IEC 80000-6:2008
(Main)Quantities and units — Part 6: Electromagnetism
Quantities and units — Part 6: Electromagnetism
In IEC 80000-6:2008, names, symbols, and definitions for quantities and units of electromagnetism are given. Where appropriate, conversion factors are also given. International Standard IEC 80000-6 has been prepared by IEC technical committee 25: Quantities and units, and their letter symbols in close cooperation with ISO/TC 12, Quantities, units, symbols, conversion factors. This first edition of IEC 80000-6 cancels and replaces the second edition of ISO 31-5, published in 1992, and its amendment 1 (1998).
Grandeurs et unités — Partie 6: Électromagnétisme
La CEI 80000-6:2008 donne les noms, symboles et définitions des grandeurs et unités d'électromagnétisme. Les facteurs de conversion sont également donnés, s'il y a lieu. La Norme internationale CEI 80000-6 a été établie par le comité d'études 25 de la CEI, Grandeurs et unités, et leurs symboles littéraux, en coopération étroite avec l'ISO/TC 12, Grandeurs, unités, symboles, facteurs de conversion. Cette première édition de IEC 80000-6 annule et remplace la deuxième édition de ISO 31 5, publiée en1992 et son amendement 1 (1998).
Veličine in enote - 6. del: Elektromagnetizem
V standardu IEC 80000-6 so podana imena, simboli in definicije za veličine na področju elektromagnetizma. Kjer je primerno, so podani tudi pretvorniki (pretvorni faktorji).
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IEC 80000-6
Edition 1.0 2008-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Quantities and units –
Part 6: Electromagnetism
Grandeurs et unités –
Partie 6: Electromagnétisme
IEC 80000-6:2008
---------------------- Page: 1 ----------------------
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IEC 80000-6
Edition 1.0 2008-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Quantities and units –
Part 6: Electromagnetism
Grandeurs et unités –
Partie 6: Electromagnétisme
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
W
CODE PRIX
ICS 01.040.29; 17.220.01 ISBN 2-8318-9624-X
---------------------- Page: 3 ----------------------
– 2 – 80000-6 © IEC:2008
CONTENTS
FOREWORD.3
0 Introduction .5
0.1 Arrangements of the tables .5
0.2 Tables of quantities .5
0.3 Tables of units.5
0.3.1 General .5
0.3.2 Remark on units for quantities of dimension one, or dimensionless
quantities.6
0.4 Numerical statements in this standard .6
0.5 Special remarks .7
0.5.1 System of quantities .7
0.5.2 Sinusoidal quantities .7
1 Scope.9
2 Normative references .9
3 Names, symbols, and definitions .9
Annex A (informative) Units in the Gaussian CGS system with special names .36
Bibliography.37
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80000-6 © IEC:2008 – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
QUANTITIES AND UNITS –
Part 6: Electromagnetism
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
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4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
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5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with an IEC Publication.
6) All users should ensure that they have the latest edition of this publication.
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expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 80000-6 has been prepared by IEC technical committee 25:
Quantities and units, and their letter symbols in close cooperation with ISO/TC 12, Quantities,
units, symbols, conversion factors.
This first edition of IEC 80000-6 cancels and replaces the second edition of ISO 31-5,
published in 1992, and its amendment 1 (1998).
The text of this standard is based on the following documents:
FDIS Report on voting
25/370/FDIS 25/376/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
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– 4 – 80000-6 © IEC:2008
The committee has decided that the contents of this publication will remain unchanged until
the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in
the data related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IEC 80000 consists of the following parts, under the general title Quantities and units:
– Part 6: Electromagnetism
– Part 13: Information science and technology
– Part 14: Telebiometrics related to human physiology
The following parts are published by ISO:
– Part 1: General
– Part 2: Mathematical signs and symbols to be used in the natural sciences and technology
– Part 3: Space and time
– Part 4: Mechanics
– Part 5: Thermodynamics
– Part 7: Light
– Part 8: Acoustics
– Part 9: Physical chemistry and molecular physics
– Part 10: Atomic and nuclear physics
– Part 11: Characteristic numbers
– Part 12: Solid state physics
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80000-6 © IEC:2008 – 5 –
0 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
th
international and the same in all languages. For further information, see the SI Brochure (8
edition 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.
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– 6 – 80000-6 © IEC: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
3
Reynolds number Re = 1,32 × 10
Considering 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
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80000-6 © IEC:2008 – 7 –
expressed 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
i = 2 I cos(ωt − ϕ)
and its complex representation (termed phasor) is expressed as
− jϕ
II= e
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.
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– 8 – 80000-6 © IEC:2008
EXAMPLE 2
The sinusoidal variation with time of a magnetic flux (item 6-22.1) can be expressed in real
representation as
ˆ
Φ =Φ cos(ωt − ϕ) = 2Φ cos(ωt − ϕ)
eff
ˆ
where Φ is the instantaneous value of the flux, Φ is its peak value and Φ is its rms value.
eff
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80000-6 © IEC:2008 – 9 –
QUANTITIES 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.
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– 10 – 80000-6 © IEC:2008
ELECTROMAGNETISM QUANTITIES
Item No. Name Symbol Definition Remarks
6-1 electric current electric current is one of the base quantities in Electric current is the
I, i
(5-1) the International System of Quantities, ISQ, on quantity that can often be
fr courant (m)
which the International System of Units, SI, is measured with an ammeter.
électrique
based
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 electric charge Electric charge is carried by
Q, q dQ = Idt
(5-2) discrete particles and can be
fr charge (f)
positive or negative. The
where I is electric current (item 6-1) and t is
électrique
sign convention is such that
time (ISO 80000-3, item 3-7)
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 electric charge density, See IEC 60050-121, item
ρ, ρ dQ
V
(5-3) volumic electric charge ρ= 121-11-07.
dV
fr charge (f)
électrique
where Q is electric charge (item 6-2) and V is
volumique
volume (ISO 80000-3, item 3-4)
6-4 surface density of See IEC 60050-121, item
dQ
ρ , σ
A
(5-4) electric charge, 121-11-08.
ρ =
A
areic electric charge dA
fr charge (f)
where Q is electric charge (item 6-2) and A is
électrique
area (ISO 80000-3, item 3-3)
surfacique
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80000-6 © IEC:2008 – 11 –
UNITS ELECTROMAGNETISM
Item No. Name Inter- Definition Conversion factors and remarks
national
symbol
6-1.a ampere A ampere is that constant electric This definition implies that the magnetic
current which, if maintained in two
constant μ (item 6-26.1) is exactly
0
parallel conductors of infinite
–7
4π × 10 H/m.
length, of negligible circular
cross-section, and placed 1 metre
apart in vacuum, would produce
In this definition “force” is used instead of
between these conductors a force
“lineic force” or “force per length”.
equal to
Accordingly the last unit should be
–7
2 × 10 newton per metre of
“newton per metre” without “of length”.
th
length [9 CGPM (1948)]
6-2.a coulomb C 1 C := 1 A · s The unit ampere hour, is used for
electrolytic devices, such as storage
batteries.
1 A · h = 3,6 kC
3
6-3.a coulomb per cubic
C/m
metre
2
6-4.a coulomb per square
C/m
metre
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ELECTROMAGNETISM QUANTITIES
Item No. Name Symbol Definition Remarks
6-5 linear density of See IEC 60050-121,
dQ
ρ ,τ
l
(5-5) electric charge, item121-11-09.
ρ =
l
lineic electric charge
dl
fr charge (f)
where Q is electric charge (item 6-2) and l is
électrique linéique
length (ISO 80000-3, item 3-1.1)
6-6 electric dipole moment The electric dipole moment
p p = q(r – r )
+ –
(5-14) of a substance within a
fr moment (m)
domain is the vector sum of
where r and r are the position vectors (ISO
+ –
électrique
electric dipole moments of all
80000-3, item 3-1.11) to carriers of electric
moment (m) de
electric dipoles included in
dipôle électrique
charges q and –q (item 6-2), respectively
the domain.
See IEC 60050-121, items
121-11-35 and 121-11-36.
6-7 electric polarization
See IEC 60050-121, item
P P = dp/dV
(5-13) 121-11-37.
fr polarisation (f) where p is electric dipole moment (item 6-6) of
électrique
a substance within a domain with volume V
(ISO 80000-3, item 3-4)
6-8 electric current
J J = ρv Electric current I (item 6-1)
(5-15) density,
through a surface S is
areic electric current
where ρ is electric charge density (item 6-3)
fr densité (f) de
I = J ⋅ e dA
n
and v is velocity (ISO 80000-3, item 3-8.1)
∫
courant électrique
S
where e dA is vector
n
surface element.
See IEC 60050-121, item
121-11-11.
6-9 linear electric current
J J = ρ v Electric current I (item
S S A
(―) density,
6-1) through a curve C on a
lineic electric current
surface is
where ρ is surface density of electric charge
A
fr densité (f) linéique
(item 6-4) and v is velocity (ISO 80000-3, item
de courant
I = J × e ⋅ dr
3-8.1) S n
∫
électrique
C
where e is a unit vector
n
perpendicular to the surface
and line vector element and
dr is the differential of
position vector r.
See IEC 60050-121, item
121-11-12.
6-10 electric field strength See IEC 60050,
E E = F/q
(5-5) item 121-11-18.
fr champ (m)
where F is force (ISO 80000-4, item
électrique
q is the charge of a test
4-9.1) and q is electric charge (item 6-2)
particle at rest.
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80000-6 © IEC:2008 – 13 –
UNITS ELECTROMAGNETISM
Item No. Name Inter- Definition Conversion factors and remarks
national
symbol
6-5.a coulomb per metre C/m
6-6.a coulomb metre C · m
2
6-7.a coulomb per metre
C/m
squared
2
6-8.a ampere per square
A/m
metre
6-9.a ampere per metre A/m
6-10.a volt per metre V/m 1 V/m = 1 N/C For the definition of the volt, see
item 6-11.a.
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ELECTROMAGNETISM QUANTITIES
Item No. Name Symbol Definition Remarks
6-11.1 electric potential The electric potential is not
V, ϕ ∂A
(5-6.1) unique, since any constant scalar
–grad V = E +
fr potential (m)
field quantity can be added to it
∂t
électrique
without changing its gradient.
where E is electric field strength (item 6-
See IEC 60050-121, item
10), A is magnetic vector potential (item 121-11-25.
6-32) and t is time (ISO 80000-3,
item 3-7)
6-11.2 electric potential
V r V = V – V
ab ab a b
b
(5-6.2) difference
∂A
where V and V are the
V = (E + ) ⋅ dr a b
ab
∫
fr différence (f) de ∂t
potentials at points a and b,
r (C)
potential
a respectively.
électrique
See IEC 60050-121,
where E is electric field strength (item 6-
item 121-11-26.
10), A is magnetic vector potential (item
6-32), t is time (ISO 80000-3, item 3-7),
and r is position vector (ISO 80000-3,
item 3-1.11) along a given curve C from
point a to point b
6-11.3 voltage, in electric circuit theory, For an electric field within a
U, U
ab
(5-6.3) electric tension medium
U = V – V
ab a b
r
b
fr tension (f) where V and V are the electric
a b
électrique
potentials (item 6-11.1) at points a and b,
U = E ⋅ dr
ab
∫
respectively
(The name “voltage”,
r (C)
a
commonly used in the
English language, is
where E is electric field strength
given in the IEV but is
(item 6-10) and r is position
an exception from the
vector (ISO 80000-3, item 3-1.11)
principle that a
along a given curve C from point a
quantity name should
to point b.
not refer to any name
of unit.)
For an irrotational electric field,
the voltage is independent of the
path between the two points a
and b.
See IEC 60050-121, item
121-11-27.
6-12 electric flux density, The electric flux density is related
D
D =ε E + P
0
(5-7) to electric charge density via
electric displacement
div D = ρ
where ε is the electric constant (item
0
fr induction (f)
6-14.1), E is electric field strength (item
where div denotes the divergence.
électrique
6-10), and P is electric polarization (item
See IEC 60050-121, item
6-7)
121-11-40.
6-13 capacitance See IEC 60050-131, item
C C = Q/U
(5-9) 131-12-13.
fr capacité (f)
where Q is electric charge (item 6-2) and
U is voltage (6-11.3)
------
...
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Grandeurs et unités - Partie 6: ÉlectromagnétismeQuantities and units - Part 6: Electromagnetism17.220.01Elektrika. Magnetizem. Splošni vidikiElectricity. Magnetism. General aspects07.030Fizika. KemijaPhysics. Chemistry01.060Quantities and unitsICS:Ta slovenski standard je istoveten z:IEC 80000-6:2008SIST IEC 80000-6:2014en01-december-2014SIST IEC 80000-6:2014SLOVENSKI
STANDARDSIST ISO 31-5+A1:2008SIST ISO 31-5:1995/Amd. 1:20011DGRPHãþD
SIST IEC 80000-6:2014
IEC 80000-6Edition 1.0 2008-03INTERNATIONAL STANDARD NORME INTERNATIONALEQuantities and units –
Part 6: Electromagnetism
Grandeurs et unités –
Partie 6: Electromagnétisme
INTERNATIONAL ELECTROTECHNICAL COMMISSION COMMISSION ELECTROTECHNIQUE INTERNATIONALE WICS 01.040.29; 17.220.01 PRICE CODECODE PRIXISBN 2-8318-9624-XSIST IEC 80000-6:2014
– 2 – 80000-6 © IEC:2008 CONTENTS FOREWORD.3
0 Introduction.5 0.1 Arrangements of the tables.5 0.2 Tables of quantities.5 0.3 Tables of units.5 0.3.1 General.5 0.3.2 Remark on units for quantities of dimension one, or dimensionless quantities.6 0.4 Numerical statements in this standard.6 0.5 Special remarks.7 0.5.1 System of quantities.7 0.5.2 Sinusoidal quantities.7 1 Scope.9 2 Normative references.9 3 Names, symbols, and definitions.9
Annex A (informative)
Units in the Gaussian CGS system with special names.36
Bibliography.37
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QUANTITIES AND UNITS –
Part 6: Electromagnetism
FOREWORD 1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work. International, governmental and non-governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations. 2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any misinterpretation by any end user. 4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications transparently to the maximum extent possible in their national and regional publications. Any divergence between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter. 5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any equipment declared to be in conformity with an IEC Publication. 6) All users should ensure that they have the latest edition of this publication. 7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and members of its technical committees and IEC National Committees for any personal injury, property damage or other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is indispensable for the correct application of this publication. 9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent rights. IEC shall not be held responsible for identifying any or all such patent rights. International Standard IEC 80000-6 has been prepared by IEC technical committee 25: Quantities and units, and their letter symbols in close cooperation with ISO/TC 12, Quantities, units, symbols, conversion factors. This first edition of IEC 80000-6 cancels and replaces the second edition of ISO 31-5, published in 1992, and its amendment 1 (1998). The text of this standard is based on the following documents: FDIS Report on voting 25/370/FDIS 25/376/RVD
Full information on the voting for the approval of this standard can be found in the report on voting indicated in the above table. This publication has been drafted in accordance with the ISO/IEC Directives, Part 2. SIST IEC 80000-6:2014
– 4 – 80000-6 © IEC:2008 The committee has decided that the contents of this publication will remain unchanged until the maintenance result date indicated on the IEC web site under "http://webstore.iec.ch" in the data related to the specific publication. At this date, the publication will be
• reconfirmed, • withdrawn, • replaced by a revised edition, or • amended. IEC 80000 consists of the following parts, under the general title Quantities and units: – Part 6: Electromagnetism – Part 13: Information science and technology – Part 14: Telebiometrics related to human physiology The following parts are published by ISO: – Part 1: General
– Part 2: Mathematical signs and symbols to be used in the natural sciences and technology – Part 3: Space and time – Part 4: Mechanics – Part 5: Thermodynamics – Part 7: Light – Part 8: Acoustics – Part 9: Physical chemistry and molecular physics – Part 10: Atomic and nuclear physics – Part 11: Characteristic numbers – Part 12: Solid state physics
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80000-6 © IEC:2008 – 5 – 0 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 ; 3 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 (8th edition 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. SIST IEC 80000-6:2014
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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 × 103 Considering 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 SIST IEC 80000-6:2014
80000-6 © IEC:2008 – 7 – expressed 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 )(cos2ϕω−=tIi and its complex representation (termed phasor) is expressed as jeIIϕ−= where i is the instantaneous value of the current, I is its root-mean-square (rms) value, (t – 3) is the phase, 3 is the initial phase. SIST IEC 80000-6:2014
– 8 – 80000-6 © IEC:2008 EXAMPLE 2 The sinusoidal variation with time of a magnetic flux (item 6-22.1) can be expressed in real representation as )()(ˆcos2coseffϕωϕω−=−=t-t-- where - is the instantaneous value of the flux, -ˆ is its peak value and eff- is its rms value.
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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. SIST IEC 80000-6:2014
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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 charge (f) électrique volumique ρ, ρV QVρ=dd where Q is electric charge (item 6-2) and V is volume (ISO 80000-3, item 3-4) See IEC 60050-121, item 121-11-07. 6-4 (5-4) surface density of electric charge,
areic electric charge fr charge (f) électrique surfacique ρA, σ AQAdd=ρ where Q is electric charge (item 6-2) and A is area (ISO 80000-3, item 3-3) See IEC 60050-121, item 121-11-08.
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UNITS ELECTROMAGNETISM Item No. Name Inter-national symbol Definition Conversion factors and remarks 6-1.a ampere A ampere is that constant electric current which, if maintained in two 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 [9th CGPM (1948)] This definition implies that the magnetic constant μ0 (item 6-26.1) is exactly 4π × 10–7 H/m.
In this definition “force” is used instead of “lineic force” or “force per length”. Accordingly the last unit should be “newton per metre” without “of length”. 6-2.a coulomb C 1 C := 1 A · s The unit ampere hour, is used for electrolytic devices, such as storage batteries. 1 A · h = 3,6 kC 6-3.a coulomb per cubic metre C/m3
6-4.a coulomb per square metre C/m2
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ELECTROMAGNETISM QUANTITIES Item No. Name Symbol Definition Remarks 6-5 (5-5) linear density of electric charge, lineic electric charge fr charge (f) électrique linéique ,lρτ lQlρ=dd where Q is electric charge (item 6-2) and l is length (ISO 80000-3, item 3-1.1) See IEC 60050-121, item121-11-09. 6-6 (5-14) electric dipole moment fr moment (m) électrique moment (m) de dipôle électrique p p = q(r+ – r–) where r+ and r– are the position vectors (ISO 80000-3, item 3-1.11) to carriers of electric charges q and –q (item 6-2), respectively The electric dipole moment of a substance within a domain is the vector sum of electric dipole moments of all electric dipoles included in the domain. See IEC 60050-121, items 121-11-35 and 121-11-36. 6-7 (5-13) electric polarization fr polarisation (f) électrique
P P = dp/dV
where p is electric dipole moment (item 6-6) of a substance within a domain with volume V (ISO 80000-3, item 3-4) See IEC 60050-121, item 121-11-37. 6-8 (5-15) electric current density, areic electric current fr densité (f) de courant électrique J J = v where ρ is electric charge density (item 6-3) and v is velocity (ISO 80000-3, item 3-8.1)
Electric current I (item 6-1) through a surface S is I = ∫SJ ⋅ en dA where en dA is vector surface element. See IEC 60050-121, item 121-11-11. 6-9 () linear electric current density, lineic electric current fr densité (f) linéique de courant électrique JS JS = Av where ρA is surface density of electric charge (item 6-4) and v is velocity (ISO 80000-3, item 3-8.1) Electric current I (item 6-1) through a curve C on a surface is ∫⋅×=CnSdreJI where en is a unit vector perpendicular to the surface and line vector element and dr is the differential of position vector r. See IEC 60050-121, item 121-11-12. 6-10 (5-5) electric field strength fr champ (m) électrique E E = F/q where F is force (ISO 80000-4, item
4-9.1) and q is electric charge (item 6-2) See IEC 60050, item 121-11-18. q is the charge of a test particle at rest.
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UNITS ELECTROMAGNETISM Item No. Name Inter-national symbol Definition Conversion factors and remarks 6-5.a coulomb per metre C/m
6-6.a coulomb metre C · m
6-7.a coulomb per metre squared C/m2
6-8.a ampere per square metre A/m2
6-9.a ampere per metre A/m
6-10.a volt per metre V/m 1 V/m = 1 N/C For the definition of the volt, see item 6-11.a.
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ELECTROMAGNETISM QUANTITIES Item No. Name Symbol Definition Remarks 6-11.1 (5-6.1) electric potential fr potential (m) électrique V, ϕ –grad V = E + t∂∂A where E is electric field strength (item 6-10), A is magnetic vector potential (item 6-32) and t is time (ISO 80000-3, item 3-7) The electric potential is not unique, since any constant scalar field quantity can be added to it without changing its gradient. See IEC 60050-121, item
121-11-25. 6-11.2 (5-6.2) electric potential difference fr différence (f) de potential électrique Vab Vab =∫⋅∂∂+baC)(d)(rrrAEt where E is electric field strength (item 6-10), A is magnetic vector potential (item 6-32), t is time (ISO 80000-3, item 3-7), and r is position vector (ISO 80000-3, item 3-1.11) along a given curve C from point a to point b Vab = Va – Vb where Va and Vb are the potentials at points a and b, respectively. See IEC 60050-121, item 121-11-26. 6-11.3 (5-6.3) voltage,
electric tension fr tension (f) électrique (The name “voltage”, commonly used in the English language, is given in the IEV but is an exception from the principle that a quantity name should not refer to any name of unit.) U, Uab in electric circuit theory, Uab = Va – Vb where Va and Vb are the electric potentials (item 6-11.1) at points a and b, respectively For an electric field within a medium ∫⋅=ba(C)abdrrrEU where E is electric field strength (item 6-10) and r is position vector (ISO 80000-3, item 3-1.11) along a given curve C from point a to point b. For an irrotational electric field, the voltage is independent of the path between the two points a
and b. See IEC 60050-121, item
121-11-27. 6-12 (5-7) electric flux density, electric displacement fr induction (f) électrique D D =ε0E + P where ε0
is the electric constant (item 6-14.1), E is electric field strength (item 6-10), and P is electric polarization (item 6-7) The electric flux density is related to electric charge density via div D = ρ where div denotes the divergence. See IEC 60050-121, item
121-11-40. 6-13 (5-9) capacitance fr capacité (f) C C = Q/U where Q is electric charge (item 6-2) and U is voltage (6-11.3) See IEC 60050-131, item
131-12-13.
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UNITS ELECTROMAGNETISM Item No. Name Inter-national symbol Definition Conversion factors and remarks 6-11.a volt V 1 V := 1 W/A
6-12.a coulomb per metre squared C/m2
6-13.a farad F 1 F := 1 C/V
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ELECTROMAGNETISM QUANTITIES Item No. Name Symbol Definition Remarks 6-14.1 (5-10.2) electric constant, permittivity of vacuum fr constante (f) électrique, permittivité (f) du vide 00 0cεμ=2001 where μ0 is the magnetic constant (item 6-26.1) and c0 is the speed of light (item 6-35.2) 00 ≈ 8,854 188 × 10–12 F/m See IEC 60050-121, item 121-11-03. 6-14.2 (5-10.1) permittivity fr permittivité (f) 0 D = 0E where D is electric flux density (item 6-12) and E is electric field strength (item 6-10) This definition applies to an isotropic medium. For an anisotropic medium, permittivity is a second order tensor. See IEC 60050-121, item 121-12-12. 6-15 (5-11) relative permittivity fr permittivité (f) relative 0r 0r = 0/00 where ε is permittivity (item 6-14.2) and 00 is the electric constant (item 6-14.1) See IEC 60050-121, item 121-12-13. 6-16 (5-12) electric susceptibility fr susceptibilité (f) électrique χ P = ε0χE where P is electric polarization (item 6-7), ε0 is the electric constant (item 6-14.1) and E is electric field strength (item 6-10) χ = εr – 1 The definition applies to an isotropic medium. For an anisotropic medium, electric susceptibility is a second order tensor. See IEC 60050-121, item 121-12-19. 6-17 (5-8) electric flux fr flux (m) électrique
AdnSeD∫⋅=Ψ over a surface S, where D is electric flux density (item 6-12) and en dA is the vector surface element (ISO 80000-3, item 3-3) See IEC 60050-121, item 121-11-41. 6-18 () displacement current density fr densité (f) de courant de déplacement JD tD∂∂=DJ where D is electric flux density (item 6-12) and t is time (ISO 80000-3, item 3-7) See IEC 60050-121, item 121-11-42.
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UNITS ELECTROMAGNETISM Item No. Name Inter-national symbol Definition Conversion factors and remarks 6-14.a farad per metre F/m 1 F/m = 1 C/(V · m)
6-15.a one 1
See the introduction, 0.3.2. 6-16.a one 1
See the introduction, 0.3.2. 6-17.a coulomb C
6-18.a ampere per square metre A/m2
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ELECTROMAGNETISM QUANTITIES Item No. Name Symbol Definition Remarks 6-19.1 () displacement current fr courant (m) de déplacement ID DDIA=⋅∫nSdJe over a surface S, where JD is displacement current density (item 6-18) and en dA is the vector surface element (ISO 80000-3, item 3-3) See IEC 60050-121, item 121-11-43. 6-19.2 () total current fr courant (m) total
Itot, It Itot = I + ID where I is electric current (item 6-1) and ID is displacement current (item 6-19.1) See IEC 60050-121, item 121-11-45. 6-20 () total current density fr densité (f) de courant total Jtot, Jt Jtot = J + JD where J is electric current density (item 6-8) and JD is displacement current density (item 6-18) See IEC 60050-121, item 121-11-44. 6-21 (5-19) magnetic flux density fr induction (f) magnétique
B F = qv × B where F is force (ISO 80000-4, item 4-9.1) and v is velocity (ISO 80000-3, item 3-8.1) of any test particle with electric charge q (item 6-2)The magnetic flux density has zero divergence, div B = 0. See IEC 60050-121, item 121-11-19. 6-22.1 (5-20) magnetic flux fr flux (m) magnétique, flux (m) d’induction magnétique - AΦ=⋅∫nSdBe over a surface S, where B is magnetic flux density (item 6-21) and en dA is vector surface element (ISO 80000-3, item 3-3) See IEC 60050-121, item 121-11-21. 6-22.2 () linked flux
fr flux (m) totalisé m,
m = ∫CA ⋅ dr where A is magnetic vector potential (item 6-32) and dr is line vector element of the curve C Line vector element dr is the differential of position vector r (ISO 80000-3, item 3-1.11). See IEC 60050-121, item 121-11-24. 6-23 (5-27) magnetic moment, magnetic area moment fr moment (m) magnétique, moment (m) magnétique ampérien m m = I en A where I is electric current (item 6-1) in a small closed loop, en is a unit vector perpendicular to the loop, and A is area (ISO 80000-3, item 3-3) of the loop The magnetic moment of a substance within a domain is the vector sum of the magnetic moments of all entities included in the domain. See IEC 60050-121, items 121-11-49 and 121-11-50. 6-24 (5-28) magnetization fr aimantation (f) M, Hi M = dm/dV where m is magnetic moment (item 6-23) of a substance in a domain with volume V (ISO 80000-3, item 3-4) See IEC 60050-121, item 121-11-52.
SIST IEC 80000-6:2014
80000-6 © IEC:2008 – 19 –
UNITS ELECTROMAGNETISM Item No. Name Inter-national symbol Definition Conversion factors and remarks 6-19.a ampere A
6-20.a ampere per square metre A/m2
6-21.a tesla T 1 T:= 1 N/(A · m) 1 T = 1 Wb/m2 6-22.a weber Wb 1 Wb:= 1 V · s
6-23.a ampere square metre A · m2
6-24.a ampere per metre A/m
SIST IEC 80000-6:2014
– 20 – 80000-6 © IEC:2008
ELECTROMAGNETISM QUANTITIES Item No. Name Symbol Definition Remarks 6-25 (5-17) magnetic field strength, magnetizing field fr champ (m) magnétique, excitation (f) magnétique
H MBH−=0μ where B is magnetic flux density (item 6-21), 0 is the magnetic constant (item 6-26.1), and M is magnetization (item 6-24) The magnetic field strength is related to the total current density Jtot (item 6-20) via rot H = Jtot See IEC 600
...
SLOVENSKI SIST IEC 80000-6
STANDARD
december 2014
Veličine in enote – 6. del: Elektromagnetizem
Quantities and units – Part 6: Electromagnetism
Grandeurs et unités – Partie 6: Électromagnétisme
Referenčna oznaka
ICS 01.060; 07.030; 17.220.01 SIST IEC 80000-6:2014 (sl)
Nadaljevanje na straneh od 2 do 37
© 2014-12: Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST IEC 80000-6 : 2014
NACIONALNI UVOD
Standard SIST IEC 80000-6 (sl), Veličine in enote – 6. del: Elektromagnetizem, 2014, ima status
slovenskega standarda in je istoveten mednarodnemu standardu IEC 80000-6 (en), Quantities and
units – Part 6: Electromagnetism, 2008-03.
NACIONALNI PREDGOVOR
Mednarodni standard IEC 80000-6:2008 je pripravil tehnični odbor IEC/TC 25 Veličine in enote ter
njihovi črkovni simboli v tesnem sodelovanju s tehničnim odborom ISO/TC 12 Veličine, enote, simboli,
pretvorniki.
Slovenski standard SIST IEC 80000-6:2014 je prevod mednarodnega standarda IEC 80000-6:2008. V
primeru spora glede besedila slovenskega prevoda v tem standardu je odločilen izvirni mednarodni
standard v angleškem jeziku. Slovensko izdajo standarda je pripravil tehnični odbor SIST/TC TRS
Tehnično risanje, veličine, enote, simboli in grafični simboli.
Odločitev za izdajo tega standarda je 4. aprila 2014 sprejel SIST/TC TRS Tehnično risanje, veličine,
enote, simboli in grafični simboli.
ZVEZA Z NACIONALNIMI STANDARDI
S privzemom tega mednarodnega standarda veljajo za omejeni namen referenčnih standardov vsi
standardi, navedeni v izvirniku, razen standardov, ki so že sprejeti v nacionalno standardizacijo:
SIST ISO 80000-3:2012 (sl) Veličine in enote – 3. del: Prostor in čas
SIST ISO 80000-4:2012 (sl) Veličine in enote – 4. del: Mehanika
PREDHODNA IZDAJA
SIST ISO 31-5+A1:2008 (sl) Veličine in enote – 5. del: Elektrika in magnetizem
SIST ISO 31-5:1995/Amd.1:2001 Veličine in enote – 5. del: Elektrika in magnetizem
OPOMBE
– Povsod, kjer se v besedilu standarda uporablja izraz “mednarodni standard”,
v SIST IEC 80000-6:2014 to pomeni “slovenski standard”.
– Nacionalni uvod in nacionalni predgovor nista sestavna dela standarda.
2
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SIST IEC 80000-6 : 2014
VSEBINA Stran
Predgovor .4
0 Uvod .6
0.1 Razvrstitev preglednic .6
0.2 Preglednice veličin.6
0.3 Preglednice enot.6
0.3.1 Splošno.6
0.3.2 Opomba glede enot veličin z dimenzijo ena oziroma brezdimenzijskih veličin.7
0.4 Številske navedbe v tem standardu .7
0.5 Posebne opombe .7
0.5.1 Sistem veličin.8
0.5.2 Sinusne veličine.8
1 Področje uporabe .9
2 Zveza z drugimi standardi .9
3 Imena, simboli in definicije .9
Dodatek A (informativni): Enote v Gaussovem sistemu CGS s posebnimi imeni .36
Literatura.37
3
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SIST IEC 80000-6 : 2014
MEDNARODNA ELEKTROTEHNIŠKA KOMISIJA
Veličine in enote
6. del: Elektromagnetizem
PREDGOVOR
1) Mednarodna elektrotehniška komisija (IEC) je svetovna organizacija za standardizacijo, ki zajema vse
nacionalne elektrotehniške odbore (nacionalni odbori IEC). Cilj IEC je pospeševati mednarodno sodelovanje v
vseh vprašanjih standardizacije s področja elektrotehnike in elektronike. S tem namenom IEC izdaja
mednarodne standarde, tehnične specifikacije, tehnična poročila, javnosti dostopne specifikacije (PAS) in
vodila (v nadaljevanju: publikacije IEC) in izvaja še druge dejavnosti. Za njihovo pripravo so odgovorni tehnični
odbori; vsak nacionalni odbor IEC, ki ga zanima obravnavana tema, lahko sodeluje v tem pripravljalnem delu.
Prav tako lahko v pripravi sodelujejo mednarodne organizacije ter vladne in nevladne ustanove, ki so
povezane z IEC. IEC deluje v tesni povezavi z Mednarodno organizacijo za standardizacijo ISO skladno s
pogoji, določenimi v soglasju med obema organizacijama.
2) Uradne odločitve ali sporazumi IEC o tehničnih vprašanjih izražajo, kolikor je mogoče, mednarodno soglasje o
obravnavani temi, doseženo v tehničnih odborih, v katerih sodelujejo predstavniki vseh nacionalnih odborov
IEC, ki jih tema zanima.
3) Publikacije IEC imajo obliko priporočil za njihovo uporabo na mednarodni ravni in jih kot take sprejmejo
nacionalni odbori IEC. Čeprav IEC skuša na vse primerne načine zagotavljati točnost tehničnih vsebin v svojih
publikacijah IEC, ne more biti odgovoren za način, kako se določila uporabljajo, ter za morebitne napačne
razlage končnih uporabnikov.
4) Da bi pospeševali mednarodno poenotenje, so se nacionalni odbori IEC zavezali, da bodo v svojih nacionalnih
in regionalnih standardih jasno uporabljali mednarodne standarde. Vsako odstopanje med publikacijo IEC in
ustrezno nacionalno ali regionalno publikacijo je treba v slednji jasno označiti.
5) IEC z nobenim postopkom označevanja ne izraža svoje odobritve in ne more biti odgovoren za nobeno
opremo, ki bi bila deklarirana kot skladna z eno od njegovih publikacij.
6) Vsi uporabniki naj si zagotovijo zadnjo izdajo te publikacije.
7) IEC ali njegovi direktorji, zaposleni, uslužbenci ali agenti, vključno s samostojnimi strokovnjaki ter člani
tehničnih odborov in nacionalnih odborov IEC, ne prevzemajo nobene odgovornosti za kakršno koli osebno
poškodbo, škodo na premoženju ali kakršno koli drugo vrsto škode, bodisi posredne ali neposredne, ali za
stroške (vključno s sodnimi taksami) in izdatke, povezane z izdajo, uporabo ali sklicevanjem na to publikacijo
IEC ali katero koli drugo publikacijo IEC.
8) Pozornost je treba nameniti zvezam s standardi, na katere se sklicuje ta publikacija. Uporaba navedenih
publikacij je nujna za pravilno uporabo te publikacije.
9) Opozarjamo na možnost, da je lahko nekaj elementov te publikacije IEC predmet patentnih pravic. IEC ne
prevzema odgovornosti za ugotavljanje istovetnosti katerihkoli ali vseh takih patentnih pravic.
Mednarodni standard IEC 80000-6 je pripravil tehnični odbor IEC/TC 25 Veličine in enote ter njihovi
črkovni simboli v tesnem sodelovanju s tehničnim odborom ISO/TC 12 Veličine, enote, simboli,
pretvorniki.
Prva izdaja standarda IEC 80000-6 razveljavlja in nadomešča drugo izdajo ISO 31-5, ki je
izšla leta 1992, ter njeno dopolnilo 1 (1998).
Besedilo tega standarda temelji na naslednjih dokumentih:
FDIS Poročilo o glasovanju
25/370/FDIS 25/376/RVD
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SIST IEC 80000-6 : 2014
Vse informacije o glasovanju za potrditev tega standarda lahko najdete v poročilu o glasovanju,
navedenem v zgornji preglednici.
Ta publikacija je pripravljena v skladu z Direktivami ISO/IEC, 2. del.
Odbor je sklenil, da bo vsebina te publikacije ostala nespremenjena do datuma objave rezultatov
vzdrževanja na spletni strani IEC, na naslovu "http://webstore.iec.ch", v zvezi s podatki, povezanimi s
to publikacijo. Na ta datum bo publikacija:
– ponovno potrjena,
– razveljavljena,
– zamenjana z revidirano izdajo ali
– dopolnjena.
IEC 80000 s skupnim naslovom Veličine in enote sestavljajo naslednji deli:
– 6. del: Elektromagnetizem
– 13. del: Informacijska znanost in tehnologija
– 14. del: Telebiometrija, povezana s fiziologijo človeka
ISO izdaja naslednje dele:
– 1. del: Splošno
– 2. del: Matematični znaki in simboli za uporabo v naravoslovnih vedah in tehniki
– 3. del: Prostor in čas
– 4. del: Mehanika
– 5. del: Termodinamika
– 7. del: Svetloba
– 8. del: Akustika
– 9. del: Fizikalna kemija in molekulska fizika
– 10. del: Atomska in jedrska fizika
– 11. del: Značilna števila
– 12. del: Fizika trdne snovi
5
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SIST IEC 80000-6 : 2014
0 Uvod
0.1 Razvrstitev preglednic
V ISO/IEC 80000 so veličine in enote v preglednicah razvrščene tako, da so veličine na levih, enote
pa na ustreznih desnih straneh.
Vse enote med vodoravnima polnima črtama na desni strani pripadajo veličinam med ustreznima
polnima črtama na levi strani.
Če je bila pri reviziji dela ISO 31 zaporedna številka veličine spremenjena, je številka iz prejšnje izdaje
navedena v oklepaju na levi strani pod novo številko veličine; pomišljaj pomeni, da prejšnja izdaja ni
vsebovala te veličine.
0.2 Preglednice veličin
Imena najpomembnejših veličin v tem dokumentu so podana skupaj s svojimi simboli in največkrat tudi
z definicijami. Ta imena in simboli so priporočila. Definicije so podane samo za opredelitev veličin v
mednarodnem sistemu veličin (ISQ), navedenih na levih straneh preglednice 1, in niso nujno popolne.
Skalarni, vektorski ali tenzorski značaj nekaterih veličin je prikazan, zlasti kadar je to potrebno za
definicijo.
Večina veličin ima podano samo eno ime in samo en simbol; če sta za eno veličino podani dve imeni
ali več oziroma dva simbola ali več in razlika ni opredeljena, so enakovredni. Kadar obstajata dva tipa
poševnih črk (kot npr. ϑ in θ, ϕ in φ, а in a ter g in g), je uporabljen samo eden; to pa ne pomeni, da
drugi ni enako sprejemljiv. Takšnim različicam ni priporočljivo pripisovati različnih pomenov. Če je
simbol v oklepaju, pomeni, da je "rezervni" in se v besedilu uporablja takrat, kadar ima glavni simbol
drugačen pomen.
V angleški izdaji so francoska imena veličin v poševnem tisku, pred njimi pa stoji oznaka fr. Spol je pri
francoskem imenu označen z oznako (m) za moški in (f) za ženski spol in stoji neposredno za
samostalnikom v francoskem imenu.
0.3 Preglednice enot
0.3.1 Splošno
Imena enot za ustrezne veličine so podana skupaj z mednarodnimi simboli in definicijami. Ta imena
enot so odvisna od jezika, simboli pa so mednarodni in enaki v vseh jezikih. Več informacij o tem
najdete v Brošuri SI (8. izdaja, 2006), ki jo je izdal BIPM, in v ISO 80000-1 (v pripravi).
Enote so razporejene na naslednji način:
a) Najprej so podane koherentne enote SI. Enote SI so bile sprejete na Generalni konferenci za
uteži in mere (Conférence Générale des Poids et Mesures, CGPM). Priporoča se uporaba
koherentnih enot SI; desetiški večkratniki in manjkratniki, ki se tvorijo s predponami SI, se
priporočajo, tudi če niso posebej navedeni.
b) Sledi nekaj enot, ki niso enote SI, a so jih za uporabo skupaj z enotami SI sprejeli Mednarodni
odbor za uteži in mere (Comité International des Poids et Mesures, CIPM) ali Mednarodna
organizacija za zakonsko meroslovje (Organisation Internationale de Métrologie Légale, OIML) ali
ISO in IEC.
Take enote so od ustreznih enot SI ločene s črtkano vodoravno črto.
c) Enote, ki niso enote SI, in jih je CIPM sprejel za začasno uporabo skupaj z enotami SI, so v
stolpcu "Pretvorniki in opombe" natisnjene z manjšimi črkami kot drugo besedilo.
d) Enote, ki niso enote SI in se ne priporočajo, so podane samo v dodatkih k nekaterim delom
ISO/IEC 80000. Ti dodatki so informativni, namenjeni predvsem pretvornikom, in niso sestavni
del standarda. Te odsvetovane enote so razvrščene v dve skupini:
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SIST IEC 80000-6 : 2014
1) enote s posebnimi imeni v sistemu CGS;
2) enote, ki temeljijo na enotah čevelj, funt, sekunda, ter nekatere druge, sorodne enote.
e) Druge enote, ki niso enote SI in so podane za informacijo, zlasti glede pretvornikov, so podane v
drugem informativnem dodatku.
0.3.2 Opomba glede enot veličin z dimenzijo ena oziroma brezdimenzijskih veličin
Koherentna enota za katerokoli veličino z dimenzijo ena, ki se imenuje tudi brezdimenzijska veličina,
je število ena, simbol 1. Pri izražanju vrednosti takšne veličine se simbol enote 1 navadno ne piše.
PRIMER:
Lomni količnik n = 1,53 × 1 = 1,53
Za večkratnike ali manjkratnike te enote se predpone ne smejo uporabljati. Namesto predpon se
priporoča uporaba potenc števila 10.
PRIMER:
3
Reynoldsovo število Re = 1,32 × 10
Ker je ravninski kot na splošno izražen z razmerjem med dvema dolžinama in prostorski kot z
razmerjem med dvema ploščinama, je CGPM leta 1995 določila, da sta v mednarodnem sistemu enot
radian, rad, in steradian, sr, brezdimenzijski "izpeljani" enoti. Torej se veličini ravninski kot in prostorski
kot obravnavata kot izpeljani veličini z dimenzijo ena. Enoti radian in steradian sta tako enaki ena;
lahko se izpustita ali pa uporabljata v izrazih za izpeljane enote, da je lažje razlikovati med veličinami
različnih vrst, vendar enakih dimenzij.
0.4 Številske navedbe v tem standardu
Znak = se uporablja za označevanje, da "je točno enako", znak ≈ se uporablja za označevanje, da "je
približno enako" in znak := se uporablja za označevanje, da "je po definiciji enako".
Številske vrednosti fizikalnih veličin, ki so določene eksperimentalno, imajo vedno pripadajočo merilno
negotovost. Ta negotovost naj se vedno navede. V tem standardu se velikost negotovosti izrazi tako,
kot kaže naslednji primer.
PRIMER:
l = 2,347 82(32) m
V tem primeru, l = a(b) m, se številska vrednost negotovosti b, navedena v oklepaju, domnevno
nanaša na zadnje (in najmanj pomembne) števke številske vrednosti a dolžine l. Ta zapis se uporabi,
kadar b izraža standardno negotovost (ocenjeni standardni odklon) v zadnjih števkah vrednosti a.
Zgoraj navedeni številski primer se lahko razlaga, kot da pomeni, da je najboljša ocena številske
vrednosti dolžine l (če je l izražen v enoti meter) 2,347 82, in da je neznana vrednost l domnevno med
(2,347 82 – 0,000 32) m in (2,347 82 + 0,000 32) m, s tem da je verjetnost določena s standardno
negotovostjo 0,000 32 m in porazdelitvijo verjetnosti vrednosti l.
0.5 Posebne opombe
Točke, podane v ISO 80000-6, so na splošno v skladu z Mednarodnim elektrotehniškim slovarjem
(IEV), zlasti IEC 60050-121 in IEC 60050-131. Za vsako veličino je sklic na IEV podan v obliki: “Glej
IEC 60050-121, točka 121-xx-xxx.”.
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0.5.1 Sistem veličin
Za uporabo v elektromagnetizmu je razvitih več različnih sistemov veličin, odvisno od števila in izbire
osnovnih veličin, na katerih sistem temelji. Vendar pa sta v elektromagnetizmu in elektrotehniki
priznana samo mednarodni sistem veličin ISQ in z njim povezani mednarodni sistem enot SI, ki se
odražata v standardih ISO in IEC. Mednarodni sistem SI ima sedem osnovnih enot, med njimi meter,
simbol m, kilogram, simbol kg, sekunda, simbol s, in amper, simbol A.
0.5.2 Sinusne veličine
Za veličine, ki se sinusno spreminjajo s časom, in za njihove kompleksne predstavitve je IEC
standardiziral dva načina tvorbe simbolov. Velike in male črke se praviloma uporabljajo za električni
tok (točka 6-1) in za napetost (točka 6-11.3), dodatne oznake pa za druge veličine. Te so podane v
IEC 60027-1.
1. PRIMER:
Sinusno spreminjanje električnega toka (točka 6-1) s časom se lahko dejansko izrazi v obliki
i = 2 I cos(ωt – ϕ)
njegov kompleksen prikaz (imenovan fazor) pa se izrazi v obliki
–jϕ
I = I e
kjer je i trenutna vrednost toka, I njegova kvadratna sredina, (ωt – φ) faza, φ začetna faza.
2. PRIMER:
Sinusno spreminjanje magnetnega pretoka (točka 6-22.1) s časom se lahko izrazi z dejanskim
prikazom v obliki
ˆ
Φ = Φ cos(ωt – ϕ) = 2 Φ cos(ωt – ϕ)
eff
ˆ
kjer je Φ trenutna vrednost pretoka, Φ njegova temenska vrednost in Φ njegova kvadratna sredina.
eff
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SIST IEC 80000-6 : 2014
Veličine in enote –
6. del: Elektromagnetizem
1 Področje uporabe
V standardu IEC 80000-6 so podana imena, simboli in definicije za veličine na področju
elektromagnetizma. Kjer je primerno, so podani tudi pretvorniki (pretvorni faktorji).
2 Zveza z drugimi standardi
Za uporabo tega dokumenta so nujno potrebni spodaj navedeni dokumenti. Pri datiranem sklicevanju
se upošteva samo navedena izdaja. Pri nedatiranem sklicevanju se upošteva zadnja izdaja
navedenega dokumenta (vključno z morebitnimi dopolnili).
IEC 60027-1:1992, Črkovni simboli, ki se uporabljajo v elektrotehniki – 1. del: Splošno
IEC 60050-111, Mednarodni elektrotehniški slovar – 111. del: Fizika in kemija
IEC 60050-121, Mednarodni elektrotehniški slovar – 121. del: Elektromagnetizem
IEC 60050-131, Mednarodni elektrotehniški slovar – 131. del: Teorija vezij
ISO 31-0:1992, Veličine in enote – 0. del: Splošna načela (v reviziji)
ISO 80000-3:2006, Veličine in enote – 3. del: Prostor in čas
ISO 80000-4:2006, Veličine in enote – 4. del: Mehanika
3 Imena, simboli in definicije
Imena, simboli in definicije za veličine in enote na področju elektromagnetizma so podani na
naslednjih straneh.
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ELEKTROMAGNETIZEM VELIČINE
Zap. št. Ime Simbol Definicija Opombe
6-1 električni tok električni tok je ena od Električni tok je veličina, ki se
I, i
osnovnih veličin v pogosto lahko meri z merilnikom
(5-1)
mednarodnem sistemu (električnega) toka.
veličin ISQ, na katerem
temelji mednarodni sistem
Električni tok skozi površino je
enot SI
količnik med električnim nabojem
(točka 6-2), ki se v časovnem
intervalu prenaša skozi površino,
in trajanjem tega intervala.
Za popolnejšo definicijo glej
točko 6-8 in IEC 60050-121,
točka 121-11-13.
6-2 električni Električni naboj nosijo diskretni
Q, q dQ = Idt
naboj delci in je lahko pozitiven ali
(5-2)
negativen. Po dogovoru je
kjer je I električni tok (točka
predznak naboja določen tako,
6-1) in t čas (ISO 80000-3,
da je električni naboj protona, e,
točka 3-7)
pozitiven.
Glej IEC 60050-121,
točka 121-11-01.
Za označevanje točkastega
naboja se pogosto uporablja q,
tudi v tem dokumentu.
d
6-3 gostota Glej IEC 60050-121, točka
ρ, ρ
Q
V
d
električnega ρ = 121-11-07.
(5-3)
V
naboja,
prostorninski
električni kjer je Q električni naboj
naboj
(točka 6-2) in
V prostornina
(ISO 80000-3, točka 3-4)
d
6-4 površinska Glej IEC 60050-121,
ρ , σ
A Q
d
gostota točka 121-11-08.
ρ =
(5-4) A
A
električnega
naboja,
kjer je Q električni naboj
ploščinski
električni (točka 6-2) in A ploščina
naboj (ISO 80000-3, točka 3-3)
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ENOTE ELEKTROMAGNETIZEM
Zap. št. Ime Mednarodni simbol Definicija Pretvorniki in opombe
6-1.a amper A amper je konstantni Ta definicija pomeni, da
električni tok, ki pri je magnetna konstanta
prehodu skozi dva
µ (točka 6-26.1)
0
–7
vzporedna, neskončno
točno 4π × 10 H/m.
dolga vodnika z
zanemarljivim krožnim
V tej definiciji se
prerezom, postavljena v
namesto “dolžinska sila”
vakuum in v medsebojni
oziroma “sila na
razdalji 1 m, povzroči med
dolžino” uporablja samo
–7
njima silo 2 × 10
“sila”.
newtona na meter dolžine
Skladno s tem naj bo
[9. CGPM (1948)]
zadnja enota “newton
na meter” brez
“dolžine”.
6-2.a coulomb C Enota amper ura se
1 C := 1 A · s
uporablja pri
elektrolitskih napravah,
kot so npr. akumulatorji.
1 A · h = 3,6 kC
3
6-3.a coulomb na C/m
kubični
meter
2
coulomb na
6-4.a C/m
kvadratni
meter
11
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SIST IEC 80000-6 : 2014
ELEKTROMAGNETIZEM VELIČINE
Zap. št. Ime Simbol Definicija Opombe
d
6-5 dolžinska Glej IEC 60050-121,
ρ , τ Q
l
d
ρ =
l
gostota točka 121-11-09.
l
električnega
kjer je Q električni naboj
naboja,
(točka 6-2) in l dolžina
dolžinski
(ISO 80000-3, točka 3-1.1)
električni
naboj
6-6 električni Električni dipolni moment snovi
p p = q(r – r )
+ –
dipolni znotraj domene je vektorska vsota
(5-14)
moment električnih dipolnih momentov vseh
kjer sta r in r položajna
+ –
električnih dipolov, vključenih v to
vektorja (ISO 80000-3,
domeno.
točka 3-1.11) za nosilca
električnega naboja q
oziroma –q (točka 6-2)
Glej IEC 60050-121,
točki 121-11-35 in 121-11-36.
6-7 električna Glej IEC 60050-121,
P P = dp/dV
polarizacija točka 121-11-37.
(5-13)
kjer je p električni dipolni
moment (točka 6-6) snovi
znotraj domene s
prostornino V
(ISO 80000-3, točka 3-4)
6-8 gostota
J J = ρυ Električni tok I (točka 6-1)
električnega
(5-15)
skozi površino S je
toka,
kjer je ρ gostota
d
n
ploščinski
električnega naboja (točka
I = J ⋅ e A
∫
S
električni tok
6-3) in υ hitrost
(ISO 80000-3, točka 3-8.1)
kjer je e dA vektorski element
n
površine.
Glej IEC 60050-121,
točka 121-11-11.
6-9 dolžinska
J J = ρυ Električni tok I (točka 6-1) skozi
s s A
gostota
krivuljo C na površini je
(―)
električnega
kjer je ρ površinska
A
d
S n
toka,
gostota električnega
I = J × e ⋅ r
∫
C
dolžinski naboja (točka 6-4) in
električni tok
υ hitrost (ISO 80000-3,
kjer je e enotski vektor pravokotno
n
točka 3-8.1)
na površino in dolžinski vektorski
element in dr diferencial
položajnega vektorja r.
Glej IEC 60050-121,
točka 121-11-12.
6-10 električna Glej IEC 60050, točka 121-11-18.
E E = F/q
poljska jakost
(5-5)
q je naboj preskusnega delca v
kjer je F sila (ISO 80000-4,
mirovanju.
točka 4-9.1)
in q električni naboj
(točka 6-2)
12
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SIST IEC 80000-6 : 2014
ENOTE ELEKTROMAGNETIZEM
Zap. št. Ime Mednarodni simbol Definicija Pretvorniki in opombe
6-5.a coulomb na C/m
meter
6-6.a coulomb C · m
meter
2
6-7.a coulomb na C/m
meter
kvadrat
2
6-8.a amper na A/m
kvadratni
meter
6-9.a amper na A/m
meter
6-10.a volt na meter V/m 1 V/m = 1 N/C Za definicijo volta
glej 6-11.a.
13
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SIST IEC 80000-6 : 2014
ELEKTROMAGNETIZEM VELIČINE
Zap. št. Ime Simbol Definicija Opombe
6-11.1 električni ∂A Električni potencial ni enkraten, saj
V, ϕ
–grad V = E +
potencial mu je mogoče dodati katero koli
(5-6.1)
∂t
skalarno poljsko veličino, ne da bi
kjer je E električna poljska
se spremenil njegov gradient.
jakost (točka 6-10),
A magnetni vektorski
Glej IEC 60050-121,
potencial (točka 6-32) in
točka 121-11-25.
t čas (ISO 80000-3,
točka 3-7)
b
r
6-11.2 razlika d V = V – V
V
ab a b
ab ∂A
ab ⎛ ⎞
V = E + ⋅ r
⎜ ⎟
električnih
∫
(5-6.2)
C ∂t
⎝ ⎠
potencialov a
r() kjer sta V in V potenciala na
a b
točkah a oziroma b.
kjer je E električna poljska
jakost (točka 6-10),
Glej IEC 60050-121,
A magnetni vektorski
točka 121-11-26.
potencial (točka 6-32),
t čas (ISO 80000-3, točka
3-7), in r položajni vektor
(ISO 80000-3, točka
3-1.11) vzdolž dane krivulje
C od točke a do točke b
v teoriji električnega Za električno polje znotraj medija je
6-11.3 napetost, U, U
ab
b
r
tokokroga je
d
(5-6.3) električna
ab
U = E ⋅ r
napetost ∫
U = V – V
ab a b C
a
r()
(Ime “voltaža”, ki
kjer je E električna poljska jakost
kjer sta V in V električna
a b
se pogosto
potenciala (točka 6-11.1) v (točka 6-10) in r položajni vektor
uporablja v
točkah a oziroma b (ISO 80000-3, točka 3-1.11) vzdolž
angleškem
dane krivulje C od točke a do točke b.
jeziku, je sicer
navedeno v IEV,
Za nekrožno električno polje je
vendar je izjema
napetost neodvisna od poti med
glede na načelo,
točkama a in b.
da naj se ime
veličine ne bi
Glej IEC 60050-121,
nanašalo na
točka 121-11-27.
nobeno ime
enote.)
6-12 gostota Gostota električnega pretoka je z
D
D = ε0E + P
električnega gostoto električnega naboja
(5-7)
pretoka, povezana z enačbo:
kjer je ε električna
0
električna
div D = ρ
konstanta (točka 6-14.1),
indukcija
E električna poljska jakost
kjer div označuje divergenco.
(točka 6-10) in P električna
polarizacija (točka 6-7)
Glej IEC 60050-121, tč. 121-11-40.
6-13 kapacitanca, Glej IEC 60050-131, točka
C C = Q/U
131-12-13.
(5-9) kapacitivnost
kjer je Q električni naboj
(točka 6-2) in
U napetost (6-11.3)
14
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SIST IEC 80000-6 : 2014
ENOTE ELEKTROMAGNETIZEM
Zap. št. Ime Mednarodni simbol Definicija Pretvorniki in opombe
6-11.a volt V 1 V := 1 W/A
2
6-12.a coulomb na C/m
meter
kvadrat
6-13.a farad F 1 F := 1 C/V
15
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SIST IEC 80000-6 : 2014
ELEKTROMAGNETIZEM VELIČINE
Zap. št. Ime Simbol Definicija Opombe
1
–12
6-14.1 električna
ε ε ≈ 8,854 188 × 10 F/m
0 0
0
ε = 2
konstanta,
(5-10.2)
0
0
µ c
Glej IEC 60050-121,
permitivnost
točka 121-11-03.
vakuuma
kjer je µ magnetna konstanta
0
(točka 6-26.1) in
c hitrost svetlobe
0
(točka 6-35.2)
6-14.2 permitivnost, ε Ta definicija velja za izotropni
D = ε E
medij. Za anizotropni medij je
(5-10.1) dielektričnost
permitivnost tenzor drugega reda.
kjer je D gostota električnega
pretoka (točka 6-12) in
Glej IEC 60050-121,
E električna poljska jakost
točka 121-12-12.
(točka 6-10)
6-15 relativna Glej IEC 60050-121,
ε ε = ε /ε
r r 0
permitivnost točka 121-12-13.
(5-11)
kjer je ε permitivnost
(točka 6-14.2) in
ε električna konstanta
0
(točka 6-14.1)
6-16 električna
χ P = ε χE
χ = ε – 1
0 r
suscepti-
(5-12)
bilnost
kjer je P električna polarizacija Ta definicija velja za izotropni
medij. Za anizotropni medij je
(točka 6-7),
električna susceptibilnost tenzor
ε električna konstanta
0
drugega reda.
(točka 6-14.1) in
E električna poljska jakost
Glej IEC 60050-121,
(točka 6-10)
točka 121-12-19.
d
n
6-17 električni Glej IEC 60050-121,
Ψ
D ⋅ e A
Ψ =
∫
S
pretok točka 121-11-41.
(5-8)
po površini S, kjer je
D gostota električnega
pretoka (točka 6-12) in
e dA vektorski površinski
n
element
(ISO 80000-3, točka 3-3)
6-18 gostota ∂D Glej IEC 60050-121,
J
D
J =
D
premikalne- točka 121-11-42.
∂t
(–)
ga toka
kjer je D gostota električnega
pretoka (točka 6-12) in t čas
(ISO 80000-3, točka 3-7)
16
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SIST IEC 80000-6 : 2014
ENOTE ELEKTROMAGNETIZEM
Zap. št. Ime Mednarodni simbol Definicija Pretvorniki in opombe
6-14.a farad na meter F/m 1 F/m = 1 C/(V · m)
6-15.a ena 1 Glej uvod, točka 0.3.2.
6-16.a ena 1 Glej uvod, točka 0.3.2.
6-17.a coulomb C
2
6-18.a amper na A/m
kvadratni
meter
17
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SIST IEC 80000-6 : 2014
ELEKTROMAGNETIZEM VELIČINE
Zap. št. Ime Simbol Definicija Opombe
d
6-19.1 premikalni Glej IEC 60050-121,
I n
D
J ⋅e A
D
I =
D ∫
(―) tok S točka 121-11-43.
po površini S, kjer je J gostota
D
premikalnega toka (točka 6-18) in
e dA vektorski površinski element
n
(ISO 80000-3, točka 3-3)
I = I + I
6-19.2 celotni tok Glej IEC 60050-121,
I , I tot D
tot t
točka 121-11-45.
(―) kjer je I električni tok (točka 6-1) in
I premikalni tok (točka 6-19.1)
D
6-20 gostota Glej IEC 60050-121,
J , J J = J + J
tot t tot D
celotnega točka 121-11-44.
(―)
kjer je J gostota električnega toka
toka
(točka 6-8) in J gostota
D
premikalnega toka (točka 6-18)
6-21 gostota Gostota magnetnega
B F = qυ × B
magnetnega pretoka ima divergenco nič,
(5-19)
pretoka, kjer je F sila (ISO 80000-4, točka
div B = 0.
magnetna 4-9.1) in υ hitrost (ISO 80000-3,
indukcija
točka 3-8.1) vsakega preskusnega
Glej IEC 60050-121,
delca z električnim nabojem q
točka 121-11-19.
(točka 6-2)
d
6-22.1 magnetni n Glej IEC 60050-121,
Φ
Φ = B ⋅e A
∫
S
pretok točka 121-11-21.
(5-20)
po površini S, kjer je B gostota
magnetnega pretoka (točka 6-21) in
e dA vektorski površinski element
n
(ISO 80000-3, točka 3-3)
d
m
sklenjeni
...
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