# IEC 80000-6:2022

(Main)## Quantities and units - Part 6: Electromagnetism

## Quantities and units - Part 6: Electromagnetism

IEC 80000-6:2022 gives names, symbols, and definitions for quantities and units of electromagnetism. 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 and units.

This standard is based on classical electromagnetism, i.e. mainly Maxwell’s equations. No reference is made to quantum field theories.

IEC 80000-6:2022 cancels and replaces the first edition published in 2008. This edition constitutes a technical revision.

This edition includes the following significant technical changes with respect to the previous edition:

1) With the new definitions in SI, some previously exact values for quantities now must be determined experimentally while other quantities are given as exact values;

2) Item 6-2.2, elementary charge added;

3) Item 6-11.4, induced voltage, added;

4) Index of entries added;

5) Editorial alignment to other parts of the IEC and ISO 80000 series.

## Grandeurs et unités - Partie 6: Electromagnétisme

L'IEC 80000-6:2022 donne des noms, des symboles et des définitions pour les grandeurs et les unités d'électromagnétisme. Le cas échéant, des facteurs de conversion sont également indiqués.

Cette norme est basée sur l'électromagnétisme classique, c'est-à-dire principalement les équations de Maxwell. Aucune référence n'est faite aux théories quantiques des champs.

L’IEC 80000-6 a été établie par le comité d'études 25 de l’IEC: Grandeurs et unités, et leurs symboles littéraux, en coopération étroite avec l'ISO/TC 12, Grandeurs et unités. Il s'agit d'une Norme internationale.

Cette deuxième édition de l’IEC 80000-6 annule et remplace la première édition parue en 2008. Cette édition constitue une révision technique.

Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente:

1) avec les nouvelles définitions du SI, certaines valeurs auparavant exactes pour des grandeurs doivent maintenant être déterminées de manière expérimentale, tandis que d'autres grandeurs sont données comme des valeurs exactes;

2) ajout de l’article 6-2.2, charge élémentaire;

3) ajout de l’article 6-11.4, tension induite;

4) ajout d’un index des entrées;

5) alignement rédactionnel sur d'autres parties des séries IEC et ISO 80000.

### General Information

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### Standards Content (Sample)

IEC 80000-6

Edition 2.0 2022-11

INTERNATIONAL

STANDARD

NORME

INTERNATIONALE

Quantities and units –

Part 6: Electromagnetism

Grandeurs et unités –

Partie 6: Électromagnétisme

IEC 80000-6:2022-11(en-fr)

---------------------- Page: 1 ----------------------

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---------------------- Page: 2 ----------------------

IEC 80000-6

Edition 2.0 2022-11

INTERNATIONAL

STANDARD

NORME

INTERNATIONALE

Quantities and units –

Part 6: Electromagnetism

Grandeurs et unités –

Partie 6: Électromagnétisme

INTERNATIONAL

ELECTROTECHNICAL

COMMISSION

COMMISSION

ELECTROTECHNIQUE

INTERNATIONALE

ICS 01.040.29; 17.220.01 ISBN 978-2-8322-5706-7

Warning! Make sure that you obtained this publication from an authorized distributor.

Attention! Veuillez vous assurer que vous avez obtenu cette publication via un distributeur agréé.

---------------------- Page: 3 ----------------------

– 2 – IEC 80000-6:2022 © IEC 2022

CONTENTS

FOREWORD . 3

INTRODUCTION . 5

0.1 Tables of quantities. 5

0.2 Units . 5

0.2.1 General . 5

0.2.2 Remark on units for quantities of dimension one, or dimensionless

quantities . 5

0.3 Numerical statements in this document . 6

0.4 Special remarks . 6

0.4.1 General . 6

0.4.2 System of quantities . 6

0.4.3 Sinusoidal quantities. 7

0.4.4 Root-mean-square value, RMS value . 7

1 Scope . 8

2 Normative references . 8

3 Names, symbols, definitions and units of quantities . 8

Annex A (informative) Units in the CGS system with special names . 27

Alphabetical index . 28

Bibliography . 34

Table 1 – Quantities and units in electromagnetism . 9

Table A.1 – Deprecated units with special names taken from the CGS system . 27

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IEC 80000-6:2022 © IEC 2022 – 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

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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

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rights. IEC shall not be held responsible for identifying any or all such patent rights.

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 and units. It is an International

Standard.

This second edition of IEC 80000-6 cancels and replaces the first edition published in 2008.

This edition constitutes a technical revision.

This edition includes the following significant technical changes with respect to the previous

edition:

a) With the new definitions in SI, some previously exact values for quantities now must be

determined experimentally while other quantities are given as exact values;

b) Item 6-2.2, elementary charge added;

c) Item 6-11.4, induced voltage, added;

d) Index of entries added;

e) Editorial alignment to other parts of the IEC and ISO 80000 series.

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– 4 – IEC 80000-6:2022 © IEC 2022

The text of this International Standard is based on the following documents:

Draft Report on voting

25/732/FDIS 25/740/RVD

Full information on the voting for its approval can be found in the report on voting indicated in

the above table.

The language used for the development of this International Standard is English.

IEC 80000 consists of the following parts, under the general title Quantities and units:

1) Part 6: Electromagnetism

2) Part 13: Information science and technology

3) Part 15: Logarithmic and related quantities, and their units

4) Part 16: Printing and writing rules

5) Part 17: Time dependency

The following parts are published by ISO:

1) Part 1: General

2) Part 2: Mathematical signs and symbols to be used in the natural sciences and technology

3) Part 3: Space and time

4) Part 4: Mechanics

5) Part 5: Thermodynamics

6) Part 7: Light

7) Part 8: Acoustics

8) Part 9: Physical chemistry and molecular physics

9) Part 10: Atomic and nuclear physics

10) Part 11: Characteristic numbers

11) Part 12: Condensed matter physics

This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in

accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available

at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are

described in greater detail at www.iec.ch/publications.

The committee has decided that the contents of this document will remain unchanged until the

stability date indicated on the IEC website under webstore.iec.ch in the data related to the

specific document. At this date, the document will be

• reconfirmed,

• withdrawn,

• replaced by a revised edition, or

• amended.

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IEC 80000-6:2022 © IEC 2022 – 5 –

INTRODUCTION

0.1 Tables of quantities

The names in English of the most important quantities within the field of this document are given

together with their symbols and, in most cases, their definitions. The definitions are given for

identification of the quantities in the International System of Quantities (ISQ), listed in 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 an alternative symbol, to be used when,

in a particular context, the main symbol is in use with a different meaning.

0.2 Units

0.2.1 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 (9

edition 2019) from BIPM and ISO 80000-1.

The units are arranged in the following way:

a) The base 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 base 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. The order of the units is kg, m, s, A, K, mol, cd.

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.

c) Non-SI units that are not recommended are given only in annexes in some parts of

ISO 80000 and 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, see Annex A;

2) units based on the foot, pound, and some other related units.

0.2.2 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

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– 6 – IEC 80000-6:2022 © IEC 2022

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.

0.3 Numerical statements in this document

The sign = is used to denote "is exactly equal to" and the sign ≈ is used to denote "is

approximately 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

document, 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 can be interpreted to mean

that the best estimate of the numerical value of the length l, when l is 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.

0.4 Special remarks

0.4.1 General

The items given in IEC 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 60050-121:20XX, 121-xx-xxx.".

The font used for text is sans serif; that used for quantities is serif.

0.4.2 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 are

the kilogram (kg), the metre (m), the second (s), and the ampere (A).

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IEC 80000-6:2022 © IEC 2022 – 7 –

0.4.3 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 symbols 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

i = I e

where i is the instantaneous value of the current, I, is its root-mean-square (RMS) value

2

(see 0.4.4), (ωt − φ) is the phase, φ is the initial phase, and j is the imaginary unit (j = −1), in

mathematics often denoted by i.

EXAMPLE 2

The sinusoidal variation with time of a magnetic flux (item 6-22.1) can be expressed in real

representation as

Φ Φ cos ωt – φφ 2 Φ cos ωt –

( ) ( )

eff

where Φ is the instantaneous value of the flux, is its peak value and Φ is its RMS value.

Φ

eff

0.4.4 Root-mean-square value, RMS value

For a time-depending quantity a, the positive square root of the mean value of the square of the

quantity taken over a given time interval is called root-mean-square value, i.e.

T

1

2

atd

∫

T

0

The root-mean-square value of a periodic quantity is usually taken over an integration interval,

the range of which is the period multiplied by a natural number. For a sinusoidal quantity

a(t) = Â cos(ωt + φ), the root-mean-square value is Â/ 2 .

The root-mean-square value of a quantity may be denoted by adding one of the subscripts "eff"

or "RMS" to the symbol of the quantity. In electrical technology, the root-mean-square values

of electric current i(t) and voltage u(t) are usually denoted I and U, respectively.

==

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– 8 – IEC 80000-6:2022 © IEC 2022

QUANTITIES AND UNITS –

Part 6: Electromagnetism

1 Scope

This part of IEC 80000 gives names, symbols, and definitions for quantities and units of

electromagnetism. Where appropriate, conversion factors are also given.

This document is based on classical electromagnetism, i.e. mainly Maxwell’s equations. No

reference is made to quantum field theories.

2 Normative references

There are no normative references in this document.

3 Names, symbols, definitions and units of quantities

The names, symbols, and definitions for quantities and units of electromagnetism are given in

the tables on the following pages. For units in the CGS system with special names, see Annex A.

NOTE 1 In general, these quantities can depend on time even when not explicitly noted. All surfaces are assumed

to be oriented surfaces (see IEC 60050-102, item 102-04-37)

NOTE 2 The font in the formulas is different from the font of the main text.

ISO and IEC maintain terminological databases for use in standardization at the following

addresses:

• IEC Electropedia: available at https://www.electropedia.org/

• ISO Online browsing platform: available at https://www.iso.org/obp

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IEC 80000-6:2022 © IEC 2022 – 9 –

Table 1 – Quantities and units in electromagnetism

Quantity Unit

Item No. Remarks

Name Symbol Definition Symbol

6-1 electric current I scalar quantity equal to the quotient of the net A Electric current is one of the base

quasi-infinitesimal (see IEC 60050-121, item quantities in the International System of

i

121-11-06) electric charge dQ (item 6-2.1) Quantities, ISQ, on which the

transferred through a surface during a quasi- International System of Units, SI, is

infinitesimal time interval and the duration dt of based.

that interval:

Electric current I through a surface S

can also be written as

dQ

I =

dt

IA J⋅ e d

∫ n

S

where J is the electric current density

(item 6-8) and where e dA is the vector

n

surface element.

Electric current produces a magnetic

field.

For related definitions, see item 6-8 and

IEC 60050-121:1998, 121-11-13.

6-2.1 electric charge Q additive scalar quantity attributed to any particle C To denote a point charge, q is often

and, generally, any system of them, to used, as is done in this document.

q A s

characterize its electromagnetic interactions

Electromagnetic interactions are

s A

Coulomb-Lorentz forces, see

IEC 60050 121:1998, 121-11-20.

The coherent SI unit of charge is

coulomb, C. Another frequently used unit

is the ampere-hour (Ah) mentioned in

IEC 60050-313:2020, 313-01-16, widely

used for battery characteristics.

=

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– 10 – IEC 80000-6:2022 © IEC 2022

Quantity Unit

Item No. Remarks

Name Symbol Definition Symbol

6-2.2 elementary charge e magnitude of the negative electric charge carried C In the SI system the elementary charge,

by a single electron, which has charge −1 e e, is one of the fundamental constants

A s

with an exact value

s A

−19

e = 1,602 176 634 × 10 C, see the SI

Brochure.

Electric charge can be positive, negative

or zero. The sign convention is such that

the elementary electric charge, e, of the

proton, is positive. See IEC 60050-113,

item 113-02-12.

3

6-3 electric charge density, scalar quantity representing the spatial distribution See IEC 60050-121:1998, 121-11-07.

ρ C/m

volumic electric charge of electric charge,

−3

m s A

volumic charge

dQ

ρ r =

( )

dV

where dQ is quasi-infinitesimal (see

IEC 60050-121:2008, 121-11-06) electric charge

(item 6-2.1) contained in a quasi-infinitesimal 3D

domain located at position r and dV is quasi-

infinitesimal volume (ISO 80000-3) of this domain

2

6-4 surface density of electric charge, scalar quantity representing the areal distribution See IEC 60050-121:1998, 121-11-08.

σ C/m

areic electric charge of electric charge,

−2

m s A

areic charge

dQ

σσ r

( )

dA

where dQ is a quasi-infinitesimal (see

IEC 60050-121:2008, 121-11-06) electric charge

(item 6-2.1) contained in a quasi-infinitesimal 2D

domain located at position r, and dA is a quasi-

infinitesimal area (ISO 80000-3) of this domain

==

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IEC 80000-6:2022 © IEC 2022 – 11 –

Quantity Unit

Item No. Remarks

Name Symbol Definition Symbol

6-5 linear density of electric charge, scalar quantity representing the linear distribution C/m See IEC 60050-121, item 121-11-09.

τ

lineic electric charge of electric charge,

−1

m s A

lineic charge

dQ

τ τ (r )

dl

where dQ is a quasi-infinitesimal (see

IEC 60050-121:2008, 121-11-06) electric charge

(item 6-2.1) contained in a quasi-infinitesimal

domain located at position r and dl is a quasi-

infinitesimal length (ISO 80000-3) of this domain

6-6 electric dipole moment p vector quantity given by C m The electric dipole moment of a

substance within a domain is the vector

p = q(r – r ) m s A

+ – sum of electric dipole moments of all

electric dipoles contained in the domain.

where r and r are the position vectors

+ –

See IEC 60050-121:1998, 121-11-35

(ISO 80000-3) of the carriers of electric charges q

and 121-11-36.

and −q (item 6-2), respectively

2

6-7 electric polarization P vector quantity representing the spatial distribution See IEC 60050-121:1998, 121-11-37.

C/m

of electric dipole moment,

−2

m s A

dp

Pr( ) =

dV

where dp is quasi-infinitesimal (see

IEC 60050-121:2008, 121-11-06) electric dipole

moment (item 6-6) of a substance in a quasi-

infinitesimal domain at position r and dV is quasi-

infinitesimal volume (ISO 80000-3) of this domain

2

6-8 electric current density J vector quantity equal to the sum, for the charge There can be different charge carriers

A/m

carriers within a volume element of quasi- with different velocities.

−2

m A

infinitesimal volume V, of the products of their

Electric current I (item 6-1) through a

electric charge Q and their velocity v , divided by

i i

surface S is

the volume V, given by

I = J e dA

Jr( ) J ρv n

∫

S

where i is the rank of the charge carrier

where e dA is the vector surface

n

element.

See IEC 60050-121:1998, 121-11-11.

= =

==

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– 12 – IEC 80000-6:2022 © IEC 2022

Quantity Unit

Item No. Remarks

Name Symbol Definition Symbol

6-9 linear electric current density J vector quantity equal to the sum, for the charge A/m See IEC 60050-121:1998, 121-11-12.

S

carriers confined to a surface element of quasi-

−1

m A

infinitesimal area S, of the products of their electric

charge Q and their velocity v , divided by the area

i i

S

J r J σv

( )

SS

where i is the rank of the charge carrier

6-10 electric field strength E additive vector field quantity that exerts on any V/m See IEC 60050-121:1998, 121-11-18.

charged particle located at position r a force F

−3 −1

kg m s A

(ISO 80000-4) equal to the product of E and

electric charge q (item 6-2.1) of the particle, thus:

F

Er( ) =

q

6-11.1 electric potential V scalar quantity expressed by V The electric potential is not unique since

any constant scalar field quantity can be

2 −3 −1

φ

kg m s A

added to it without changing its gradient.

∂A

–grad V = E +

The electric potential, the electric field,

∂t

and the magnetic vector potential

where E is electric field strength (item 6-10),

**...**

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