Erg (unit) - definition of Erg (unit) by The Free Dictionary Erg (unit) - definition of Erg (unit) by The Free Dictionary (ûrg) n. The centimeter-gram-second unit of energy or work equal to the work done by a force of one dyne acting over a distance of one centimeter. [From Greek ergon, work; see werg- in the Appendix of Indo-European roots.] erg 2 n. An extensive area of desert covered with shifting sand dunes. [Colloquial Arabic (Maghrebi dialect) 'arq, 'arg, from Arabic 'irq, vein, small mountain, thin tract of sand extending along the ground (in reference to the veinlike appearance of the dunes); see ʕrq1 in the Appendix of Semitic roots.] erg (ɜːɡ) n (Units) the cgs unit of work or energy.

1 erg is equivalent to 10–7 joule [C19: from Greek ergon work] erg n, pl ergs or areg (Physical Geography) an area of shifting sand dunes in a desert, esp the Sahara [C19: from Arabic `irj] (Rowing) informal short for ergometer 2 erg (ɜrg) n. the centimeter-gram-second unit of work or energy, equal to the work done by a force of one dyne when its point of application moves through a distance of one centimeter in the direction of the force; 10−7 joule. [1870–75; < Greek érgon work ] erg- var. of ergo- 1 before a vowel: ergodic. erg (ûrg) A unit used to measure energy or work, equal to the force of one dyne over a distance of one centimeter. This unit has been mostly replaced by the joule. erg 1. An area in a desert where there are shifting sand dunes, for example in the Sahara. 2. A unit of energy equal to the energy produced by a force of 1 dyne acting through a distance of 1 cm.

Replaced in the inernational system by the joule (J): 1 erg = 10-7 J. ThesaurusAntonymsRelated WordsSynonymsLegend: Units: E a symbol for energy factor (see below) or for the Enhanced Fujita scale for tornado intensity. effective dose (ED) a measure used in pharmacology to express the percentage of a population that receives the desired benefit from a dose of the substance being studied. The measurement is usually given as a subscript. For example, the ED50 dose is the amount of the substance that benefits 50% of the test population. eighth means 1/8, of course; in meteorology the eighth is the unit for measuring the proportion of the sky covered by clouds. See okta . einstein, Einstein unit (E) a unit of light energy concentration sometimes used in physical chemistry. One einstein (or Einstein unit) is the energy per mole of photons carried by a beam of monochromatic light. Suppose a beam of light (in vacuum) has frequency v (in hertz ) and wavelength l (in meters).

Then one einstein is equal to (3.990 313 x 10-10)v or (0.119 627)/l joules per mole (J/mol). The unit is named for the physicist Albert Einstein (1879-1955), who explained how light carries energy in a famous 1905 paper. el the Dutch ell, a traditional unit of length equal to about 68-70 centimeters (roughly 27 inches). See the discussion of the ell, below. electric horsepower a unit of power, equal to exactly 746 watts (550.221 foot pounds per second), used in the electric industry. This is slightly larger than the ordinary or mechanical horsepower of exactly 550 foot pounds per second. electron (me) the mass of the electron, often used as a unit of mass in particle physics.

An electron has a mass of about 9.109 382 x 10-31 kilogram, 9.109 382 x 10-28 gram, or 0.510 9989 million electronvolts (MeV, see next two entries). electronvolt (eV) [1] a unit of work or energy used in physics. One electronvolt is the work required to move an electron through a potential difference of one volt . The size of the electronvolt must be determined experimentally; the currently accepted value (2014) is 160.176 620 8 x 10-21 joule , or 1.601 766 208 x 10-12 erg . This unit is accepted for use with SI units. The official spelling is electronvolt (one word) rather than electron volt. electronvolt (eV) [2] a unit of mass used in particle physics. Mass and energy are related by Einstein's famous equation, E = mc2.

The constant c is the speed of light, 299.79 x 106 m/sec. An energy of 1 electronvolt is therefore equivalent to a mass of about 1.782 662 x 10-33 gram, or about 1.073 544 x 10-9 atomic mass unit . This is such a small unit that most particle masses are measured in MeV or GeV. ell a traditional unit of length used primarily for measuring cloth. In the English system, one ell equals 20 nails, 45 inches , or 1.25 yards (exactly 1.143 meters). The word comes from the Latin ulna, which originally meant the elbow and is now the name of the bone on the outside of the forearm. The history of the unit is not clear. Some authorities believe the ell was originally a double forearm length, that is, 2 cubits or 36 inches, the same length as a yard .

The ell and the yard do seem to be identified in some medieval documents, with ulna being used for both, and in Scotland the ell was equal to 37 Scots inches or 37.2 English inches (94.5 centimeters), only slightly longer than the yard. (This Scottish length might also reflect an old practice of cloth merchants in giving an extra inch with each yard, to allow for any irregular cutting at the ends of the piece.) However, the English cloth ell is definitely longer than the yard; it seems to be the distance from the shoulder to the fingers of the opposite hand. This reflects a practice of cloth merchants of holding the cloth at the shoulder with one hand and pulling the piece through with the opposite hand. This cloth ell was used with a similar length in France, where it was called the aune. The Dutch el and German elle are a little more than half the English ell; they may represent "arm's-length" units like the Italian braccio , the Russian sadzhen , and the Turkish pik . elle a traditional unit of distance in German speaking countries. The elle varied considerably, but it was always shorter than the English ell or French aune.

A typical value in northern Germany was exactly 2 fuss (German feet), which would be close to 24 inches or 60 centimeters. In the south, the elle was usually longer, about 2.5 fuss. In Vienna, the elle was eventually standardized at 30.68 inches (77.93 centimeters). Although the German word Elle is often translated "yard" in English, this is not a very good equivalent. em a printer's unit of relative distance. One em is the height of the type size (in points) being used. If 12 point type is being set, then one em is 12 points, and so on. See point [2]. emu [1] an abbreviation for "electromagnetic unit." See ab- . emu [2] a CGS unit of magnetic dipole moment equal to 4pi micro- oersteds (1.256 637 x 10-5 Oe). In SI units, one emu equals 0.001 A·m2. emu/cm3 or emu/cc a CGS unit of magnetization.

In SI units, one emu/cm3 can be interpreted either as 4pi/10 milli teslas (1.256 637 mT) as a unit of magnetic polarization or excess magnetic induction, or as 1000 amperes per meter as a unit of magnetic dipole moment per unit volume. en a printer's unit of relative distance, equal to 1/2 em. If 12 point type is being set, then one en is 6 points, and so on. encablure a traditional French unit of distance corresponding to the English cable . The encablure was equal to 120 brasses or 600 pieds; this is about 194.88 meters or 639.37 English feet. Most navies, including the French, now use a metric cable equal to exactly 200 meters; in French this metric unit is sometimes called the encablure nouvelle (new cable). energy factor (EF) a measure of the energy efficiency of an appliance. In the U.S., the Department of Energy has defined energy factors for a variety of appliances.

For dishwashers, the energy factor is the number of cycles per kilowatt hour of power input. For clothes washers, it is the capacity of the washer in cubic feet divided by the number of kilowatt hours of power input per washing cycle. For clothes dryers, it is the number of pounds of clothes dried per kilowatt hour of power consumed. engineer's chain see chain . Engler degree a unit of kinematic viscosity given by readings on an Engler viscometer. The reading is the time (in seconds) required for 200 milliliters of the liquid being tested to flow through the device. The conversion of Engler degrees to absolute units requires an appropriate table, but for liquids having a viscosity of 100 centi stokes or more the Engler degree is roughly equal to 7.6 centistokes. enhanced Fujita scale (EF) the revised Fujita scale for estimating the strength of tornados, implemented by the U.S. National Weather Service in 2007. ennead a unit of quantity equal to 9, coined from the Greek word for nine, ennea.

enzyme unit (U or EU) a unit used by biochemists to measure the activity of enzymes, which are proteins produced by living cells to cause or facilitate necessary chemical reactions within the cell. One enzyme unit is the quantity of enzyme needed to cause a reaction to process 1 micro mole of substance per minute under specified conditions. Thus, one enzyme unit has a catalytic activity of 1/60 micro katal (µkt) or 16.667 nanokatals (nkt). eon alternate spelling for aeon, a unit of time equal to 1 billion years. Eotvos unit (E) a unit used in geophysics to measure the change in the acceleration of gravity with horizontal distance. One Eotvos unit equals 10-9 Gal per centimeter or 10-4 Gal per kilometer. In proper SI terms, the Eotvos unit equals 10-9 per second squared (s-2). The unit honors the Hungarian physicist Roland von Eötvös (1848-1919). ephah a ancient unit of volume for grains and dry commodities, used in the Bible.

The ephah is believed to equal about 40.32 liters or 1.4239 cubic feet. This is equivalent to about 1.144 U.S. bushel . epoch [1] a measure of time used in astronomy. In an epoch system, times are specified as years and fractions of years (such as epoch 1998.5). To set a starting point for the system, a specific epoch time must be fixed as a particular clock time of a particular date. In 1984, the International Astronomical Union agreed that epoch times should be fixed by requiring that epoch 2000.0 equals 12 hours Universal Time of the day 2000 January 1. Other epoch conventions were used in the past. See also Julian epoch . The name comes from a Greek word epoche meaning a stopping point or fixed point. epoch [2] a unit of time equal to 19 years, used in predictions of the tides. In this use, an epoch is another name for a Metonic cycle .

All possible alignments of the sun and moon occur in this 19-year cycle, so tidal heights and other tidal phenomena are averaged over this period. equivalent or equivalent weight (Eq) a unit of relative amount of substance used in chemistry. One equivalent weight of an element, compound, or ion is the weight in grams of that substance which would react with or replace one gram of hydrogen. Since one gram of hydrogen is very nearly equal to one mole and since hydrogen has one electron free to react with other substances, 1 Eq of a substance is effectively equal to one mole divided by the valence of the substance (the number of electrons the substance would engage in participating in the reaction). In practice, this is a large unit and measurements are more likely to be in milliequivalents (mEq or meq). erg the unit of work or energy in the CGS system, equal to the work done by a force of one dyne acting through a distance of one centimeter. Equivalently, one erg is the kinetic energy of a mass of 2 grams moving at a velocity of 1 cm/sec.

This is equal to 0.1 micro joule , or about 7.375 x 10-8 foot-pound. The name of the unit is from the Greek word ergon, work. There is no symbol; the word is spelled out in full. Adding prefixes is a problem: 1000 ergs is usually called a kiloerg, but one million ergs is a megalerg, the "l" being added to ease pronunciation. erlang (E) a measure of telecommunications traffic density. The erlang is a dimensionless "unit" representing a traffic density of one call-second per second (or one call-hour per hour, etc.). The erlang is sometimes divided into 36 unit calls or 30 EBHC. Also called the traffic unit (TU), the erlang honors A. K. Erlang (1878-1929), a Danish mathematician who studied the mathematics of telephone networks. estadio a traditional unit of distance in Spain and Portugal. The estadio, like the stade and the English furlong , is equal to 1/8 mile.

The Spanish estadio is equal to 1/8 milla or 625 pies; this is about 571 feet or 174 meters. The Portuguese unit is 1/8 milha, which is much longer: about 856 feet or 261 meters. esu an abbreviation for "electrostatic unit." See stat- . ett- or etto- (h-) Italian spelling for the metric prefix hecto- (100). The hectare, for example, is ettaro in Italian. The International System allows national variations in spelling of the names of units, but not in the symbols used for them; thus the symbol for etto- is h-. etto (hg) an informal Italian name for the hectogram, a unit of mass equal to 100 grams or about 3.5274 ounces . EU a symbol sometimes used for the enzyme unit (see above). exa- (E-) a metric prefix denoting 1018 (one quintillion in U.S. nomenclature).

The Latin and Greek prefix ex- means "out of," and is often used to indicate "a long way," as in the words "expanse" or "extreme." In addition, the prefix suggests the Greek hexa, meaning 6, this being the prefix for 10006. exajoule (EJ) a metric unit of energy. One exajoule equals 947.817 (U.S.) trillion Btu , 277.7778 petawatt hours, or about 9480 mega therms . The unit is often used in discussing global energy production, which is measured in hundreds of exajoules per year. exameter (Em) a metric unit of distance equal to 1015 kilometers. This is equivalent to about 621.371 trillion miles , 105.7 light years , or 32.408 parsecs . One exameter is approximately the distance from the earth to the Hyades star cluster in Taurus.

exbi- (Ei-) a binary prefix meaning 260 = 1 152 921 504 606 846 976. This prefix, adopted by the International Electrotechnical Commission in 1998, replaces exa- for binary applications in computer science. The prefix is a contraction of "exabinary." exposure value (EV) a unit used in photography to describe relative exposure. EV 0 is assigned to a specific combination of exposure time and lens aperture, such as 1 second at f/ 1. The difference between two exposure values is equal to the number of stops separating the two exposure settings. Different combinations of exposure time and lens aperture can have the same exposure value; the unit was invented to simplify the relationship. Regardless of camera settings, EV 6 is one stop "faster" than EV 5, that is, an EV 6 setting records an image with half as much light as an EV 5 setting.

eyesight The international system of units (SI) 1.1.1 1.1.1 The international system of units (SI) History In the second half of the nineteenth century the centimetre, gram and second were in fairly general use as base units for scientific work even in such countries as the UK and the USA where the foot and the pound were employed for commerce and engineering. As a result, the units required by the rapidly emerging science of electricity were based on the centimetre, gram and second, with which they formed a coherent system known as the CGS electromagnetic system. A system of units is said to be coherent when derived units are formed from the base units without the insertion of factors of proportionality other than unity. There was also the CGS electrostatic system, but the only quantities frequently expressed in electrostatic units were electric charge, electric potential, and capacitance. The young but fast-growing electrical industry soon found that many CGS electromagnetic units were of an extremely inconvenient size for its needs. Accordingly, in 1881, international agreement was reached to fix the practical unit of potential, to be called the volt, at 108 CGS units (which is approximately equal to the e.m.f.

of a primary cell), and the unit of resistance, the ohm, at 109 CGS units (which is approximately the resistance of a column of mercury 1 m long and 1 mm2 in cross-section). The unit of electric current, the ampere, was made a tenth of the CGS unit. A coherent system of practical electric units was thus secured which, however, was not coherent with the mechanical units based on the centimetre and gram. The practical electric units suited the needs of telegraphy, which was then the main electrical industry, and they also happen to be convenient for heavy electrical engineering and for electronics. The magnetic units, however, were left at their CGS values, presumably because the CGS unit of magnetic flux density, subsequently called ‘gauss’, is of the order of the flux density of the Earth’s field, and, as it was suitable for geomagnetism, there seemed no point in changing it for a unit 104 times larger. Coherence was thereby lost to electromagnetism as it had already been lost to the system embracing the mechanical units and the practical electric units.

Whereas the electric units, by the agreement of 1881, were chosen to be of suitable magnitude for everyday use, and whereas the centimetre and the second have acceptable sizes, the gram is too small for the practical needs of man, which are better served by a unit nearer the size of the pound or the kilogram. Moreover, the CGS unit of force, the dyne, and the unit of energy, the erg, are much too small. On the other hand, the unit of energy provided by the practical electric units, the volt-ampere-second, called the joule—which equals 107 ergs—is of a satisfactory size. These considerations—the advantages of coherence and the fortuitous circumstance that a mechanical system based on the metre and the kilogram has precisely the same unit of energy as is provided by the practical electric units—led G. Giorgi in 1902 to propose a system based on the metre, the kilogram, the second, and one of the practical electric units.

He pointed out that if magnetic field strength were expressed as amperes per metre instead of 4π times amperes per metre, which is the definition corresponding to that of the CGS unit, the number π would disappear from most electric and magnetic formulae involving rectilinear geometry, but would appear, as is to be expected, in those involving cylinders or spheres. The International Electrotechnical Commission eventually chose the ampere as the fourth base unit of the MKSA or ‘Giorgi’ system, and in 1948 the 9th General Conference of Weights and Measures† recommended it for science and technology, as well as for commerce and industry. This system admirably covers mechanics and electromagnetism, but it does not provide for other branches of science such as heat. In 1960, in the hope of securing world-wide uniformity in the units employed in natural science, the 11th CGPM added to the units metre, kilogram, second and ampere, the kelvin for thermodynamic temperature, the candela for luminous intensity, and the radian and steradian for plane and solid angle.

The first two joined the original four in being called ‘base’ units, and the last two were called ‘supplementary’ units. Any unit formed from two or more base units is called ‘derived’. The radian and steradian are regarded as derived units. The MKSA system thus broadened is called the International System of Units, often abbreviated to SI, and is the most satisfactory system of units we have had so far, in that it caters for the commercial and industrial activities of man as well as for the needs of science. In 1971, the 14th CGPM added the mole, the unit of amount of substance used in chemistry, to the list of base units, thus making them seven in all. † The General Conference of Weights and Measures ( CGPM ) is the authority set up by the Metre Convention of 1875 to promote and improve the metric system, and to secure international uniformity in metric units and standards of measurement. Definitions of some SI units The seven base quantities, each with its unit and unit symbol, are listed below.

SI base quantities and units Quantity The SI base units are defined as follows: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. 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. The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per metre of length. The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. 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.

When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of (1/683) watt per steradian. Derived units. The table below lists some of the more common SI derived quantities, each with its unit and unit symbol. Some of these derived units have special names in the SI. Quantity Units and Dimensions Units and Dimensions System of Units 2.1 UNITS AND DIMENSIONS A measured or counted quantity has a numerical value (2.47) and a unit (whatever there are 2.47 of). It is useful in most engineering calculations -- and essential in many -- to write both the value and the unit of each quantity appearing in an equation: 2 feet, 1/3 second, 4.29 miles, 6 tomatoes, ...

A dimension is a property that can be measured, such as length, time, mass, or temperature, or calculated by multiplying or dividing other dimensions, such as length/time (velocity), length3 (volume), or mass/length3 (density). Measurable units (as opposed to countable units) are specific values of dimensions that have been defined by convention, custom, or law, such as grams for mass, seconds for time, centimeters or feet for length, and so on. Units can be treated like algebraic variables when quantities are added, subtracted, multiplied, or divided. The numerical values of two quantities may be added or subtracted only if the units are the same: 3 ft - 1 ft = 2 ft (3x - x = 2x) but 3 ft - 1 in. (or 1 sec) = ? (3x - y = ?) On the other hand, numerical values and their corresponding units may always be combined by multiplication or division: 2.2 CONVERSION OF UNITS A measured quantity can be expressed in terms of any units having the appropriate dimension.

A particular velocity, for instance, may be expressed in ft/sec, miles/hr, cm/year or any other ratio of a length unit to a time unit. The numerical value of the velocity naturally depends on the unit chosen. The equivalence between two expressions of a given quantity may be defined in terms of a ratio: Ratios of the form of Equations 2.2-1. 2. and 3 are known as conversion factors. To convert a quantity expressed in terms of one unit to its equivalent in terms of another unit, multiply the given quantity by the conversion factor (new unit/old unit). For example, to convert 36 inches to its equivalent in feet, write (Note how the old units cancel, leaving the desired unit.) An alternative away to write this equation is to use a vertical line instead of the multiplication symbol Carrying along units in calculations of this type is the best way of avoiding the common mistake of multiplying when you mean to divide and vice versa. In the given example, the result is known to be correct because inches cancel out leaving only feet on the left-hand side, whereas is clearly wrong.

(More precisely, it is not what you intended to calculate.) If you are given a quantity having a compound unit (e.g., miles/hr, calories/gram°C), and you wish to convert it to its equivalent in terms of another set of units, set up a dimensional equation: write the quantity and its units on the left, write the units of conversion factors that cancel the old units and replace them with the desired ones, then fill in the values of the conversion factors, and carry out the indicated arithmetic operations to find the desired value. (See Example 2.2-1 .) TEST YOURSELF 1. What is a conversion factor? 2. What is the conversion factor for s/min (s = second)? 3. What is the conversion factor for min2/s2? (See Equation 2.2-3.) 4. What is the conversion factor for ft3/in.3? TABLE 2.3-1. SI and CGS Units 1 J/s = 1 kg · m2/s2 2.3 SYSTEM OF UNITS A system of units has the following components: 1. Base units, or units for the dimensions of mass, length, time, temperature, electrical current, and light intensity.

2. Multiple units, which are defined as multiples or fractions of base units such as minutes, hours, and milliseconds, all of which are defined in terms of the base unit of a second. Multiple units are defined for convenience rather than necessity: it is simply more convenient to refer to 3 years than to 94 608 000 seconds. 3. Derived units, obtained in one of two ways: (a) By multiplying and dividing base or multiple units (cm2, ft/min, kg · m/s2, etc.). Derived units of this type ar referred to as compound units. (b) As defined equivalents of compound units (e.g., 1 erg = 1 g · cm/s2, 1 lbf = 32.174 lbm · ft/s2). In 1960 an international conference formulated a system of metric units that is rapidly gaining acceptance in the scientific and engineering community. It is known as the "Systeme Internationale d'Unites," or the SI system for short. Two of the base units of the SI system -- the ampere for electrical current and the candela for luminous intensity -- will not concern us in this book.

A third, the degree Kelvin for temperature, will be discussed later. The others are the meter (m) for length, the kilogram (kg) for mass, and the second (s) for time. Unit prefixes are used in the SI system to indicate powers of ten. the most common of these prefixes and their abbreviations are mega (M) for 106 (1 megawatt = 1 MW = 106 watts), kilo (k) for 103, centi (c) for 10-2, milli (m) for 10-3, micro (µ) for 10-4, and nano (n) for 10-9. The conversion factors between, say, centimeters and meters are therefore 10-2m/cm and 102cm/m. The principal SI units and prefixes are summarized in Table 2.3-1 . An SI convention is to use blanks rather than commas when writing large numbers: for example, 34 607 for 34,607. We will use this notation throughout the text.

The CGS system is almost identical to the SI system, the principal difference being that grams (g) and centimeters (cm) are used instead of kilograms and meters as the base units of mass and length. The principal units of the CGS system are shown in Table 2.3-1 . The base units of the American engineering system are the foot (ft) for length, the pound-mass (lbm) for mass, and the second (s) for time. This system has two principal difficulties associated with it. The first is the occurrence of conversion factors (such as 1 ft/12 in.) which, unlike those in metric systems, are not multiples of ten; the second, which has to do with the unit of force, is discussed in the next section. Factors for converting from one system of units to another may be obtained by taking ratios of quantities listed in the table on the inside front cover of this book. A larger table of conversion factors is given on the inside back cover of the Chemical Engineers' Handbook 1 , and still another table is given on pp 1-24 through 1-27 of the Handbook. TEST YOURSELF 1.

What are the factors (numerical values and units) needed to convert (a) meters to millimeters? (c) square centimeters to square meters? (d) cubic feet to cubic meters? (e) horsepower to British Thermal Units per second? 2. What is the derived unit for velocity in the SI system? The CGS system? The American engineering system? _____________________ 1 R.H. Perry and C. H. Chilton, Eds., Chemical Engineers' Handbook, 5th Ed., McGraw-Hill, New York (1973). Unit Systems in Electromagnetism Unit Systems in Electromagnetism A guide to the different approaches used to define measurement units in the physics of magnetism and electrostatics. Contents ↓ The laws of Ampère and Coulomb ↓ The approach taken by the CGS system ↓ The e.m.u. subsystem ↓ The approach taken by the SI ↓ The evolution of unit systems ↓ The ratio of the e.s.u. to the e.m.u.

↓ Dimensional calculations ↓ Using units and symbols ↓ A note on spelling About your browser: if this character '×' does not look like a multiplication sign, or you see lots of question marks '?' or symbols like ' ' or sequences like '&cannot;' then please accept my apologies . See also ... [ ↑ Producing wound components] [ ↑ The terminology of electromagnetism] [ → Air coils] [ ↓ Ampère's Law of Force] [ W A Dictionary of Units of Measurement] Multiple Systems Our methods of measurement define who we are and what we value. Ken Alder , The Measure of All Things Units are no longer taught extensively. Their bland and pedantic nature makes study of drying paint more exciting. However, you don't go far in magnetism before you encounter the problem of its unit systems. That's right: systems, plural. You can understand that the world has different unit systems for length or mass. One half talks of pounds, feet and inches while the other says grams, millimetres and metres * . Hundreds of millions of people find that the older 'imperial' or British system works for them (despite the occasional mishap ). They conclude it not to be worth effort and expense changing.

Magnetism, you might think, would be different. It's only scientists and engineers who calculate it, and that it would be easy for them to concur about units. Having more than one set of units makes life hard for beginners in a subject which is difficult enough already. Sadly, scientists have spent at least sixty years disagreeing about the units for electromagnetism. Even were everyone to adopt the 'new' SI units the need for familiarity with the older CGS systems would remain in order to understand the large number of original works published in the latter. We'll spend a couple of paragraphs on the historical reasons for this schism because it also sheds light on the science. [ ↑ Top of page] The laws of Ampère and Coulomb The trouble starts with the definitions for the units of electric current and electric charge. Three simple, but fundamental, equations are crucial here. The first is Ampère's Force Law from which may be derived the electromechanical force, Fm, between two thin, parallel wires (see fig USA). The length of the wires, s, has to be much greater than their separation, a, and the wires must be thin in comparison with a.

These conditions ensure that - The field produced by each wire decays at a rate proportional to 1 / a, and Field lines produced by wire 1 which intersect wire 2 do so at right angles both to wire 2 and a line joining 1 to 2 normally, and vice versa. If s > 15a then the error will be below 1%. The Force Law predicts the force on these wires to be - Fm = 2 km I 1 I 2 s / a Equation USA where the magnetic force constant, km or κm, is a constant whose value depends upon the unit system used to measure the currents, forces and distances. In other words, having decided how to define distance and force, you can then choose a km that defines how large your unit of current will be. The factor of 2 here is not intrinsic to Ampère's Force Law but arises through its application to the particular case of parallel wires. Some writers incorporate it into km, but most do not.

The second equation is Coulomb's Law which gives the electrostatic force, Fe, between two isolated particles, separated by a distance, r, and carrying electric charges Q1 and Q2 - Fe = ke Q1 Q2 / r2 Coulomb's Law Where ke is a constant whose value depends upon the unit system used to measure the charges, forces and distances. In other words, having decided how to define distance and force, you can then choose a ke that defines how large your unit of charge will be. Or, at least you could do if you had not already decided upon km. Why? To understand this we need to introduce our third equation which expresses the fact that electric charge, Q, and current, I, are dependent quantities - Q = I × T Equation USQ where T is the time, in seconds, for which a given current, I, flows. Equation USQ must hold regardless of the unit system chosen; one unit of charge being represented by the passage of one unit of current for one second. You should now be able to see that it is possible either to invent some convenient value for km and then calculate ke or else invent some convenient value for ke and then calculate km.

You cannot choose both ke and km independently because that would violate Equation USQ. Performing both Ampere's and Coulomb's experiments ( Weber and Kohlrausch , 1856) gives you a value for the relationship between ke and km - Equation USJ where c is the speed of light in a vacuum. This equation is considered further below. That's the basic physics out of the way. However, the freedom to select an arbitrary value for either ke or km leads to the profusion of unit systems from which we suffer today. Consider next how the choices just described are made in the two major unit systems: the CGS and the SI. [ ↑ Top of page] The approach taken by the CGS systems Every electromagnetic quantity may be defined with reference to the fundamental units of Length, Mass, and Time. James Clerk Maxwell , A Treatise on Electricity and Magnetism In the unit system called CGS (for Centimetres Grams Seconds) force is measured in dynes: the force required to accelerate a mass of one gram at one centimetre per second squared.

Conversion between the SI and CGS System dyn 1.0×10-5 N However, the CGS system doesn't like to pick winners and losers in the km & ke game. Instead it defines two subsystems known as electromagnetic units (e.m.u. or CGSm) and electrostatic units (e.s.u. or CGSe). [ ↑ Top of page] The electromagnetic units subsystem In the e.m.u. subsystem it is Monsieur Ampère who is the winner, but kmCGSm takes the value of 1.0. That is, two wires one centimetre apart carrying 1 e.m.u. of current experience a force of two dynes for each centimetre of their length. What is the value of this current in SI units?

Rewriting Ampère's Force Law shows - I = √(FSI aSI / (2 kmSI smSI)) Equation USL This is consistently in SI units so we must translate the CGS force and length before substituting them - I = √(2×10-5 × 0.01 / (2×10-7 × 0.01)) = 10 amps Equation USM In CGS electromagnetic units this is sometimes called the abampere, or the biot or sometimes just 'one e.m.u. of current'. Conversion between the SI and e.m.u. System - 10 coulombs Sometimes no name is given for this unit other than an 'e.m.u. unit of charge'. You can, with the assistance of figure USU , continue from here to derive values in the rest of the e.m.u. such as potential (1 abvolt = 1.0×10-8 volts), capacitance resistivity and so on. The abvolt is so small in comparison with customary potentials because the dyne is feeble. Trouble brews faster yet. [ ↑ Top of page] The electrostatic units subsystem In the CGS e.s.u.

it is Monsieur Coulomb who gets first prize and a value of keCGSe equal to 1.0. Coulomb's Law now looks like - FCGS = keCGSe QCGSe1 QCGSe2 / rCGS2 Coulomb's Law (in CGSe) That means two charges of one electrostatic unit each, separated by one centimetre, experience a force of 1 dyne . How much is this quantity of charge in SI units: coulombs? First we re-arrange Coulomb's Law - QSI = √(FSI rSI2 / keSI ) 1 / cCGS abampere This curious factor of c is considered further below. It's worth pointing out here that the 'equivalence' shown between e.m.u. current and e.s.u. current does not extend to the units, which differ by that velocity: c. Ditto, of course, for the other quantities. The e.m.u. and e.s.u. systems were principally the work of Gauss and Weber . [ ↑ Top of page] The Gaussian subsystem The e.m.u. and e.s.u. subsystems described above are not adopted in their pure forms.

Instead a composite system is devised called Gaussian Units. This takes a 'pick and mix' selection from the e.m.u. and the e.s.u. . From the former it takes the 'magnetic units' of field strength, flux, flux density, magnetization etc.. From the latter it takes the 'electric units' charge, current, permittivity etc.. See table USS below. The Gaussian unit of magnetic flux density, the gauss, is defined using the Force Law - FCGS = ICGSm sCGS BGSN dynes Equation USF Equation USF says that a wire 1 centimetre long, sitting in a flux density equal to one gauss and carrying a current of 1 abampere experiences a force equal to 1 dyne . What is this flux density in the SI?

The SI defining relationship is - BSI = FSI / (ISI sSI) Substituting the current, force and length values converted from their CGS definitions - BSI = 10-5 / (10 × 0.01) = 10-4 tesla Equation USI The Gaussian unit of magnetic field strength, the oersted , was defined as equal to unity (1.0) at the centre of a circular loop of thin wire, radius one centimetre, carrying 1/(2π) abampere of current. Modern definitions rest on Maxwell's equation for H, but, under steady current conditions, it all boils down to Ampère's circuital law (and it's more refined sibling the Biot-Savart equation ). Let's convert the oersted into SI using the result for the field at the centre of a current loop : HSI = ISI / (2 a) = (10 / (2π)) / (2 × 0.01) = 250 / π amps per metre Equation USO where a is the radius of the loop. Table USS: Dimensions of CGS units, the Gaussian pick highlighted.

Quantity Name +0 -1 A most important fact to grasp is that the Gaussian has no separate concepts of absolute and relative permeability. If you take the Gaussian flux density (in gausses) and divide by the field strength (in oersteds) then you still get a result which is called permeability. That result, however, is numerically equal to what in the SI is the relative permeability. So, for a vacuum, oersteds/gausses = 1.0 and for iron it might be 8000. The same calculation in the SI, using teslas/(amps per metre), would yield values lower by a factor of 4π×10-7 and are designated absolute. It follows that, Gaussian permeability being a dimensionless ratio (just like 'relative permeability'), the fundamental units for flux density and field strength are the same: cm-½ g½ s-1 . Another trap for the unwary is the use of the symbol μ0 by some authors (eg Bozorth ) to represent initial permeability. This is not, repeat not, the permeability of a vacuum as used by authors working in the SI.

Oh, me 'ead :-( The Gaussian system, adopted in 1881, was (despite its name) principally the work of Heinrich Hertz and Maxwell . Its success meant that the term 'CGS units' become a synonym for it. [ ↑ Top of page] The approach taken by the SI In the SI, distance is measured in metres and force is measured in newtons (the force which when applied to a mass of one kilogram accelerates it at one metre per second squared). Now the important bit: Monsieur Ampère is again the winner and kmSI is given the value of 10-7. In the SI current is measured in amperes - One ampere is that constant electric current which, if maintained in two straight parallel conductors of infinite length, of negligible cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2×10-7 newton per metre of length. If you were wondering why the constant is 2×10-7 then the short answer is that this definition of the amp is compatible with earlier definitions of it. The ampere was in use long before the SI.

However, you also have a field strength ( H ) of one ampere per metre at the centre of a circular loop of wire of diameter one metre when it carries one ampere of current. See the Biot-Savart page for more details. Anyway, the runner up, Monsieur Coulomb, has to define his unit of electric charge via Equation USQ and then equation USJ gives the electrostatic force constant - keSI = cSI 2 kmSI ≅ 8.988×109 Equation USK In passing you might note that this means that two charges, of one coulomb each, placed one metre apart exert a force upon each other that exceeds the weight of two fully laden oil super-tankers. Do not try this at home. One ampere is a significant amount of current, yet it still produces a feeble magnetostatic force. One ampere second, i.e. one coulomb, produces an enormous electrostatic force. That is why Monsieur Ampère and Monsieur Coulomb do not see eye to eye and why science has had such a hard time reconciling all this Gallic discord.

It's easy to be confused by this stark definition of the ampere, in terms of the mechanical forces produced by it, into thinking that it is a derived unit from the base units of mass, length and time in the same way that joules, watts or pascals are. This indeed is how earlier systems treated current. The SI produces instead, depending on your point of view, either a stroke of genius or a fudge. it says "OK, we have said that you can tell how large an amp is in terms of force and length; but forget that we told you that. As far as the rest of the SI goes we treat the ampere as a fundamental unit which cannot be decomposed into more basic ones - in the same way that the second or the kilogram cannot". Immediately, however, we hit a problem. Re-arranging ampere's force law slightly - I2 = a Fm / (2 km s) Equation USR On the left we have amperes2 (A2). On the right we just have the old mechanical units. The equation is not dimensionally balanced . The workaround is to say that kmSI is not just a constant but a quantity with units of its own.

Remembering that the length (s) and the separation (a) both have dimensions of metres, inspection of Equation USR tells us that the units of kmSI must be newtons per ampere squared (N A-2). Another problem with the SI is that, after its introduction in 1960, a number of 'loose ends' were left concerning its application to magnetics. This led to the Kennelly and Sommerfeld subsystems of units. Each of these is based on a different model of the way magnetism works. The Kennelly subsystem makes use of the concept of 'magnetic poles' to model the interaction of materials with a field at an atomic level. The Sommerfeld system ascribes 'dipole moments' instead to circulating electric currents. The end result is that different definitions (and units) are used for magnetization. On a brighter note, modern authors appear to favour the Sommerfeld system - as will these web pages. The evolution of unit systems The amp, the volt and ohm agree to live together peacefully ...

(As not drawn by) Joseph Barbera , The Truce Hurts Devising a unit system is difficult because of the conflicting requirements which a good one should meet - The units should be of a size that is appropriate for use in science and engineering and in everyday ('customary') use by the wider commercial and public community. The units should be defined in a manner that is both precise and capable of being reproduced anywhere in the world. The units should be coherent. In a coherent system all the subsidiary or derived units can be expressed as combinations of the basic or fundamental units without the introduction of any multiplier. Compromise is unavoidable. First to adopt a customary metric system was France in 1799. Progress towards its adoption elsewhere has been distinctly less rapid now that those opposed to it are no longer decapitated. Anyway, the CGS system enjoyed wide acceptance until the electricity industry decided that the e.m.u. abvolt was too small for practical use and succeeded in introducing a value 108 times larger: our present value for the volt. The ohm and the amp were also re-scaled. Electricians were happy, but coherence with mechanical units was lost.

That is the fundamental reason why kmSI takes the value it does: it's what's needed to make electrical units a 'sensible' size for the installers of electric heat and light. In case anybody was still able to understand the state of the unit system it was decided in 1932 that what had been called the gauss would thereafter be known as the oersted. Only since then has the gauss been a unit of flux density. In 1948 it was decided that the centimetre, the gram and the erg (the CGS unit of energy) should be replaced by the larger metre, kilogram and joule. This was called the MKSA system and it restored coherence (as foreseen shortly after 1901 by Giovanni Giorgi ). In 1960 the radian, steradian, kelvin and the candela were added to the MKSA system to form the International System of Units, abbreviated to SI (Système International d'Unités). It is little changed to this day, apart from the introduction in 1971 of the mole . Why then, a hundred years after Giorgi's proposal, does everyone not use a coherent system?

The reasons are varied. They include, for example, a reluctance to specify flux density in teslas because Carl Friedrich Gauss was a greater intellect than Nikola Tesla . More importantly the SI permeability and permittivity are altogether nastier affairs compared to the CGS equivalents. That, though, is a fundamental difference - because the SI includes the ampere as a base unit, which CGS does not. It also explains why the dimensions of magnetic induction in the SI are different from those of magnetizing force . People with knowledge of the B-field and H-field only in the SI tend to see them as physically different. That the two exist for the sake of computational convenience alone is more obvious in Gaussian Units. Some have argued ( Larson ) that the unit system is in a mess because physics is in a mess. They say that ascribing units to kmSI is not science but computational legerdemain. Perish the thought. So, the answer to our original question "Why use different unit systems?" is not simple reluctance to change. It is, as Ken Alder says, about what you hold to be important.

Pragmatists favour the SI's utilitarian approach to calculation, want all the factors of c kept out of sight, accept the embarrassing units for km and will never replace a 3 abampere fuse. OTOH, philosophically minded physicists want only the three base quantities of the Gaussian system to better reflect the underlying science. They dream of a visit to Woolworths where they enquire of the sales assistant "Excuse me, have you any 600,000,000 ergs per second light bulbs?" "Why, certainly, sir. We sell all our electrical goods by Gaussian units because in advanced texts on electrodynamics we find that the tensor calculus equations which unify the electric and magnetic fields are just so much clearer!" "Great, I'll take 59,958,491,600 / c of them, please." "While you're here, may I interest you in our 0.005 statvolt AA cells?" Stuck in between these groups are the engineers; we must cope both with text books written by the latter and problems set by the former. What system should we adopt? It's anybody's gauss.

Whatever your own view may be, don't expect a truce soon :-( [ ↑ Top of page] The ratio of the e.s.u. to the e.m.u. This velocity, therefore, which indicates the relation between electrostatic and electromagnetic phenomena, is a natural quantity of definite magnitude, and the measurement of this quantity is one of the most important researches in electricity. James Clerk Maxwell , A Treatise on Electricity and Magnetism Although not essential to understanding unit systems, this topic does relate to equation USJ above. Examine the first entry in table USS above: that for electric charge, and divide the electrostatic units by the electromagnetic units. You obtain a velocity: cm s-1. You obtain the same for current, electric flux density and magnetic field strength. For magnetic flux, magnetic flux density, voltage, and electric field strength you obtain the reciprocal of a velocity: cm-1 s. For capacitance and permittivity you obtain the square of a velocity: cm2 s-2. Finally, for permeability, inductance and resistance you obtain the reciprocal of the square of a velocity: cm-2 s2.

Fundamentally, what this boils down to is that a dimensional analysis of the ratio ke / km , via a rearrangement of Ampère's Force Law and Coulomb's Law , shows that it has units of velocity squared. This seems a bit curious since nothing in either Ampère's or Coulomb's experiments needs to move (apart from the electrons themselves). Even more curious is the experimental value of this ratio - ke / km = c 2 Equation USW where c is the speed of light in a vacuum. This fact lent real proof to the proposal made many years previously by Leonard Euler that light had something to do with electromagnetism. It can be shown that the magnetic force is just the electrostatic force after adjustment by the relativistic Lorentz transform. You may already know that the speed of light features heavily in the theory of relativity too. The constants keSI and kmSI are not used directly in the rest of SI electromagnetism.

Instead new constants are defined as - μ0 = 4πkmSI = 4π ×10-7 ≅ 1.256 637×10-6 H m-1 Equation USX ε0 = 1 / (4π keSI ) = 1 / (4π×10-7 c2) ≅ 8.854 186×10-12 F m-1 Equation USY Introducing the factor of π at this early stage (called rationalisation) prevents it from infesting later formulæ as in the Gaussian system . Note that because kmSI is defined as exactly 10-7 that μ0 is also exact. Since 1983 the speed of light has been defined to be exactly 2.997 924 58×108 m s-1 . Therefore keSI and ε0 also acquire exact values. Also, although μ0 has retained the units of kmSI these are translated into the equivalent H m-1. Trivia point: designation of the letter c is from the word celerity : quickness, or rapidity of motion. Its Latin root also gives accelerate.

[ ↑ Top of page] Dimensional calculations An advantage of the SI is the ease with which dimensional calculations can be performed. To assist these table USF below lists the base units for a few quantities which are not listed elsewhere in these web pages. Table USF: Quantities and their units in the SI Quantity Rowland 's Law is the equation dimensionally correct? On the right hand side we have Fm in amps, divided by Rm in per henry, A / (A2 s2 kg-1 m-2) = A (A-2 s-2 kg m2) = kg m2 s-2 A-1 and these are the base units for the left hand side of the equation: flux in webers. Dimensional calculations are not merely party tricks which enable you to check your working. When you can follow the process by which the higher level (derived) units are composed from the simpler, more intuitive base units then you obtain a better understanding of quantities like resistance or inductance. Even the strangest and most abstract quantities eventually boil down to metres, kilograms, seconds and amps. Is there anything abstract or hard to grasp about them? These pages are particular about units because of this.

You could also impress your friends by mentioning your 10 million kilogram metre squared per second cubed per ampere squared resistor. Uhh ... well, maybe not. Dimensional analysis, in the form we use today, was first proposed by Maxwell . [ ↑ Top of page] Turns of wire As mentioned in the section on current , many engineers prefer that the number of turns is included explicitly in the units of magneto-motive force . They say, for example, that the coil in figure TMX carries '12 ampere turns' of MMF, or '12 A t'. Similarly, inductance factor has units of henries per turn squared. Now, units come in one of two flavours: basic (like kilograms) or derived (like ohms). The former group, of which the SI has seven, are starting points for the units system, and cannot be decomposed into more fundamental ones. The latter group, on the other hand, is each made up from a combination of two or more of the basic units. The question arises, then, into which category you fit the unit for turns. The established view is that turns aren't really part of either. Instead, they are regarded as having 'unit dimensions'.

That is, they have the same units as the digit '1'. Informally, you say they are ' dimensionless '. So, as far as dimensional calculations are concerned - 13 = 12 = 11 = 10 = 1 = t0 = t1 = t2 Equation UNA nH t-2 = nH 1 = nH Equation UNB From which you see that, in a technical sense, turns are redundant. Their inclusion, or omission, whenever or wherever you like, makes no difference to the dimensional validity of an equation. You could, for example, specify MMF as 'amperes per turn squared' and be no more and no less correct than 'ampere turns'. 'Turnified' units -2 -2 "That's not very helpful.", you complain, "Yah, boo, sucks to the SI ! Let's just treat turns as an eighth basic unit alongside amps, seconds and the rest." Well, as figure USU shows, all the electric units are related in a kind of 'family tree'; with amperes as the common ancestor. A change to one quantity has a 'knock-on' effect with the units from which and to which it relates.

If you go tinkering with MMF then you face a dilemma. Either you have to accept that, in at least one equation, you will have dimensional inconsistency, or you must make the same alteration to all the other electric quantities, substituting 'A t' wherever 'A' appears originally - If you do this then the physicists will ask if you have gone mad. They don't care about turns. Whether a coil has four turns carrying three amps or three turns carrying four amps then it's all just '12 amps' to them. The magnetic field will be identical - so quit fussing. Consider the 'dual' case of a battery. No one is confused if it's described as having '9 volts'. No one imagines that each cell within it has an EMF of 9 volts. We accept that it's the overall potential that's being specified, without a special unit called the 'volt cell'. If engineers were consistent then they wouldn't need 'ampere turns' to talk about MMF. We can only stutter "Yes, but ...", or else eschew the ampere, use Gaussian Units and the 'gilbert' for MMF instead. Dohhh!

Some other conversions Fields If you have a quantity expressed in CGS units then multiply by k to find the equivalent in SI units. Magnetics in the CGS Gaussian system Quantity 7.962×10-3 J m-3 Converting formulae between the two systems requires care. You may also see flux being specified in 'lines' - this is synonymous with maxwells. Magnetic susceptibility Much data on susceptibility is still only available in CGS units. In CGS the susceptibility is defined as χ = (μ - 1) / (4 π) Equation USY Where μ is the permeability. If this surprises you then recall that CGS permeability also differs from SI permeability (by a factor of 4 π×10-7). Where you have a susceptibility expressed in CGS units then multiply by the factor tabulated below to obtain the susceptibility in the corresponding SI units. Converting susceptibilities Wb Unit names An interval of time might be 20 seconds, a mass may be forty kilograms, a resistance ten ohms, a temperature 600 kelvins and an energy ninety joules.

The point is that we write all these unit names without a capital letter - even where the unit is named after a scientist. Unit symbols Strictly speaking, the m, Ω and Wb above are symbols and not abbreviations. Thus you don't use a full stop after one (as you would an abbreviation) nor need you follow them by an s to denote a plural. Like other symbols you can put them in formulas. Where the unit name is that of a scientist you then capitalize the unit symbol, e.g. C = 1.8×10-6 F. You need to include a space between the numerical value and the unit symbol. For example, L = 2.753 mH rather than L = 2.753mH. Also, L = 2.753 millihenries is better than L = 2.753 milli henries or L = 2.753 milli-henries. Table headings and graph axis labels You sometimes see tables headed like that on the left Table USTa: Incorrect column headings River name

Question: Derived from the Greek for 'work', what is the CGS unit of energy?
Answer: ERG