SIST EN 62226-2-1:2005

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

This part of EN 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.

Sicherheit in elektrischen oder magnetischen Feldern im niedrigen und mittleren Frequenzbereich - Verfahren zur Berechnung der induzierten Körperstromdichte und des im menschlichen Körper induzierten elektrischen Feldes -- Teil 2-1: Exposition gegenüber magnetischen Feldern - 2D-Modelle

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

La présente partie de la EN 62226 introduit le facteur de couplage K, pour permettre l'évaluation de l'exposition dans des situations d'expositions complexes, telles que les champs magnétiques non uniformes ou les champs électriques perturbés. Le facteur de couplage K peut avoir différentes interprétations physiques selon qu'il se réfère à l'exposition à un champ électrique ou un champ magnétique. L'objet de cette partie est de définir plus en détail ce facteur de couplage K, pour les cas de modèles simples de corps humain, exposé à des champs magnétiques non uniformes. Dans le cas présent, il est appelé facteur de couplage pour champ magnétique non uniforme.

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

General Information

• Status: Published
• Publication Date: 31-May-2005
• ICS: 13.280 - Radiation protection
• ICS: 17.220.20 - Measurement of electrical and magnetic quantities
• Technical Committee: INIR - Electromagnetic fields in human enviornment
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 01-Jun-2005
• Due Date: 01-Jun-2005
• Completion Date: 01-Jun-2005
• Ref Project: EN 62226-2-1:2005 - 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

Standards Content (Sample)

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
SIST EN 62226-2-1:2005(en)
©  Standard je založil in izdal Slovenski inštitut za standardizacijo. Razmnoževanje ali kopiranje celote ali delov tega dokumenta ni dovoljeno

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

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

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EN 62226-2-1:2005 - 2 -
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.

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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
© IEC 2004 Droits de reproduction réservés ⎯ Copyright - all rights reserved
Aucune partie de cette publication ne peut être reproduite ni No part of this publication may be reproduced or utilized in any
utilisée sous quelque forme que ce soit et par aucun procédé, form or by any means, electronic or mechanical, including
électronique ou mécanique, y compris la photocopie et les photocopying and microfilm, without permission in writing from
microfilms, sans l'accord écrit de l'éditeur. the publisher.
International Electrotechnical Commission, 3, rue de Varembé, PO Box 131, CH-1211 Geneva 20, Switzerland
Telephone: [phone] Telefax: [phone] E-mail: [e-mail] Web: www.iec.ch
CODE PRIX
PRICE CODE XA
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International Electrotechnical Commission
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Pour prix, voir catalogue en vigueur
For price, see current catalogue

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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

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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

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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

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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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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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3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
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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 62226-2-1 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.

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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.

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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.

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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.

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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),
...