IEC 62226-3-1:2007

INTERNATIONAL IEC
STANDARD
CEI
62226-3-1
NORME
First edition
INTERNATIONALE
Première édition
2007-05
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 3-1:
Exposure to electric fields –
Analytical and 2D numerical models

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 3-1:
Exposition à des champs électriques –
Modèles analytiques et numériques 2D
Reference number
Numéro de référence
IEC/CEI 62226-3-1:2007
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form
or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from
either IEC or IEC's member National Committee in the country of the requester.
If you have any questions about IEC copyright or have an enquiry about obtaining additional rights to this publication,
please contact the address below or your local IEC member National Committee for further information.

Droits de reproduction réservés. Sauf indication contraire, aucune partie de cette publication ne peut être reproduite
ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie
et les microfilms, sans l'accord écrit de la CEI ou du Comité national de la CEI du pays du demandeur.
Si vous avez des questions sur le copyright de la CEI ou si vous désirez obtenir des droits supplémentaires sur cette
publication, utilisez les coordonnées ci-après ou contactez le Comité national de la CEI de votre pays de résidence.

IEC Central Office
3, rue de Varembé
CH-1211 Geneva 20
Switzerland
Email: inmail@iec.ch
Web: www.iec.ch
About the IEC
The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes
International Standards for all electrical, electronic and related technologies.

About IEC publications
The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the
latest edition, a corrigenda or an amendment might have been published.
ƒ Catalogue of IEC publications: www.iec.ch/searchpub
The IEC on-line Catalogue enables you to search by a variety of criteria (reference number, text, technical committee,…).
It also gives information on projects, withdrawn and replaced publications.
ƒ IEC Just Published: www.iec.ch/online_news/justpub
Stay up to date on all new IEC publications. Just Published details twice a month all new publications released. Available
on-line and also by email.
ƒ Customer Service Centre: www.iec.ch/webstore/custserv
If you wish to give us your feedback on this publication or need further assistance, please visit the Customer Service
Centre FAQ or contact us:
Email: csc@iec.ch
Tel.: +41 22 919 02 11
Fax: +41 22 919 03 00
A propos de la CEI
La Commission Electrotechnique Internationale (CEI) est la première organisation mondiale qui élabore et publie des
normes internationales pour tout ce qui a trait à l'électricité, à l'électronique et aux technologies apparentées.

A propos des publications CEI
Le contenu technique des publications de la CEI est constamment revu. Veuillez vous assurer que vous possédez
l’édition la plus récente, un corrigendum ou amendement peut avoir été publié.
ƒ Catalogue des publications de la CEI: www.iec.ch/searchpub/cur_fut-f.htm
Le Catalogue en-ligne de la CEI vous permet d’effectuer des recherches en utilisant différents critères (numéro de
référence, texte, comité d’études,…). Il donne aussi des informations sur les projets et les publications retirées ou
remplacées.
ƒ Just Published CEI: www.iec.ch/online_news/justpub
Restez informé sur les nouvelles publications de la CEI. Just Published détaille deux fois par mois les nouvelles
publications parues. Disponible en-ligne et aussi par email.
ƒ Service Clients: www.iec.ch/webstore/custserv/custserv_entry-f.htm
Si vous désirez nous donner des commentaires sur cette publication ou si vous avez des questions, visitez le FAQ du
Service clients ou contactez-nous:
Email: csc@iec.ch
Tél.: +41 22 919 02 11
Fax: +41 22 919 03 00
INTERNATIONAL IEC
STANDARD
CEI
62226-3-1
NORME
First edition
INTERNATIONALE
Première édition
2007-05
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 3-1:
Exposure to electric fields –
Analytical and 2D numerical models

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 3-1:
Exposition à des champs électriques –
Modèles analytiques et numériques 2D
PRICE CODE
XA
CODE PRIX
Commission Electrotechnique Internationale
International Electrotechnical Commission
МеждународнаяЭлектротехническаяКомиссия
For price, see current catalogue
Pour prix, voir catalogue en vigueur

– 2 – 62226-3-1 © IEC:2007
CONTENTS
FOREWORD.5
INTRODUCTION.7

1 Scope.8
2 Exposure to electric field .8
3 General procedure.11
3.1 Shape factor.11
3.2 Procedure .11
4 Human body models .12
4.1 General .12
4.2 Surface area .12
4.3 Semi-spheroidal model.13
4.4 Axisymmetrical body model .15
5 Calculation of induced current .16
5.1 General .16
5.2 Semi-spheroid .16
5.3 Axisymmetrical models .20
5.4 Comparison of the analytical and numerical models .27
6 Influence of electrical parameters .27
6.1 General .27
6.2 Influence of permittivity .27
6.3 Influence of conductivity.28
6.4 Non-homogeneous conductivity.28
7 Measurement of currents induced by electric fields.28
7.1 General .28
7.2 Current flowing to the ground .28

Annex A (normative) Analytical solutions for a spheroid in a uniform electric field.30
Annex B (normative) Human body axisymmetrical model .33
Annex C (informative) Child body model .38
Annex D (informative) Example of use of this standard .40
Annex E (informative) Numerical calculation methods .44

Bibliography.52

Figure 1 – Illustration of the phenomenon of currents induced by electric field in a
human body standing on the ground .10
Figure 2 – Potential lines of the electric field generated by an energised wire in the
absence of any objects (all distances in metres) .10
Figure 3 – A realistic body model .12
Figure 4 – Scheme of the semi-spheroid simulating a human being standing on a zero
potential plane .13
Figure 5 – Equivalent spheroid radius, R, versus height, L, and for different mass, M .15
Figure 6 – The axisymmetrical body model for the reference man (left) and woman
(right).15

62226-3-1 © IEC:2007 – 3 –
Figure 7 – Conductive spheroid exposed to electric field.16
Figure 8 – Calculation of the shape factor for electric field K for an spheroid exposed
E
to an unperturbed electric field.17
Figure 9 – Current density J induced by an unperturbed electric field (1 kV/m, 50 Hz)
S
in a spheroid versus parameter L/R (values in µA/m²).18
Figure 10 – Dimensions and mesh of the semi-spheroid .19
Figure 11 – Distortion of power frequency electric field lines close to the conductive
semi-spheroid .19
Figure 12 – Calculated induced current density J (h) in the body standing in a vertical
A
50 Hz electric field of 1 kV/m .21
Figure 13 – Computation domain .23
Figure 14 – Mesh of the man body model and distortion of power frequency electric
field lines close to model.23
Figure 15 – Distribution of potential lines and 50 Hz electric field magnitude (man
model) .24
Figure 16 – Computation of induced currents J along a vertical axis, and distribution
A
of induced currents in the man model at 50 Hz .24
Figure 17 – Mesh of the woman body model and distortion of power frequency electric
field lines close to model.25
Figure 18 – Distribution of potential lines and 50 Hz electric field magnitude (woman
model) .26
Figure 19 – Computation of induced currents J along a vertical axis, and distribution
A
of induced currents in the woman model at 50 Hz .26
Figure A.1 – Conductive spheroid exposed to electric field .30
Figure B.1 – Normalised axisymmetrical models. Left: man, Right: woman .35
Figure C.1 – Computation of induced currents J along a vertical axis, and distribution
Z
of induced currents in the 10 years reference child model.39
Figure E.1 – Spheroid model.45
Figure E.2 – Space potential model .46
Figure E.3 – Exemple of charge simulation method using rings.47
Figure E.4 – Superficial charges integral equation method, cutting of the body into N
elements.48
Figure E.5 – Mesh of the body using finite element method .49
Figure E.6 – Impedance method .50
Figure E.7 – Yee-method: Electric and magnetic grids for spatial discretization .51

Table 1 – Data for reference man and reference woman .13
Table 2 – Values of arcsin(e) / e for different values of L/R.14
Table 3 – Derived data using spheroid model at 50 Hz .20
Table 4 – Electric field E required to produce basic restrictions J in the neck at
BR BR
50 Hz.22
Table 5 – Comparison of values of the shape factor for electric field K and
E
corresponding current densities for an unperturbed 50 Hz electric field of 1 kV/m .27
Table B.1 – Measures from antropomorphic survey used to construct vertical
dimensions of axisymmetrical model [56] .34

– 4 – 62226-3-1 © IEC:2007
Table B.2 – Measures from antropomorphic survey used to construct the radial
dimensions of axisymmetrical model [56] .34
Table B.3 – Normalised model dimensions.36
Table B.4 – Axisymmetric model dimensions for reference man and reference woman
whose mass and height are defined by ICRP [38] and are given in Table 1.37
Table C.1 – Reference values provided by ICRP for male and female children.38
Table C.2 – Dimensions of the reference children (in m excepted SB in m²) .38
R
Table C.3 – Results of analytical method for the reference children .39
Table D.1 – Normalised dimensions of the women model.41
Table D.2 – Calculation of the dimensions for a specific person.42

62226-3-1 © IEC:2007 – 5 –
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 3-1: Exposure to electric fields –
Analytical and 2D numerical 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
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 62226-3-1 has been prepared by IEC technical committee 106:
Methods for the assessment of electric, magnetic and electromagnetic fields associated with
human exposure.
This standard is 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.
– 6 – 62226-3-1 © IEC:2007
The text of this standard is based on the following documents:
FDIS Report on voting
106/125/FDIS 106/128/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 3-1 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.
A list of all parts of the IEC 62226 series, published under the general title 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, can be found on the IEC
website.
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.
62226-3-1 © IEC:2007 – 7 –
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 models 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 progressing. 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.
– 8 – 62226-3-1 © IEC:2007
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 3-1: Exposure to electric fields –
Analytical and 2D numerical models

1 Scope
This part of IEC 62226 applies to the frequency range for which exposure limits are based on
the induction of voltages or currents in the human body when exposed to electric fields.
This part defines in detail the coupling factor K – introduced by the IEC 62226 series to
enable exposure assessment for complex exposure situations, such as non-uniform magnetic
field or perturbed electric field – for the case of simple models of the human body, exposed to
uniform electric fields. The coupling factor K has different physical interpretations depending
on whether it relates to electric or magnetic field exposure. It is the so called “shape factor for
electric field”.
This part of IEC 62226 can be used when the electric field can be considered to be uniform,
for frequencies up to at least 100 kHz.
This situation of exposure to a “uniform” electric field is mostly found in the vicinity of high
voltage overhead power systems. For this reason, illustrations given in this part are given for
power frequencies (50 Hz and 60 Hz).
2 Exposure to electric field
Alternating electric fields are generated by energised conductors (i.e. under voltage). In the
immediate vicinity of domestic electrical equipment, such as lights, switches, food mixers and
irons, local electric-field strengths about 100 V/m may be found. Such fields are non-uniform,
but their strengths are far below the levels recommended in safety guidelines, so there is no
need of calculation of induced currents in such exposure situations.
Higher electric-field strengths may be found in the vicinity of high voltage equipment such as
electric power line. In the frequency range covered by this standard, it is considered that
exposure from power lines is the only significant exposure source for public regarding safety
guidelines limits.
Guidelines on human exposure to electric fields are generally expressed in terms of induced
current density or internal electric field. These quantities cannot be measured directly and the
purpose of this document is to give guidance on how to assess these quantities induced in the
human body by external (environmental) electric fields E .
62226-3-1 © IEC:2007 – 9 –
The induced current density J and the internal electric field E are closely linked by the simple
i
relation:
J =σ.E (1)
i
where σ is the conductivity of the body tissue under consideration.
For reason of simplification, the content of this standard is presented in terms of induced
current densities J, from which values of internal electric field E can be easily derived using
i
the previous formula.
All the calculation developed in this document use the low frequency approximation in which
displacement currents are negligible, such that εω/σ is less than 1 in the body. This
)
approximation has been checked using published tissue data [29,31] in the low frequency
range and it has been found to be valid for frequencies up to at least 100 kHz and is probably
valid at higher frequencies.
Computations based on sophisticated numerical models of the human body [24] also
demonstrate that this assumption is valid at frequencies up to more than 100 kHz by showing
that the relationship between the induced current density in the body and the product of
frequency and external electric field hardly varies at all between 50 Hz and 1 MHz, and is only
slightly altered at 10 MHz.
Analytical models can be used for simple cases of calculations.
Electric fields cause displacement of electric charges in conductive objects (including living
bodies) and, because these fields are alternating, the electric charges move backwards and
forwards. The result is an “induced” alternating current inside the conductive object. This
current depends only on:
– the shape and size of the conducting object;
– the characteristics (magnitude, polarisation, degree of non-uniformity, etc.) of the
unperturbed field (field which is measured in the absence of any conducting object);
– the frequency of the field
– the variation of conductivity of the object (in homogeneous media, the current density
induced by electric fields does not depend on conductivity).
Figure 1 illustrates this induction phenomenon for the case where the body is in electrical
contact with the ground.
—————————
1)
Figures in square brackets refer to the Bibliography.

– 10 – 62226-3-1 © IEC:2007
Electric fields
Induced currents
IEC  750/07
Figure 1 – Illustration of the phenomenon of currents induced by an electric field in a
human body standing on the ground
The typical case of public exposure to an electric field is under high voltage power
transmission lines. In this case, the distance between the source of field and the human body
is large and the field in the zone close to the ground, in the absence of any conductive object,
can be considered to be uniform (see Figure 2).

2 4 6 8 10 12 14 16
Horizontal distance  m
IEC  751/07
Figure 2 – Potential lines of the electric field generated by an energised wire in the
absence of any objects (all distances in metres)
Height from ground  m
62226-3-1 © IEC:2007 – 11 –
3 General procedure
3.1 Shape factor
In the low and intermediate frequency range, the relation between the induced current in the
human body (J) and a uniform electric field (E ) can be reduced to:
J = K . f .E
E 0 (2)
Where:
f is the frequency;
E is the magnitude of the unperturbed electric field;
K is defined as the “shape factor for the electric field”.
E
K is dependant on the size, the conductivity, the form and the position of the model of the
E
human body. It is also dependant on the location within the body where the induced current
density is evaluated. K is independent of the frequency for analytical assessment of the
E
induced current produced by electric fields (see Annex A).
-1 -1
K is given in units of A⋅s⋅V ⋅m or Farad per metre (F/m), which relates to the fact that the
E
exposure to the electric field corresponds physically to a capacitive coupling between the field
source and the conductive object exposed to the field.
3.2 Procedure
The current density inside an individual can be estimated analytically, following a three stage
process. The first stage is to compute the current density in a semi-spheroid, whose
dimensions are chosen to best represent the particular body. As it will be shown in 5.3 of this
standard, the current density is uniform throughout the spheroid but depends on the ratio L/R
of its semi-major axis and semi-minor axis.
The second stage is to use a realistic axisymmetrical model of a human body to determine the
current density as a function of vertical position within the body.
The third stage is to convert the average current density at a particular vertical position to the
local current density in the different tissues at that height. Health guidelines on exposure to
EMF refer specifically to current density in the central nervous system, so the particular area
of interest within the body is the spinal cord in the neck, due to the small cross section of the
neck, which concentrates the current in that region.
Induced currents are calculated for men and women as well as children using reference
values for their height, mass and surface area published by ICRP [38]. Sufficient information
is given here to apply the method to persons of any weight and height.
Numerical calculations are also presented demonstrating the validity of the analytical
procedure.
– 12 – 62226-3-1 © IEC:2007
4 Human body models
4.1 General
In scientific literature, many models of different complexity have been used for the
assessment of currents and internal fields induced by electric or magnetic field (Figure 3).
Examples of such sophisticated calculations are given in the bibliography. It must be
emphasised that these computations have been performed using dedicated softwares which
require highly specialised competences and are not widely available. Therefore, it is
considered that such computational techniques are not relevant with regard to standardisation
objectives.
IEC  752/07
Figure 3 – A realistic body model
Analytical calculations are possible when using simple models, such as the model of a
spheroid in a uniform electric field.
4.2 Surface area
The surface area of a body (SB) is used to scale both the spheroidal and the axisymmetrical
body models for different sized bodies. It depends on the height and the mass of the body.
The report of the ICRP [38], Basic Anatomical and Physiological Data for Use in Radiological
Protection: Reference Values, provides an algorithm giving the total surface area (SB ) of a
T
person as a function of its height L (in metres) and mass M (in kg):
0,514 56 0,422 46
SB = 0,164 4 M L (3)
T
In our case, only the outwards-facing surface area of the body is considered, which is
approximately 82 % of the total surface area SB The 18 % reduction comprises 3 % for
T.
excluding the soles of the feet, 6 % for excluding the touching surface of the legs, and 8 % for
excluding the inner surface of the arms and hands and 1 % for the perineum. The reduced
surface area (SB ) is therefore:
R
SB = 0,82 SB (4)
R T
Table 1 gives the results for the reference man and the reference woman which are
introduced in 4.4 and Annex B.

62226-3-1 © IEC:2007 – 13 –
Table 1 – Data for reference man and reference woman
Reference Reference
man woman
Height, m 1,76 1,63
Mass, kg 73 60
Total surface area SB , m 1,889 1,662
T
Reduced surface area SB , m 1,557 1,363
R
4.3 Semi-spheroidal model
To calculate the induced current density inside a human standing on a conducting plane it is
necessary to model the reflection of the body in the ground. Thus the body is represented by
half of the spheroid (Figure 4) and the reflection by the other half (Figure 7). The semi-major
axis L of the spheroid is set to the height of the person being represented.
z
E
0Z
L
R
y
Ground plane
x
IEC  753/07
Figure 4 – Scheme of the semi-spheroid simulating a human being standing
on a zero potential plane
The semi-minor axis (i.e. the radius) R is chosen to give the same total current flowing into the
ground through the feet when the body is grounded as for the body it represents. This is
achieved by ensuring that the spheroid has the same outward-facing surface area SB as the
R
body it represents.
The surface area SB of a half spheroid of height L and radius R is given by:
S
()
⎡ L arcsin e ⎤
SB = πR 1+ (5)
S
⎢ ⎥
R e
⎣ ⎦
where e is the eccentricity:
– 14 – 62226-3-1 © IEC:2007
R
e = 1−
L
R is determined from the mass M and L by solving equation (5) for R, with SB = SB and
S R,
where SB is given by equations (3) and (4). Thus
R
B B SB
⎛ ⎞
S
R = − ± ⎜ ⎟ + (6)
2 2 π
⎝ ⎠
where
arcsin(e)
B = L
e
B is a function of R, but as arcsin(e)/e varies only slowly with L/R, as shown in Table 2, B also
varies only slowly with L/R, and therefore B can be determined using an approximate value for
L/R.
Table 2 – Values of arcsin(e) / e for different values of L/R
L/R 9,0 9,2 9,4 9,6 9,8 10
Arcsin(e)/e 1,469 1,471 1,473 1,474 1,476 1,478
Using L/R = 9,8 gives
B = 1,476 L
This is substituted into equation (6) to give the equation for R in terms of L and SB :
S
SB
2 S
R = −0,738L + 0,545L + (7)
π
Figure 5 presents the result graphically. It can be used to find the radius R from the height L
and mass M of a person. For example, the reference man, whose mass is 73 kg and height is
1.76 m, the radius R is 0,178 m and L/R is 9,86.

62226-3-1 © IEC:2007 – 15 –
0,35
0,30
0,25
0,20
0,15
0,10
1,0 1,5 2,0
L m
IEC  754/07
Figure 5 – Equivalent spheroid radius, R, versus height, L,
and for different mass, M
4.4 Axisymmetrical body model
The axisymmetrical body model represents the essential features of the body: its height, total
surface area, neck dimensions, and approximate vertical profile. However it cannot be a
perfect representation of the body because the body is not axisymmetrical. Figure 6 illustrates
the radial cross section of the axisymmetrical model for the reference man and woman.

1.80
1,80 1,1.80 80
1.60
1.60
1,60 1,60
1,1.40 40 1,40
1.40
1,1.20 20 1,20
1.20
1.00
1,00 1,1.00 00
0,0.80 80 0,80
0.80
0.60
0,60 0,0.60 60
0.40
0,40 0,0.40 40
0.20
0,20 0,0.20 20
0,00 0,00
0.00
0.00
0.0 0.2
0,0 0,2 0,0 0,2
0.0 0.2
IEC  755/07
Figure 6 – The axisymmetrical body model for the reference
man (left) and woman (right)
R m
M  kg
– 16 – 62226-3-1 © IEC:2007
Annex B describes how data from an anthropometric survey of 2 208 women and 1 174 men,
chosen as a representative sample from the US Army, were used to develop the
axisymmetrical model. The model is defined by 13 (radius, height) coordinates.
5 Calculation of induced current
5.1 General
Analytical models to quantify the relationship between induced currents in conductive bodies
and external electric fields are generally based upon the most simple assumption that the
external fields are uniform and at a single frequency, and that the bodies are homogeneous
and with a shape that can be described analytically (as is the case of spheres, spheroids,
etc.). Therefore, they cannot easily take into account the fact that the human body is a non-
homogeneous structure with a complex shape.
Nevertheless, analytical models can be used for simple cases of calculations and/or to
validate numerical calculations.
In the particular case of the homogeneous models developed in this standard, the induced
current density is independent of the conductivity and the permittivity (low frequency
approximation).
5.2 Semi-spheroid
5.2.1 Analytical
In Annex A, the detailed analytical solutions for a spheroid in a uniform electric field are
presented as a function of spheroid's geometrical and electrical parameters and of the
magnitude and direction of the electric field vector (Figure 7). The spheroid representation is
equivalent to the semi-spheroid in the presence of the ground plane as explained in 4.3.

z
E
0Z
L
R
E
0R
y
x
IEC  756/07
Figure 7 – Conductive spheroid exposed to electric field
L is the length of the semi-major (rotational) axis of the spheroid (axis Z),
R is the length of the semi-minor axis of the spheroid (R is also the radius of the circular cross
section of the spheroid at the symmetry plane (plane XY)).

62226-3-1 © IEC:2007 – 17 –
The shape factor for electric field K is calculated for 2 orientations of the field vector: E
E 0
parallel to Z axis (therefore K and E are called K and E ) and E perpendicular to Z axis
E 0 EZ 0Z 0
(therefore K and E are called K and E ).
E 0 ER 0R
The results of this analytical calculation are summarised hereunder in Figures 8 and 9.
and K as a function of
Figure 8 gives in a graphic form the result of the calculation of K
EZ ER
the ratio L/R (shape parameter).
Figure 9 gives the result of the analytical calculation of the local current density, for a field
magnitude of 1 kV/m at 50 Hz.
–7
K
EZ
E-field parallel to Z axis
–8
–9
K
ER
E-field perpendicular to Z axis
–10
1 10 100
L/R
IEC  757/07
Figure 8 – Calculation of the shape factor for electric field K for an spheroid
E
exposed to an unperturbed electric field
K (F/M)
E
– 18 – 62226-3-1 © IEC:2007
J
sz
E-Field parallel to Z axis
J
sr
E-Field perpendicular to Z axis
1 10 100
L/R
IEC  758/07
Figure 9 – Current density J induced by an unperturbed electric field (1 kV/m, 50 Hz)
S
in a spheroid versus parameter L/R (values in µA/m²)
Direct application:
Considering the values for the reference man (see 4.3) L/R = 9,86 and L = 1,76 m, exposed
to 50 Hz vertical electric field with a magnitude of 1 kV/m, the curves in Figures 8 and 9 give:
−9
K ≅ 2,68 ×10 A.s/V.m
EZ
and
J = K . f .E ≅ 0,134 mA/m²
SZ EZ 0Z
5.2.2 Numerical
Different methods can be used to determine the current induced by an external electric field
E in a conductive object. In the following computations, a finite elements method was used.
Physical parameters for the air are [27,33,51]:
ε = 1
r
σ = 0 S/m
Characteristics of the semi-spheroid model are:
L = 1,76 m ε = 10
r
R = 0,178 m σ = 0,2 S/m
In the example given here, the mesh of the semi-spheroid is composed of 2744 surface
elements (see Figure 10).
J (μA/m )
62226-3-1 © IEC:2007 – 19 –
L = 1,76 m
R = 0,178 m
IEC  759/07
Figure 10 – Dimensions and mesh of the semi-spheroid
In the computation domain, the external 50 Hz electric field E is generated by a plane
electrode at 10 m from the ground plane, with an electrical potential of 10 000 V. The domain
is assumed to be axisymmetrical.
Figure 11 shows the perturbed electric field in the air, close to the semi-spheroid. The semi-
spheroid distorts the lines of electric field, which become perpendicular to the surface of the
spheroid. Without the semi-spheroid or far from it, these lines of electric field are vertical.

E =1 kV/m
IEC  760/07
Figure 11 – Distortion of power frequency electric field lines close
to the conductive semi-spheroid

– 20 – 62226-3-1 © IEC:2007
The current density in the centre of the semi-spheroid is very similar to the current density
value from analytical calculation.
The variation is less than 1 % along the vertical axis and the current density should be
considered as constant. As a result, it can be considered that this simple numerical model
gives results identical to those of the analytical calculation.
5.3 Axisymmetrical models
5.3.1 Analytical
Table 3 gives values derived in the course of calculating the current density in the spheroid.
The surface area in the third row was calculated from the height and mass using Equation (3).
In the next row the 0,82 factor was applied (Equation (4)) to remove non-outward facing
surfaces when standing. Using the outward-facing surface area and Equation (7) gives in the
next row the radius R for a half spheroid having the same surface area. The following row
presents the corresponding L/R. It is approximately the same for both reference man and
reference woman.
Table 3 – Derived data using spheroid model at 50 Hz
Reference man Reference woman
Height L, m 1,76 1,63
Mass M, kg 73 60
Total surface area of body SB , m 1,899 1,662
T
Reduced surface area of body SB , m 1,557 1,363
R
Spheroid radius R, m 0,178 0,168
L/R
9,86 9,68
Current density J in spheroid per kV/m, mA/m 0,134 0,130
SZ
Ground current per kV/m, µA 13,4 11,6

The current density J in the spheroid depends only on the parameter L/R, the electric field
SZ
and frequency. For L/R = 9,86 the current density throughout the spheroid is
J = 0,134 mA/m per kV/m of electric field at 50 Hz. For 60 Hz, it is 20 % higher.
SZ
The vertical current density J is uniform throughout the spheroid. The vertical current flowing
SZ
through a horizontal layer of the spheroid therefore increases progressively from zero at the
top to a maximum at the ground. This is because of the displacement current is entering the
spheroid progressively over its whole height.
In practice the human body is not a half spheroid but has an effective horizontal radius that
varies unevenly with vertical position as represented by the axisymmetrical model.
The assumption is made that at a particular height the same overall current flows as in the
spheroid, but it flows in the different cross sectional area
...