# BS EN 80000-6-2008

BRITISH STANDARD BS EN 80000-6:2008 Quantities and units — Part 6: Electromagnetism ICS 01.040.29; 01.060; 17.220.01 BS EN 80000-6:2008 This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 September 2008 © BSI 2008 ISBN 978 0 580 54866 6 National foreword This British Standard is the UK implementation of EN 80000-6:2008. It is identical to IEC 80000-6:2008. It supersedes BS ISO 31-5:1992 which is withdrawn. The UK participation in its preparation was entrusted to Technical Committee SS/7, General metrology, quantities, units and symbols. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. Compliance with a British Standard cannot confer immunity from legal obligations. Amendments/corrigenda issued since publication Date Comments EUROPEAN STANDARD EN 80000-6 NORME EUROPÉENNE EUROPÄISCHE NORM May 2008 CENELEC European Committee for Electrotechnical Standardization Comité Européen de Normalisation Electrotechnique Europäisches Komitee für Elektrotechnische Normung Central Secretariat: rue de Stassart 35, B - 1050 Brussels © 2008 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members. Ref. No. EN 80000-6:2008 E ICS 01.040.29. 17.220.01 English version Quantities and units - Part 6: Electromagnetism (IEC 80000-6:2008) Grandeurs et unités - Partie 6: Électromagnétisme (CEI 80000-6:2008) Größen und Einheiten - Teil 6: Elektromagnetismus (IEC 80000-6:2008) This European Standard was approved by CENELEC on 2008-04-01. CENELEC members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CENELEC member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CENELEC member into its own language and notified to the Central Secretariat has the same status as the official versions. CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom. Foreword The text of document 25/370/FDIS, future edition 1 of IEC 80000-6, prepared by IEC TC 25, Quantities and units, and their letter symbols, in close cooperation with ISO TC 12, Quantities, units, symbols, conversion factors, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as EN 80000-6 on 2008-04-01. The following dates were fixed: – latest date by which the EN has to be implemented at national level by publication of an identical national standard or by endorsement (dop) 2009-01-01 – latest date by which the national standards conflicting with the EN have to be withdrawn (dow) 2011-04-01 Annex ZA has been added by CENELEC. __________ Endorsement notice The text of the International Standard IEC 80000-6:2008 was approved by CENELEC as a European Standard without any modification. __________ – 2 – BS EN 80000-6:2008CONTENTS 0 0.1 0.2 0.3 0.3.1 0.3.2 Remark on units for quantities of dimension one, or dimensionless 0.4 0.5 0.5.1 0.5.2 1 2 3 – 3 – BS EN 80000-6:2008 Introduction 4 Arrangements of the tables .4 Tables of quantities .4 Tables of units.4 General .4 quantities.5 Numerical statements in this standard.5 Special remarks 6 System of quantities 6 Sinusoidal quantities .6 Scope.8 Normative references .8 Names, symbols, and definitions 8 Annex A (informative) Units in the Gaussian CGS system with special names .35 Bibliography36 AnnexZA(normative)Normativereferencestointernationalpublicationswiththeir correspondingEuropeanpublications .370 Introduction 0.1 Arrangements of the tables The tables of quantities and units in ISO/IEC 80000 are arranged so that the quantities are presented on the left-hand pages and the units on the corresponding right-hand pages. All units between two full lines on the right-hand pages belong to the quantities between the corresponding full lines on the left-hand pages. Where the numbering of an item has been changed in the revision of a part of ISO 31, the number in the preceding edition is shown in parenthesis on the left-hand page under the new number for the quantity; a dash is used to indicate that the item in question did not appear in the preceding edition. 0.2 Tables of quantities The names in English and in French of the most important quantities within the field of this document are given together with their symbols and, in most cases, their definitions. These names and symbols are recommendations. The definitions are given for identification of the quantities in the International System of Quantities (ISQ), listed on the left hand pages of Table 1; they are not intended to be complete. The scalar, vectorial or tensorial character of quantities is pointed out, especially when this is needed for the definitions. In most cases only one name and only one symbol for the quantity are given; where two or more names or two or more symbols are given for one quantity and no special distinction is made, they are on an equal footing. When two types of italic letters exist (for example as with ϑ and θ; φ and φ; a and a; g and g) only one of these is given. This does not mean that the other is not equally acceptable. It is recommended that such variants should not be given different meanings. A symbol within parenthesis implies that it is a reserve symbol, to be used when, in a particular context, the main symbol is in use with a different meaning. In this English edition the quantity names in French are printed in an italic font, and are preceded by fr. The gender of the French name is indicated by (m) for masculine and (f) for feminine, immediately after the noun in the French name. 0.3 Tables of units 0.3.1 General The names of units for the corresponding quantities are given together with the international symbols and the definitions. These unit names are language-dependent, but the symbols are international and the same in all languages. For further information, see the SI Brochure (8 thedition 2006) from BIPM and ISO 80000-1 (under preparation). The units are arranged in the following way: a) The coherent SI units are given first. The SI units have been adopted by the General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM). The use of coherent SI units, and their decimal multiples and submultiples formed with the SI prefixes are recommended, although the decimal multiples and submultiples are not explicitly mentioned. b) Some non-SI units are then given, being those accepted by the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), or by the International Organization of Legal Metrology (Organisation Internationale de Métrologie Légale, OIML), or by ISO and IEC, for use with the SI. – 4 – BS EN 80000-6:2008 Such units are separated from the SI units in the item by use of a broken line between the SI units and the other units. c) Non-SI units currently accepted by the CIPM for use with the SI are given in small print (smaller than the text size) in the “Conversion factors and remarks” column. d) Non-SI units that are not recommended are given only in annexes in some parts of ISO/IEC 80000. These annexes are informative, in the first place for the conversion factors, and are not integral parts of the standard. These deprecated units are arranged in two groups: 1) units in the CGS system with special names; 2) units based on the foot, pound, second, and some other related units. e) Other non-SI units given for information, especially regarding the conversion factors are given in another informative annex. 0.3.2 Remark on units for quantities of dimension one, or dimensionless quantities The coherent unit for any quantity of dimension one, also called a dimensionless quantity, is the number one, symbol 1. When the value of such a quantity is expressed, the unit symbol 1 is generally not written out explicitly. EXAMPLE Refractive index n = 1,53 × 1 = 1,53 Prefixes shall not be used to form multiples or submultiples of this unit. Instead of prefixes, powers of 10 are recommended. EXAMPLE Reynolds number Re = 1,32 × 10 3Considering that plane angle is generally expressed as the ratio of two lengths and solid angle as the ratio of two areas, in 1995 the CGPM specified that, in the SI, the radian, symbol rad, and steradian, symbol sr, are dimensionless derived units. This implies that the quantities plane angle and solid angle are considered as derived quantities of dimension one. The units radian and steradian are thus equal to one; they may either be omitted, or they may be used in expressions for derived units to facilitate distinction between quantities of different kinds but having the same dimension. 0.4 Numerical statements in this standard The sign = is used to denote “is exactly equal to”, the sign ≈ is used to denote “is approximately equal to”, and the sign := is used to denote “is by definition equal to”. Numerical values of physical quantities that have been experimentally determined always have an associated measurement uncertainty. This uncertainty should always be specified. In this standard, the magnitude of the uncertainty is represented as in the following example. EXAMPLE l = 2,347 82(32) m In this example, l = a(b) m, the numerical value of the uncertainty b indicated in parentheses is assumed to apply to the last (and least significant) digits of the numerical value a of the length l. This notation is used when b represents one standard uncertainty (estimated standard deviation) in the last digits of a. The numerical example given above may be interpreted to mean that the best estimate of the numerical value of the length l, when l is – 5 – BS EN 80000-6:2008expressed in the unit metre, is 2,347 82 and that the unknown value of l is believed to lie between (2,347 82 −0,000 32) m and (2,347 82 + 0,000 32) m with a probability determined by the standard uncertainty 0,000 32 m and the probability distribution of the values of l. 0.5 Special remarks The items given in ISO 80000-6 are generally in conformity with the International Electrotechnical Vocabulary (IEV), especially IEC 60050-121 and IEC 60050-131. For each quantity, the reference to IEV is given in the form: “See IEC 60050-121, item 121-xx-xxx.”. 0.5.1 System of quantities For electromagnetism, several different systems of quantities have been developed and used depending on the number and the choice of base quantities on which the system is based. However, in electromagnetism and electrical engineering, only the International System of Quantities, ISQ, and the associated International System of Units, SI, are acknowledged and are reflected in the standards of ISO and IEC. The SI has seven base units, among them metre, symbol m, kilogram, symbol kg, second, symbol s, and ampere, symbol A. 0.5.2 Sinusoidal quantities For quantities that vary sinusoidally with time, and for their complex representations, the IEC has standardized two ways to build symbols. Capital and lowercase letters are generally used for electric current (item 6-1) and for voltage (item 6-11.3), and additional marks for other quantities. These are given in IEC 60027-1. EXAMPLE 1 The sinusoidal variation with time of an electric current (item 6-1) can be expressed in real representation as ) ( cos 2 ϕ ω − = t I i and its complex representation (termed phasor) is expressed as j e II ϕ − = where i is the instantaneous value of the current, I is its root-mean-square (rms) value, ( ωt – φ) is the phase, φ is the initial phase. – 6 – BS EN 80000-6:2008EXAMPLE 2 The sinusoidal variation with time of a magnetic flux (item 6-22.1) can be expressed in real representation as ) ( ) ( ˆ cos 2 cos eff ϕ ω ϕ ω − = − = t Φ t Φ Φ where Φ is the instantaneous value of the flux, Φ ˆis its peak value and eff Φ is its rms value. – 7 – BS EN 80000-6:2008QUANTITIES AND UNITS – Part 6: Electromagnetism 1 Scope In IEC 80000-6 names, symbols, and definitions for quantities and units of electromagnetism are given. Where appropriate, conversion factors are also given. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. IEC 60027-1:1992, Letter symbols to be used in electrical technology – Part 1: General IEC 60050-111, International electrotechnical vocabulary – Part 111: Physics and chemistry IEC 60050-121, International electrotechnical vocabulary – Part 121: Electromagnetism IEC 60050-131, International electrotechnical vocabulary – Part 131: Circuit theory ISO 31-0:1992, Quantities and units – Part 0: General principles (under revision) ISO 80000-3:2006, Quantities and units – Part 3: Space and time ISO 80000-4:2006, Quantities and units – Part 4: Mechanics 3 Names, symbols, and definitions The names, symbols, and definitions for quantities and units of electromagnetism are given in the tables on the following pages. – 8 – BS EN 80000-6:2008 ELECTROMAGNETISM QUANTITIES Item No. Name Symbol Definition Remarks 6-1 (5-1) electric current fr courant (m) électrique I, i electric current is one of the base quantities in the International System of Quantities, ISQ, on which the International System of Units, SI, is based Electric current is the quantity that can often be measured with an ammeter. The electric current through a surface is the quotient of the electric charge (item 6-2) transferred through the surface during a time interval by the duration of that interval. For a more complete defini- tion, see item 6-8 and IEC 60050-121, item 121-11-13. 6-2 (5-2) electric charge fr charge (f) électrique Q, q dQ = Idt where I is electric current (item 6-1) and t is time (ISO 80000-3, item 3-7) Electric charge is carried by discrete particles and can be positive or negative. The sign convention is such that the elementary electric charge e, i.e. the charge of the proton, is positive. See IEC 60050-121, item121-11-01. To denote a point charge q is often used, and that is done in the present document. 6-3 (5-3) electric charge density, volumic electric charge fr cha