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IS0
I NT ERN AT I O NA L O RG A N I ZAT I O N FOR STA N DARD IZ AT1 O N
IS0 R ECOM MENDATI ON
R 31
PART V
Q'UANTITIES AND UNITS
OF ELECTRICITY AND MAGNETISM
1st EDITION
November 1965
COPYRIGHT RESERVED
The copyright of IS0 Recommendations and IS0 Standards
belongs to IS0 Member Bodies. Reproduction of these
documents, in any country, may be authorized therefore only
by the national standards organization of that country, being
a member of ISO.
For each individual country the only valid standard is the national standard of that country.
Printed in Denmark
Also issued in Fiench and Russian. Copies to be obtained through the national standards organizations.
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BRIEF HISTORY
The IS0 Recornmendation R 31, Part V - Quantities and Units of Electricily and
Ili'ngnefism, was drawn up by Technical Committee ISO/TC 12, Quantities, Units,
Synibols, Conuersion Ftrctors and Conversion Tables, the Secretariat of which is held
by the Danish Standards Association, Dansk Standardiseringsrl"id (DS).
\\'ark on this question by the Technical Committee began in 1957. The ISO/TC 12
Secretariat drew up three draft proposals in succession; the last one \\-as adopted,
in 1960, as a Draft IS0 Recommendation.
It should be noted that the following international organizations have had these
draft proposals sent to them and have taken part in the discussions at the meetings
of Technical Committee ISO/TC 12 :
International Committee on \\'eights and Measures,
International Electrotechnical Commission,
International Union of Pure and -4pplied Chemistry,
International Union of Pure and Applied Physics
and its Sub-Committee SUN,
International Commission on Illumination,
Comitk international de mktrologie légale,
World Meteorological Organization,
International Commission on Radiological Units and Measurements,
International Telegraph and Telephone Consultative Committee.
In June 1961, this halt IS0 Recommendation (No. 439) was circulated to all the
IS0 hlembcr I3odies for enquiry. It was approved, subject to some modifications
of an editorial nature, by the following Member Bodies:
Australia Hungary Poland
-Austria India Portugal
Belgium Israel Romania
Canada
Italy Sweden
Chile Japan Switzerland
Czechoslovakia Mexico U. A. R.
Denmark Netherlands United Kingdom
France New Zealand U. S. A.
Greece Norway Yugoslavia
Three Member Bodies apposed the approval of the Draft:
Germany, Ireland, U. S. S. R.
Thc Draft IS0 Recommendation was then submitted by correspondence to the
IS0 Council which decided, in November 1965, to accept it as an IS0 RECOM-
MEN DATION.
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Introduction
General remarks
This document, containing a table of Quantities and Units of Electricity and Magnetism, is part of
a more comprehensive publication dealing with quantities and units in various fields of science
and technology. Other parts of this more comprehensive publication are at present
I SO Recommendation R 31,
Part I (2nd edition): The International System of Units and Quantities and Units of Space and Time1),
Quantities and Units of Periodic and Related Phenomena,
Part II :
Part III : Quantities and Units of Mechanics,
Quantities and Units of Heat,
Part IV :
Part VI1 : Quantities and Units of Acoustics,
i./
Part XI : Mathematical Signs and Symbols for use in Physical Sciences and Technology.
General information regarding the arrangement of the tables and the symbols and abbreviations
used is to be found in the Introduction to ISO/R 31/Part I, where the full definitions of funda-
mental units are given as an appendix.
The statements in the definition columns for quantities are given merely for identification; they are
not intended to be complete definitions.
Special remarks
This document follows, unless the contrary is indicated, the IEC z, recommendations concerning the
quantities and units of electricity and magnetism. In particular, the units of the Giorgi or MKSA
system recommended by the IEC are given preference by placing them first and by printing the
item number in heavy type. These units belong to the International System of Units adopted by
the Conférence Générale des Poids et Mesures.
Items relating to units corresponding to those of the “symmetric” CGS unit system are marked
with an asterisk (*). Items and remarks relating to non-rationalized quantities are also marked
-
with the same asterisk.
Other items for which no recommendations appear in the relevant IEC publications are marked
with a dagger (t). Individual significant deviations from IEC recommendations are also marked
with the same dagger.
The numerical value of the velocity of light in vacuo, expressed in centimetres per second, is often
For simplicity, in this document, this number is denoted by 5‘.
needed for the conversion factors.
Explanatory remarks concerning quantities, equations and units in this document
In the field of electricity and magnetism, several systems of equations expressing the relations be-
tween physical quantities are used. As these equations have to be used only with corresponding
unit systems, it is necessary in this Introduction to refer to the different systems of equations
used in this field and their relation to the unit systems.
l) The title of the first edition of this document was: “Fundamental Quantities and Units of the MKSA system and
Quantities and Units of Space and Time”.
*) International Electrotechnical Commission (IEC).
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Equations and quantities
For electricity and magnetism, different c‘systcms” of equations have heen developed depending on the
number and the particular choice of basic quantities on which the system of equations is founded.
For the purpose of explaining this document only the following systems have to be mentioned:
1. Systems of equations with four basic quantities
In the cquations with four basic quantities, at least one electric quantity is included in the basic
set. In such a system the permittivity and the permeability in vacuo appear explicitly as physical
quantities in the relevant equations. Two different forms of equations, based on the same set of
four basic quantities, are in use:
I. 1 The rationalized system of equations, called “rationalized”, because in these equations factors 4x
or 2 7c only appear in cases involving spherical or circular symmetry respectively.
This rationalized system of equations is most commonly used in practical calculations in
physics and in electrical technology.
I. 2 The non-rationalized system of equations, in which the factors 4x and 27c often appear in
equations, where they would not be expected.
The equations and quantities given in the tables all belong to these two systems of equations.
Where in the document there is a “rationalized” and a corresponding “non-rationalized” quantity,
v
the word “rationalized” is generally omitted from the name of the former. Non-rationalized quanti-
ties are denoted in this document by symbols bearing a prime.
The use of rationalized equations is especially recommended.
II. Systems of equations with three basic quantities
Different systems of equations have been developed for electric and magnetic phenomena with only
three basic quantities.
II. a The electrostatic system of equations, defining the electric charge on the basis of Coulomb’s
law for the force between two electric charges, by taking the permittivity in vacuo to be a
dimensionless quantity, equal to unity.
II. b The electromagnetic system of equations, defining the electric currents on the basis of the law
for the force between two electric currents, by taking the permeability in vacuo to be a
dimensionless quantity, equal to unity.
II. c The symmetric system of equations, using the electric quantities from system II. a, and the
magnetic quantities from system II. b. As a result of combining the two sets of quantities, the
J
velocity of light in vacuo appears explicitly in some of the equations combining electric with
magnetic quantities.
Also for these systems of equations founded on three basic quantities two versions, a rationalized
and a non-rationalized version, are possible. However, only the non-rationalized version has been
commonly used.
For reasons of brevity, only equations founded on four basic quantities have been included in the tables.
Since, however, in atomic and nuclear physics, a system of equations founded on three basic quan-
tities, in particular the “symmetric” system (II. c), is commonly used, some of the essential equa-
tions of this latter system are given in the appendix, see page 18.
Units
The quantities occurring in the tables have to be measured in units belonging to a unit system
founded on four basic units. The following four basic units of the International System of Units are
used as the basic units for electricity and magnetism (MKSA system):
metre, kilogramme, second and ampere.
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The quantities occurring in the three systems of equations founded on three basic quantities have
to be measured respectively in units of
a. the electrostatic CGS system,
b. the electromagnetic CGS system,
c. the “symmetric” CGS system (or “Gauss system”),
each of which is founded on the three basic units:
centimetre, gramme and second.
Some units of the “symmetric” CGS system have been indicated in the remarks column.
MKSA system,
In order to relate the units of these CGS systems to the corresponding units of the
the tables contain also units of the following two systems:
A. the system founded on the four basic units:
centimetre, gramme, second and franklin,
B. the system founded on the four basic units:
centimetre, gramme, second and biot,
where the franklin and the biot are units of charge and current respective-y, as defined in the ta es.
The relations between the units of the systems A and B and those of the MKSA system can be
expressed in the form of equations with conversion factors which are pure numbers. The franklin
Y
and the biot correspond respectively to the electrostatic CGS unit of charge and the electromagnetic
CGS unit of current. From these correspondences others follow; beneath the names of the units for
the systems A and B, there are given in square brackets the names of the corresponding units of
the electrostatic or the electromagnetic CGS systems. In the remarks column, these corresponding
units are expressed in terms of CGS units of mechanics.
The tables contain in general the units of the system A for quantities related to electrostatics and
those of the system B for quantities related to magnetism. This selection corresponds to the “sym-
metric CGS unit system” (or “Gauss system”) which should be used in connection with the “sym-
metric’’ system of equations II. c. A particular exception is the occurrence of the unit biot (corre-
sponding to the electromagnetic CGS unit of electric current) item No. 5-1.c; where it is introduced
for the purpose of giving its definition.
For the rationalized quantities, only the MKSA units have been given. For the non-rationalized
quantities, the units of the systems A or B are given. This does not imply that these latter units can
not be used for rationalized quantities.
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5. Electricity and Magnetism
Quantities
5-1 .I . . .5-6.3
Quantity Symbol
Definition I)
Remarks
dQ
electric current
I I=-
dt
electric charge,
Q = 5 Zdt
quantity of electricity
-
___ ~-
__
volume density of charge,
Charge divided by volume.
e
:harge density
surface density of charge U
Charge divided by surface area.
slectric field strength
Force, exerted by electric field on an
electric charge, divided by that charge.
4ectric potential
For electrostatic fields, a scalar quan-
tity the gradient of which, with reversed
sign, is equal to the electric field strength.
>otential difference,
The potential difference between point 1
:ension
md point 2 is the line integral from 1 to 2
Df the electric field strength.
!lectromotive force E
') The statements in this column are given merely for identification and they are not intended to be complete definitions.
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5. Electricity and Magnetism
Units
5-1 .a. . 5-6.b
Name of unit
lnternatic
Item and in certain
Remarks
sym bo Definition Conversion factors
:ases abbreviation
No.
for uni
for this name
I
-
5-1 .a ampere A The ampere is the unit of 1 For details, see IS0 Re-
commendation R 31/Part I.
electric current defined un-
der that name by the Con-
férence Generale des Poids
et Mesures.
1 electrostatic CGS unit of elec-
franklin per See definition 5-2.b. 1 Frls = 10 e-' A
5-1. b
= 3.335 64 x IO-'' A
second, Fr/s
tric current = I cm: .g+. s-2
= 5' Bi
[corresponds to
= 1 ergt.cmt.s-'Ql Fris
the electrostatic
For velocity of light in vacuoc,
CGS unit of
see 5-40.1
electric current]
c = C cm/s and
= 2.99792 X IO"
For e, see Introduction.
1 electromagnetic CGS unit of
5-1 .c biot, Bi Thls unit of electric current 1 BI = 10A
is that constant currentwhich, electric current
[corresponds to
the electromag- when maintained in two pa-
= 1 cmt *gt .s-' = 1 dyn'sl Bi
rallel rectilinear conductors
netic CGS unit of
electric current] of infinite length and of neg-
1 biot is equal to 1 decaampere.
ligible circular cross-section
and placed at a distance of
1 centimetre apart in vacuo,
would produce between
a force
these conductors
equal to 2 dynes per centi-
metre length.
~
1 C = 1 A-s
5-2.a coulomb C
of charge is that 1 Fr = IO<-' C 1 electrostatic CGS unit of elec-
5-2.b franklin. Fr This unit
C
[corresponds to charge, which exerts on an = 3.335 64 x IO-''
tric charge = 1 cm; * gt * s-'
= c-1 Bi .s
the electrostatic equal charge at a distance of
= 1 ergt. cmtl 1 Fr
CGS unit of 1 centimetre in vacuo a force
For c, see Introduction.
electric charge] of 1 dyne.
5-3.a coulomb per C/m3
cubic metre
C/m2
5-4.a coulomb per
square metre
5-5 .a volt per metre 1 V/m = 1 N/C
1 dyn/Fr =10-6c V/m 1 electrostatic CGS unit of elec-
5-5.b dyne perfranklin,
tric field strength
= 2.997 92 x IO' Vin
dyn/Fr
[corresponds to
= 1 cm-*. gt s-lS 1 dyn/Fr
the electrostatic
For c, see Introduction.
CGS unitofelectril
field strength]
1 V 1 mZ.kg.~-~.A-'
V 1 V = 1 W/A
5-6.a volt
For watt, see 3-23.a,
iSO/R 31 /Part 111.
1 electrostatic CGS unit of elec-
1 erg/Fr = 10-8c V
5-6.b
erg per franklin,
= 2,99792 x IO2 V tric potential
erg/Fr
= 1 cm* *gt es-' 1 erg/Fr
[corresponds to
the electrostatic
For c, see Introduction.
CGS unitofelectril
potential]
* See Introduction, Special remarks.
t This is not contained in the relevant IEC publications.
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5. Electricity and Magnetism (continued)
Quantities
5-7.1 . . .5-16.1
tern
Symbol Definition l) Remarks
Quantity
No.
The displacement is a vector quantity,
5-7.1 displacement, D
the divergence of which is equal to the
(rationalized displacement)
charge density.
~-
rhis quantity is sometimes called
5-8.1 non-rationalized D' The non-rationalized displacement is a
vector quantity, the divergence of which alectric induction.
dis placement
D'= 4xD
is equal to 4n times the charge density.
electric flux, !P The electric flux across a surface element
5-9.1
is the scalar product of the surface element
flux of displacement,
(flux of rationalized and the displacement.
disolacement)
The flux of non-rationalized displacement Y/= 4x Y
5-10.1 flux of non-rationalized
across a surface element is the scalar
displacement
product of the surface element and the
non-rationalized displacement.
Charge divided by potential difference.
5-1 1 .I capacitance C
~ ~
Displacement divided by electric field
5-1 2.1 permittivity F
strength.
permittivity of vacuum = 10" 5-2(4n)-1 F/m
5-1 2.;
...