give off 4). We also know the masses of a mole of both ethane and carbon dioxide, so :30 g of ethane gives off 2 × 44 g of carbon dioxide. It is necessary to multiply the mass of carbon dioxide by 2 because two moles are produced. However, we also know that just 1/30th of a mole of ethane was burnt. Again: :1/30th of a mole of ethane gives off 2 × 1/30th of a mole of carbon dioxide, so finally: :30 × 1/30 g ethane gives off 44 × 2/30 g of carbon dioxide = 2.93 g.

References

# [http://www.bipm.org/en/si/base_units/ Official SI Unit definitions] Category:SI base units Category:Units of amount of substance ko:몰 ja:モル

Faraday

In physics, the faraday (not to be confused with the farad) is a unit of electrical charge; one faraday is equal to the charge of 6.02 × 10²³ electrons (one mole). The faraday is no longer in general use and has been replaced by the SI unit coulomb; one faraday is approximately equivalent to 96485.3415 coulombs. Like the farad, the faraday was named after Michael Faraday.

Faraday constant

In physics and chemistry, the Faraday constant is the amount of electric charge in one mole of electrons. The Faraday constant was named after British scientist Michael Faraday. It is used in electrolytic system calculations to determine the mass of a chemical species that will collect at an electrode. It has the symbol F, and is given by :

F=N_A \cdot q

, where N_A is Avogadro's number (approximately 6.02 x 10²³) and q is the charge on an electron. The value of F was first determined by weighing the amount of silver deposited in an electrochemical reaction in which a measured current was passed for a measured time. This value was used to calculate Avogadro's number. Research is continuing into more accurate ways of determining F, and thereby N_A. There are plans to use this value to redefine the kilogram in terms of a known number of atoms. [Source: NPL Annual Review 1999] :F = 96 485.3383 Coulomb/mole Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2002, published in Rev. Mod. Phys. vol. 77(1) 1-107 (2005).

Statcoulomb

The statcoulomb (statC) or franklin (Fr) or electrostatic unit of charge (esu) is the physical unit for electrical charge used in the centimetre-gram-second (cgs) electrostatic system of units. The SI system of units uses the coulomb (C) instead. The conversion is : 1 statC = 0.1 Am/c ≈ 3.3356 × 10^-10 C The conversion factor (≈ 3.3356 × 10^-10) is equal to 10 divided by the numerical value of the speed of light, c, expressed in cm/s. In the electrostatic cgs system, electrical charge is a fundamental quantity defined via the electrostatic force (see below); in the SI system, electrical current is fundamental and defined via the electromagnetic force while electrical charge is a derived quantity. The electrostatic system derives the electric charge from Coulomb's law and takes the permittivity as a dimensionless quantity whose value in a vacuum is 1/(4π). Also the use of the permeability of vacuum,

\mu_0 \

, is avoided, having the consequence that the speed of light appears explicitly in some of the equations interrelating quantities in this system. The statcoulomb is defined as follows: if two objects each carry a charge of 1 statC and are 1 cm apart, they will repel each other with a force of 1 dyne. As a result, in the electrostatic cgs system, Coulomb's law describing the force F between two charges q₁ and q₂ a distance r apart takes the simple form: :

F=\frac

Note that in order for the Coulomb's law formula to work using the electrostatic cgs system, the dimension of electrical charge must be [mass]^1/2 [length]^3/2 [time]^-1. This is different from the dimension of coulombs which accounts for the fact that the factor k mentioned below is not dimensionless. In SI units, the electrostatic constant

k=\frac

(where

\epsilon_0 \

is the permittivity of vacuum) has to be used. Several other laws of electromagnetism also become easier when all quantities are expressed in electrostatic cgs units; this is the main reason that the cgs system of units is still in use in physics and electrical engineering. The main drawback of this approach is that two other sets of cgs units and equations are defined, the electromagnetic and symmetrical systems (the latter system mixes the first two). The equations in all three systems are usually written in non-rationalized form, so-called because the factors 2π or 4π appear often in unexpected places (in situations not involving circular or spherical symmetry, respectively). It is possible, albeit less often done, to write each set of equations in rationalized form. The coulomb is an extremely large charge rarely encountered in electrostatics, while the statcoulomb is closer to everyday charges. Category:Units of electrical charge Category:CGS units

Coulomb's law

In physics, Coulomb's law is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. Coulomb's Law may be stated as follows: "The magnitude of the electrostatic force between two point charges is directly proportional to the magnitudes of each charge and inversely proportional to the square of the distance between the charges."

Scalar Form

When one is interested only in the magnitude of the force (and not in its direction), it may be easiest to consider a simplified, scalar version of the law :

F = k_C \frac

where (in SI units):

F \

is the magnitude of the force exerted, measured in newtons

q_1 \

is the charge on one body, measured in coulombs

q_2 \

is the charge on the other body, also measured in coulombs

r \

is the distance between them measured in metres

k_C \

is the electrostatic constant or Coulomb force constant, often written as

\frac

where

\epsilon_0 \

is the permittivity of free space, an important physical constant. The value of k_C is approximately 8.988 x 10⁹ F⁻¹·m or C⁻²·N·m², and

\epsilon_0 \

≈ 8.854 × 10⁻¹² F·m⁻¹ or C²·N⁻¹·m⁻². In cgs units, the unit charge, esu of charge or statcoulomb, is defined so that this Coulomb force constant is 1. This formula says that the magnitude of the force is directly proportional to the magnitude of the charges of each object and inversely proportional to the square of the distance between them. Because, when measured in units people commonly use (such as MKS), the Coulomb force constant,

k \

, is numerically much much larger than the universal gravitational constant

G \

, which means that for objects with charge that is of the order of a unit charge (C) and mass of the order of a unit mass (kg), that the electrostatic forces will be so much larger than the gravitational forces that the latter force can be ignored. This is not the case when Planck units are used and both charge and mass are of the order of the unit charge and unit mass. Ho