EN 62226-2-1:2005

SLOVENSKI SIST EN 62226-2-1:2005

STANDARD
junij 2005
Izpostavljenost električnim in magnetnim poljem v nizkem in srednjem
frekvenčnem obsegu – Metode za izračunavanje trenutne gostote in
notranjega induciranega električnega polja v človeškem telesu – 2-1. del:
Izpostavljenost magnetnim poljem – 2D model
Exposure to electric or magnetic fields in the low and intermediate frequency range –
Methods for calculating the current density and internal electric field induced in the
human body – Part 2-1: Exposure to magnetic fields – 2D models
ICS 13.280; 17.220.20 Referenčna številka
©  Standard je založil in izdal Slovenski inštitut za standardizacijo. Razmnoževanje ali kopiranje celote ali delov tega dokumenta ni dovoljeno

EUROPEAN STANDARD EN 62226-2-1
NORME EUROPÉENNE
EUROPÄISCHE NORM January 2005

ICS 17.220.20
English version
Exposure to electric or magnetic fields
in the low and intermediate frequency range –
Methods for calculating the current density
and internal electric field induced in the human body
Part 2-1: Exposure to magnetic fields –
2D models
(IEC 62226-2-1:2004)
Exposition aux champs électriques  Sicherheit in elektrischen oder
ou magnétiques à basse magnetischen Feldern im niedrigen und
et moyenne fréquence – mittleren Frequenzbereich –
Méthodes de calcul des densités Verfahren zur Berechnung der induzierten
de courant induit et des champs Körperstromdichte und des im
électriques induits dans le corps humain menschlichen Körper induzierten
Partie 2-1: Exposition à des champs elektrischen Feldes
magnétiques – Teil 2-1: Exposition gegenüber
Modèles 2D magnetischen Feldern –
(CEI 62226-2-1:2004) 2D-Modelle
(IEC 62226-2-1:2004)
This European Standard was approved by CENELEC on 2004-12-01. CENELEC members are bound to
comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration.

Up-to-date lists and bibliographical references concerning such national standards may be obtained on
application to the Central Secretariat or to any CENELEC member.

This European Standard exists in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CENELEC member into its own language and
notified to the Central Secretariat has the same status as the official versions.

CENELEC members are the national electrotechnical committees of Austria, Belgium, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden,
Switzerland and United Kingdom.

CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung

Central Secretariat: rue de Stassart 35, B - 1050 Brussels

© 2005 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.

Ref. No. EN 62226-2-1:2005 E
Foreword
The text of document 106/79/FDIS, future edition 1 of IEC 62226-2-1, prepared by IEC TC 106,
Methods for the assessment of electric, magnetic and electromagnetic fields associated with human
exposure, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as
EN 62226-2-1 on 2004-12-01.
1)
This Part 2-1 is to be used in conjunction with EN 62226-1 .
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (dop) 2005-09-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2007-12-01
__________
Endorsement notice
The text of the International Standard IEC 62226-2-1:2004 was approved by CENELEC as a
European Standard without any modification.
__________
1)
To be published.
NORME CEI
INTERNATIONALE IEC
62226-2-1
INTERNATIONAL
Première édition
First edition
STANDARD
2004-11
Exposition aux champs électriques ou
magnétiques à basse et moyenne fréquence –
Méthodes de calcul des densités de courant
induit et des champs électriques induits
dans le corps humain –
Partie 2-1:
Exposition à des champs magnétiques –
Modèles 2D
Exposure to electric or magnetic fields
in the low and intermediate frequency range –
Methods for calculating the current density
and internal electric field induced
in the human body –
Part 2-1:
Exposure to magnetic fields – 2D models
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For price, see current catalogue

62226-2-1 ” IEC:2004 – 3 –
CONTENTS
FOREWORD.9
INTRODUCTION.13
1 Scope .15
2 Analytical models .15
2.1 General .15
2.2 Basic analytical models for uniform fields .17
3 Numerical models.19
3.1 General information about numerical models .19
3.2 2D models – General approach.21
3.3 Conductivity of living tissues .23
3.4 2D Models – Computation conditions .25
3.5 Coupling factor for non-uniform magnetic field.25
3.6 2D Models – Computation results.27
4 Validation of models .31
Annex A (normative) Disk in a uniform field .33
Annex B (normative) Disk in a field created by an infinitely long wire.39
Annex C (normative) Disk in a field created by 2 parallel wires with balanced currents .55
Annex D (normative) Disk in a magnetic field created by a circular coil .77
Annex E (informative) Simplified approach of electromagnetic phenomena.101
Annex F (informative) Analytical calculation of magnetic field created by simple
induction systems: 1 wire, 2 parallel wires with balanced currents and 1 circular coil.105
Annex G (informative) Equation and numerical modelling of electromagnetic
phenomena for a typical structure: conductive disk in electromagnetic field.109
Bibliography .113
Figure 1 – Conducting disk in a uniform magnetic flux density.17
nd
Figure 2 – Finite elements meshing (2 order triangles) of a disk, and detail .21
Figure 3 – Conducting disk in a non-uniform magnetic flux density.23
Figure 4 – Variation with distance to the source of the coupling factor for non-uniform
magnetic field, K, for the three magnetic field sources (disk radius R = 100 mm) .29
Figure A.1 – Current density lines J and distribution of J in the disk .33
Figure A.2 – J = f [r]: Spot distribution of induced current density calculated along a
diameter of a homogeneous disk in a uniform magnetic field.35
Figure A.3 – J = f [r]: Distribution of integrated induced current density calculated
i
along a diameter of a homogeneous disk in a uniform magnetic field.37
Figure B.1 – Disk in the magnetic field created by an infinitely straight wire .39
Figure B.2 – Current density lines J and distribution of J in the disk (source: 1 wire,
located at d = 10 mm from the edge of the disk).41

62226-2-1 ” IEC:2004 – 5 –
Figure B.3 – Spot distribution of induced current density along the diameter AA of the
disk (source: 1 wire, located at d = 10 mm from the edge of the disk).41
Figure B.4 – Distribution of integrated induced current density along the diameter AA
of the disk (source: 1 wire, located at d = 10 mm from the edge of the disk) .43
Figure B.5 – Current density lines J and distribution of J in the disk (source: 1 wire,
located at d = 100 mm from the edge of the disk).43
Figure B.6 – Distribution of integrated induced current density along the diameter AA
of the disk (source: 1 wire, located at d = 100 mm from the edge of the disk) .45
Figure B.7 – Parametric curve of factor K for distances up to 300 mm to a source
consisting of an infinitely long wire (disk: R = 100 mm) .47
Figure B.8 – Parametric curve of factor K for distances up to 1 900 mm to a source
consisting of an infinitely long wire (disk: R = 100 mm) .49
Figure B.9 – Parametric curve of factor K for distances up to 300 mm to a source
consisting of an infinitely long wire (disk: R = 200 mm) .51
Figure B.10 – Parametric curve of factor K for distances up to 1 900 mm to a source
consisting of an infinitely long wire (disk: R = 200 mm) .53
Figure C.1 – Conductive disk in the magnetic field generated by 2 parallel wires with
balanced currents .55
Figure C.2 – Current density lines J and distribution of J in the disk (source: 2 parallel
wires with balanced currents, separated by 5 mm, located at d = 7,5 mm from the
edge of the disk).57
Figure C.3 – J = f [r]: Distribution of integrated induced current density calculated
i
along the diameter AA of the disk (source: 2 parallel wires with balanced currents,
separated by 5 mm, located at d = 7,5 mm from the edge of the disk) .57
Figure C.4– Current density lines J and distribution of J in the disk (source: 2 parallel
wires with balanced currents separated by 5 mm, located at d = 97,5 mm from the
edge of the disk).59
Figure C.5 – J f [r]: Distribution of integrated induced current density calculated
i =
along the diameter AA of the disk (source: 2 parallel wires with balanced currents
separated by 5 mm, located at d = 97,5 mm from the edge of the disk).59
Figure C.6 – Parametric curves of factor K for distances up to 300 mm to a source
consisting of 2 parallel wires with balanced currents and for different distances e
between the 2 wires (homogeneous disk R = 100 mm) .61
Figure C.7 – Parametric curves of factor K for distances up to 1 900 mm to a source
consisting of 2 parallel wires with balanced currents and for different distances e
between the 2 wires (homogeneous disk R = 100 mm) .65
Figure C.8 – Parametric curves of factor K for distances up to 300 mm to a source
consisting of 2 parallel wires with balanced currents and for different distances e
between the 2 wires (homogeneous disk R = 200 mm) .69
Figure C.9 – Parametric curves of factor K for distances up to 1 900 mm to a source
consisting of 2 parallel wires with balanced currents and for different distances e
between the 2 wires (homogeneous disk R = 200 mm) .73
Figure D.1 – Conductive disk in a magnetic field created by a coil.77
Figure D.2 –Current density lines J and distribution of J in the disk (source: coil of
radius r = 50 mm, conductive disk R = 100 mm, d = 5 mm).79
Figure D.3 – J = f [r]: Distribution of integrated induced current density calculated
i
along the diameter AA of the disk (source: coil of radius r = 50 mm, conductive disk
R = 100 mm, d = 5 mm) .79
Figure D.4 – Current density lines J and distribution of J in the disk (source: coil of
radius r = 200 mm, conductive disk R = 100 mm, d = 5 mm).81

62226-2-1 ” IEC:2004 – 7 –
Figure D.5 – J = f [r]: Distribution of integrated induced current density calculated
i
along the diameter AA of the disk (source: coil of radius r = 200 mm, conductive disk
R = 100 mm, d = 5 mm) .81
Figure D.6 – Current density lines J and distribution of J in the disk (source: coil of
radius r = 10 mm, conductive disk R = 100 mm, d = 5 mm).83
Figure D.7 – J = f [r]: Distribution of integrated induced current density calculated
i
along the diameter AA of the disk (source: coil of radius r = 10 mm, conductive disk
R = 100 mm, d = 5 mm) .83
Figure D. 8 – Parametric curves of factor K for distances up to 300 mm to a source
consisting of a coil and for different coil radius r (homogeneous disk R = 100 mm) .85
Figure D.9 – Parametric curves of factor K for distances up to 1 900 mm to a source
consisting of a coil and for different coil radius r (homogeneous disk R = 100 mm) .89
Figure D.10 – Parametric curves of factor K for distances up to 300 mm to a source
consisting of a coil and for different coil radius r (homogeneous disk R = 200 mm) .93
Figure D.11 – Parametric curves of factor K for distances up to 1 900 mm to a source
consisting of a coil and for different coil radius r (homogeneous disk R = 200 mm) .97
Table 1 – Numerical values of the coupling factor for non-uniform magnetic field K for
different types of magnetic field sources, and different distances between sources and
conductive disk (R = 100 mm) .31
Table B.1 – Numerical values of factor K for distances up to 300 mm to a source
consisting of an infinitely long wire (disk: R = 100 mm) .47
Table B.2 –Numerical values of factor K for distances up to 1 900 mm to a source
consisting of an infinitely long wire (disk: R = 100 mm) .49
Table B.3 – Numerical values of factor K for distances up to 300 mm to a source
consisting of an infinitely long wire (disk: R = 200 mm) .51
Table B.4 –Numerical values of factor K for distances up to 1 900 mm to a source
consisting of an infinitely long wire (disk: R = 200 mm) .53
Table C.1 – Numerical values of factor K for distances up to 300 mm to a source
consisting of 2 parallel wires with balanced currents (homogeneous disk: R = 100 mm) .63
Table C.2 – Numerical values of factor K for distances up to 1 900 mm to a source
consisting of 2 parallel wires with balanced currents (homogeneous disk: R = 100 mm) .67
Table C.3 – Numerical values of factor K for distances up to 300 mm to a source
consisting of 2 parallel wires with balanced currents (homogeneous disk: R = 200 mm) .71
Table C.4 – Numerical values of factor K for distances up to 1 900 mm to a source
consisting of 2 parallel wires with balanced currents (homogeneous disk: R = 200 mm) .75
Table D.1 – Numerical values of factor K for distances up to 300 mm to a source
consisting of a coil (homogeneous disk: R = 100 mm) .87
Table D.2 – Numerical values of factor K for distances up to 1 900 mm to a source
consisting of a coil (homogeneous disk: R = 100 mm) .91
Table D.3 – Numerical values of factor K for distances up to 300 mm to a source
consisting of a coil (homogeneous disk: R = 200 mm) .95
Table D.4 – Numerical values of factor K for distances up to 1 900 mm to a source
consisting of a coil (homogeneous disk: R = 200 mm) .99

62226-2-1 ” IEC:2004 – 9 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
EXPOSURE TO ELECTRIC OR MAGNETIC FIELDS
IN THE LOW AND INTERMEDIATE FREQUENCY RANGE –
METHODS FOR CALCULATING THE CURRENT DENSITY
AND INTERNAL ELECTRIC FIELD INDUCED IN THE HUMAN BODY –
Part 2-1: Exposure to magnetic fields –
2D models
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
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patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 62226-2-1 has been prepared by IEC technical committee 106:
Methods for the assessment of electric, magnetic and electromagnetic fields associated with
human exposure.
This Part 2-1 is intended to be used in conjunction with the first edition of IEC 62226-1:2004,
Exposure to electric or magnetic fields in the low and intermediate frequency range – Methods
for calculating the current density and internal electric field induced in the human body –
Part 1: General.
62226-2-1 ” IEC:2004 – 11 –
The text of this standard is based on the following documents:
FDIS Report on voting
106/79/FDIS 106/83/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.
This International Standard constitutes Part 2-1 of IEC 62226 series, which will regroup
several international standards and technical reports within the framework of the calculation
of induced current densities and internal electric fields, and will be published under the
general title of Exposure to electric or magnetic fields in the low and intermediate frequency
range – Methods for calculating the current density and internal electric field induced in the
human body.
This series is planned to be published according to the following structure:
Part 1: General
Part 2: Exposure to magnetic fields
Part 2-1 : 2D models
Part 2-2 : 3D models
Part 2-3 : Guidelines for practical use of coupling factors
Part 3: Exposure to electric fields
Part 3-1: Analytical and 2D numerical models
Part 3-2: 3D numerical models
Part 4: Electrical parameters of human living tissues (Technical Report)
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.
62226-2-1 ” IEC:2004 – 13 –
INTRODUCTION
Public interest concerning human exposure to electric and magnetic fields has led
international and national organisations to propose limits based on recognised adverse
effects.
This standard applies to the frequency range for which the exposure limits are based on the
induction of voltages or currents in the human body, when exposed to electric and magnetic
fields. This frequency range covers the low and intermediate frequencies, up to 100 kHz.
Some methods described in this standard can be used at higher frequencies under specific
conditions.
The exposure limits based on biological and medical experimentation about these
fundamental induction phenomena are usually called “basic restrictions”. They include safety
factors.
The induced electrical quantities are not directly measurable, so simplified derived limits are
also proposed. These limits, called “reference levels”, are given in terms of external electric
and magnetic fields. They are based on very simple models of coupling between external
fields and the body. These derived limits are conservative.
Sophisticated models for calculating induced currents in the body have been used and are the
subject of a number of scientific publications. These use numerical 3D electromagnetic field
computation codes and detailed models of the internal structure with specific electrical
characteristics of each tissue within the body. However such models are still developing; the
electrical conductivity data available at present has considerable shortcomings; and the
spatial resolution of models is still advancing. Such models are therefore still considered to be
in the field of scientific research and at present it is not considered that the results obtained
from such models should be fixed indefinitely within standards. However it is recognised that
such models can and do make a useful contribution to the standardisation process, specially
for product standards where particular cases of exposure are considered. When results from
such models are used in standards, the results should be reviewed from time to time to
ensure they continue to reflect the current status of the science.

62226-2-1 ” IEC:2004 – 15 –
EXPOSURE TO ELECTRIC OR MAGNETIC FIELDS
IN THE LOW AND INTERMEDIATE FREQUENCY RANGE –
METHODS FOR CALCULATING THE CURRENT DENSITY
AND INTERNAL ELECTRIC FIELD INDUCED IN THE HUMAN BODY –
Part 2-1: Exposure to magnetic fields –
2D models
1 Scope
This part of IEC 62226 introduces the coupling factor K, to enable exposure assessment for
complex exposure situations, such as non-uniform magnetic field or perturbed electric field.
The coupling factor K has different physical interpretations depending on whether it relates to
electric or magnetic field exposure.
The aim of this part is to define in more detail this coupling factor K, for the case of simple
models of the human body, exposed to non-uniform magnetic fields. It is thus called “coupling
factor for non-uniform magnetic field”.
All the calculations developed in this document use the low frequency approximation in which
displacement currents are neglected. This approximation has been validated in the low
frequency range in the human body where parameter HZ < For frequencies up to a few kHz, the ratio of conductivity and permittivity should be calculated
to validate this hypothesis.
2 Analytical models
2.1 General
Basic restrictions in guidelines on human exposure to magnetic fields up to about 100 kHz are
generally expressed in terms of induced current density or internal electric field. These
electrical quantities cannot be measured directly and the purpose of this document is to give
methods and tools on how to assess these quantities from the external magnetic field.
The induced current density J and the internal electric field E are closely linked by the simple
i
relation:
J = V E (1)
i
where Vis the conductivity of living tissues.
For simplicity, the content of this standard is presented in terms of induced current densities
J, from which values of the internal electric field can be easily derived using the previous
formula.
62226-2-1 ” IEC:2004 – 17 –
Analytical models have been used in EMF health guidelines to quantify the relationship
between induced currents or internal electric field and the external fields. These involve
assumptions of highly simplified body geometry, with homogeneous conductivity and uniform
applied magnetic field. Such models have serious limitations. The human body is a much
more complicated non-homogeneous structure, and the applied field is generally non-uniform
because it arises from currents flowing through complex sets of conductors and coils.
For example, in an induction heating system, the magnetic field is in fact the superposition of
an excitation field (created by the coils), and a reaction field (created by the induced currents
in the piece). In the body, this reaction field is negligible and can be ignored.
Annex E and F presents the analytical calculation of magnetic field H created by simple
sources and Annex G presents the analytical method for calculating the induced current in a
conductive disk.
2.2 Basic analytical models for uniform fields
The simplest analytical models used in EMF health guidelines are based on the hypothesis of
coupling between a uniform external magnetic field at a single frequency, and a homogeneous
disk of given conductivity, used to represent the part of the body under consideration, as
1) )
illustrated in Figure 1. Such models are used for example in the ICNIRP and NRPB
guidelines.
z
Excitation field
y
B uniform
Induced currents
x
IEC  1549/04
Figure 1 – Conducting disk in a uniform magnetic flux density
The objective of such a modelling is to provide a simple method to assess induced currents
and internal fields. This very first approach is simple and gives conservative values of the
electrical quantities calculated.
For alternating magnetic fields, the calculation assumes that the body or the part of the body
exposed is a circular section of radius r, with conductivity V. The calculation is made under
maximum coupling conditions i.e. with a uniform magnetic field perpendicular to this disk. In
this case, the induced current density at radius r is given by:
rV dB
(2)
J (r)
2 dt
where B is the magnetic flux density.
___________
)
Health Physics (vol. 74, n° 4, April 1998, pp 496-522).
)
NRPB, 1993, Board Statement on Restrictions on Human Exposure to Static and Time-varying Electromagnetic
Fields and Radiation, Volume 4, No 5, 1.

62226-2-1 ” IEC:2004 – 19 –
For a single frequency f, this becomes:
J (r) VSrfB (3)
As illustrated in Figure 1 (see also Annex A), induced currents are distributed inside the disk,
following a rotation symmetry around the central axis of the disk. The value of induced
currents is minimum (zero) at the centre and maximum at the edge of the disk.
3 Numerical models
3.1 General information about numerical models
Simple models, which take into consideration field characteristics, are more realistic than
those, which consider only uniform fields, such as analytical ones.
Electromagnetic fields are governed by Maxwell's equations. These equations can be
accurately solved in 2- or 3-dimensional structures (2D or 3D computations) using various
numerical methods, such as:
– finite elements method (FEM);
– boundary integral equations method (BIE or BEM), or moment method;
– finite differences method (FD);
– impedance method (IM).
Others methods derive from these. For example, the following derive from the finite
differences method:
– finite difference time domain (FDTD);
– frequency dependent finite difference time domain ((FD) TD);
– scalar potential finite difference (SPFD).
Hybrid methods have been also developed in order to improve modelling (example: FE + BIE).
Commercially available software can accurately solve Maxwell’s equations by taking into
account real geometrical structures and physical characteristics of materials, as well as in
steady state or transient current source conditions.
The choice of the numerical method is guided by a compromise between accuracy,
computational efficiency, memory requirements, and depends on many parameters, such as:
– simulated field exposure;
– size and shape of human object to be modelled;
– description level of the human object (size of voxel), or fineness of the meshing;
– frequency range, in order to neglect some parts of Maxwell’s relations (example:
displacement current term for low frequency);
– electrical supply signal (sinusoidal, periodic or transient);

62226-2-1 ” IEC:2004 – 21 –
– type of resolution (2D or 3D);
– mathematical formulation;
– linear or non linear physical parameters (conductivity, …);
– performances of the numerical method;
– etc.
Computation times can therefore vary significantly.
Computed electromagnetic values can be presented in different ways, including:
– distributions of magnetic field H, flux density B, electric field E, current density J. These
distributions can be presented in the form of coloured iso-value lines and/or curves,
allowing a visual assessment of the phenomena and the possible "hot" points;
– local or spatial averaged integral values of H, B, E, J, etc.;
– global magnitude values: active power.
These methods are very helpful for solving specific problems; however they cannot be
conveniently used to study general problems.
3.2 2D models – General approach
In order to gain quickly an understanding of induced currents in the human body, 2D
simulations can be performed using a simple representation of the body (a conductive disk:
example of modelling given in Figure 2) in a non-uniform magnetic field, as illustrated in
Figure 3.
100 0 100
IEC  1550/04
nd
Figure 2 – Finite elements meshing (2 order triangles) of a disk, and detail

62226-2-1 ” IEC:2004 – 23 –
Excitation field
B non-uniform
z
y
x
Induced currents
Source current
IEC  1551/04
Figure 3 – Conducting disk in a non-uniform magnetic flux density
Starting from Maxwell’s relations (low frequency approximation), a single equation can be
obtained with a specific mathematical formulation (see Annex G):
* *
*
1 wH wH
r ex
㱟
’ H P P
(4)
r 0 0
wt wt
where
H is the excitation field created by the source currents,
ex
H is the reaction field created by the induced currents:
r
* *
J Curl(H ) (5)
r
Equation (4) is solved for a 2D geometry using the finite element method applied to the
meshing illustrated in Figure 2.
The excitation field H is calculated for three non-uniform field sources using the analytical
ex
expressions given in Annex F. The three sources modelled are: a current flowing through an
infinitely long wire, two parallel wires with balanced currents and a current loop.
X, Y, Z co-ordinates are used. XY-plane is the study plane of the disk in which induced
currents are generated. Except for the particular case where H is uniform, source currents
ex
are in the same plane. Only the one component of H along the Z-axis is taken into account.
ex
The induced currents in the disk have two components J , J .
x y
Examples of numerical results are presented in Annexes A to D.
3.3 Conductivity of living tissues
The computation of induced currents in the body from the external magnetic field is strongly
affected by the conductivity of the different tissues in the body and their anisotropic
properties. The results presented in this document assume that the conductivity is
homogeneous and isotropic with a value of 0,2 S/m. This value is consistent with the average
value assumed in EMF health guidelines.

62226-2-1 ” IEC:2004 – 25 –
The most recent assessment of the available data indicates the average conductivity to be
slightly higher: 0,22 S/m. More experimental work is in progress to provide more reliable
conductivity information. The preferred average conductivity could be changed in the future as
improved information becomes available. In that situation the values of induced current
presented in this report should be revised in proportion to the conductivity. Nevertheless, the
coupling factor for non-uniform magnetic field K, defined previously, is independent of the
conductivity.
3.4 2D Models – Computation conditions
2D computation codes were used to simulate the current induced in a conductive disk by an
alternating magnetic field of frequency f, produced by four different field sources:
– uniform and unidirectional field in all considered space (Annex A);
– current flowing through one infinitely long wire (Annex B);
– 2 parallel wires with balanced currents (Annex C);
– current flowing through one circular coil. (Annex D).
In order to facilitate comparisons with analytical models, all numerical values of computation
parameters are fixed throughout this standard:
– radius of disk: R = 100 mm, and R = 200 mm;
– conductivity of disk: V = 0,2 S/m;
– field sources at 50 Hz frequency.
With the exception of the first of the four field sources, the magnetic field from the source is
non-uniform, decreasing with increasing distance from the source. In these cases the field
value quoted is the value at the edge of the disk closest to the source.
The reaction field created by the induced current in the disk is negligible (due to the very low
conductivity of the disk) and is ignored.
3.5 Coupling factor for non-uniform magnetic field
The current density induced in the disk by a localised source of magnetic field (therefore
generating a non-uniform field), is always lower than the current density that would be
induced by a uniform magnetic field whose magnitude is equal to the magnitude of the non-
uniform field at the edge of the disk closest to the localised source. This reduction of induced
current for non-uniform field sources is quantified using the coupling factor for non-uniform
magnetic field K, which is physically defined as:
J
nonuniform
K
(6)
J
uniform
where
J is the maximum induced current density in the disk exposed to the non-uniform
nonuniform
magnetic field from a localised source,
J is the maximum induced current density in the disk exposed to a uniform
uniform
magnetic field.
J is derived from equation (3):
uniform
ǻ
J J(r R) SRfB
(7)
uniform
62226-2-1 ” IEC:2004 – 27 –
It shall be noted that K = 1 when the field is uniform. Annex A illustrates the current
distribution in a disk of radius R = 100 mm for an applied uniform field B = 1,25 µT. The
coupling factor for non-uniform magnetic field K is calculated numerically for the three non-
uniform sources of field, in Annex B, C and D respectively.
NOTE 1 Calculated spot values of induced current densities have been averaged in this document (see Annexes
A to D). So the values of J and J given here above are averaged values, integrated over a cross
uniform nonuniform
section of 1 cm , perpendicular to the current direction.
NOTE 2 Values of K are calculated at a frequency of 50 Hz. Nevertheless, due to the low frequency
approximation, these values are also valid for the whole frequency range covered by this standard i.e. up to
100 kHz. Also, due to the low frequency approximation, K is independent of the conductivity.
For real cases, the spatial arrangement of field cannot easily be described in equations, and
the coupling factor K can only be estimated (for example using the table values given in
annexes of this document).
3.6 2D Models – Computation results
This subclause is a summary of the detailed numerical results given in Annexes B, C and D,
which deal with the three types of sources. Whatever the source, the model of human body is
treated as a homogeneous disk:
– radius of disk: R = 100 mm and R = 200 mm;
– conductivity of disk: V = 0,2 S/m .
For comparison between the different types of sources (i.e. coupling models), the value of the
local maximum magnetic field is normalised. Whatever the source, the magnetic field
magnitude at the edge of the disk closest to the source is equal to the uniform field magnitude
(i.e. B = 1,25 µT, see annex A).
Table 1 presents a selection from Annexes B, C and D of the numerical values of the factor K
for the three different sources and for a disk radius R = 100 mm. These results are also
presented in a graphic form in Figure 4.
All the values in Table 1 are less than 1, and sometimes much less than 1, by a factor up to
about 100. This demonstrates that, for a specified maximum current density in the disk, the
corresponding magnetic field at the edge of the disk can have a wide range of values
depending on the characteristics of the field source and on the distance between the disk and
source.
The uniform field approximation (for which K = 1) is appropriate only when the distance
between the source and the “human disk” becomes large relative to the size of the disk
(typically 10 times the disk radius). At more usual distance of exposure from, for example,
domestic appliances, the non-uniformity of the magnetic field with the distance has to be
taken into account in the way presented in this standard.

62226-2-1 ” IEC:2004 – 29 –
1,0
0,9
0,8
0,7
0,6
0,5
0,4
Source: coil (r = 2,5 mm)
0,3
Source: 2 wires (e = 5 mm)
0,2
Source: 1 wire
0,1
0 50 100 150 200 250 300 350
Distance between the source and the human disk (mm)
IEC  1552/04
NOTE Values for distances up to 1 900 mm, and for other wire separations and coil sizes are given in Annexes B,
C and D.
Figure 4 – Variation with distance to the source of the coupling factor for non-uniform
magnetic field, K, for the three magnetic field sources (disk radius R = 100 mm)
K (p.u.)
62226-2-1 ” IEC:2004 – 31 –
Table 1 – Numerical values of the coupling factor for non-uniform magnetic field K for
different types of magnetic field sources, and different distances between sources and
conductive disk (R = 100 mm)
K factor for different sources
Distance between the
2 parallel wires with
source and the disk 1 circular coil
1 infinite wire balanced currents,
2,5 mm radius
5 mm spaced
mm
10 0,229 0,094 0,034
20 0,350 0,172 0,080
30 0,432 0,237 0,126
40 0,492 0,291 0,169
50 0,540 0,337 0,208
60 0,579 0,378 0,244
70 0,611 0,413 0,277
80 0,638 0,444 0,308
90 0,661 0,472 0,336
100 0,682 0,497 0,361
110 0,700 0,520 0,385
120 0,716 0,540 0,407
130 0,730 0,559 0,428
140 0,743 0,576 0,447
150 0,754 0,592 0,465
160 0,765 0,607 0,482
170 0,775 0,621 0,497
180 0,783 0,634 0,512
190 0,792 0,645 0,526
200 0,799 0,657 0,539
210 0,806 0,667 0,552
220 0,813 0,677 0,563
230 0,819 0,686 0,575
240 0,824 0,695 0,585
250 0,830 0,703 0,595
260 0,835 0,711 0,605
270 0,839 0,718 0,614
280 0,844 0,725 0,623
290 0,848 0,732 0,631
300 0,852 0,738 0,639
NOTE Values for distances up to 1 900 mm, and for other wire separations and coil sizes are given in Annexes B,
C and D.
4 Validation of models
The validation of the numerical tools used for computation of induced current densities shall
be made by comparison with the results given in the annexes of this standard, which have
been validated by comparison with scientific literature.
Additional information concerning the software used for the validation of numerical
computation can be found in the bibliographic references of IEC 62226-1.

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