Penetration of non-uniform electromagnetic field into conducting body
The study is based on the exact analytical solution for the general conjugation problem of three-dimensional quasi-stationary field at a flat interface between dielectric and conducting media. It is determined that non-uniform electromagnetic field always decreases in depth faster than uniform field...
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | English Ukrainian |
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National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine
2021
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| Online Zugang: | http://eie.khpi.edu.ua/article/view/228890 |
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| Назва журналу: | Electrical Engineering & Electromechanics |
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Electrical Engineering & Electromechanics| id |
eiekhpieduua-article-228890 |
|---|---|
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ojs |
| institution |
Electrical Engineering & Electromechanics |
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| datestamp_date |
2021-04-10T12:41:46Z |
| collection |
OJS |
| language |
English Ukrainian |
| topic |
three-dimensional electromagnetic field electromagnetic field formation exact analytical solution skin effect |
| spellingShingle |
three-dimensional electromagnetic field electromagnetic field formation exact analytical solution skin effect Vasetsky, Yu. M. Penetration of non-uniform electromagnetic field into conducting body |
| topic_facet |
трехмерное электромагнитное поле формирование электромагнитного поля точное решение задачи скин-эффект three-dimensional electromagnetic field electromagnetic field formation exact analytical solution skin effect |
| format |
Article |
| author |
Vasetsky, Yu. M. |
| author_facet |
Vasetsky, Yu. M. |
| author_sort |
Vasetsky, Yu. M. |
| title |
Penetration of non-uniform electromagnetic field into conducting body |
| title_short |
Penetration of non-uniform electromagnetic field into conducting body |
| title_full |
Penetration of non-uniform electromagnetic field into conducting body |
| title_fullStr |
Penetration of non-uniform electromagnetic field into conducting body |
| title_full_unstemmed |
Penetration of non-uniform electromagnetic field into conducting body |
| title_sort |
penetration of non-uniform electromagnetic field into conducting body |
| title_alt |
Проникновение неоднородного электромагнитного поля в электропроводное тело |
| description |
The study is based on the exact analytical solution for the general conjugation problem of three-dimensional quasi-stationary field at a flat interface between dielectric and conducting media. It is determined that non-uniform electromagnetic field always decreases in depth faster than uniform field. The theoretical conclusion is confirmed by comparing the results of analytical and numerical calculations. The concept of strong skin effect is extended to the case when penetration depth is small not only compare to the characteristic body size, but also when the ratio of the penetration depth to the distance from the surface of body to the sources of the external field is small parameter. For strong skin effect in its extended interpretation, the influence of external field non-uniformity to electromagnetic field formation both at the interface between dielectric and conducting media and to the law of decrease field in conducting half-space is analyzed. It is shown, at the interface the expressions for the electric and magnetic intensities in the form of asymptotic series in addition to local field values of external sources contain their derivatives with respect to the coordinate perpendicular to the interface. The found expressions made it possible to generalize the approximate Leontovich impedance boundary condition for diffusion of non-uniform field into conducting half-space. The difference between the penetration law for the non-uniform field and the uniform one takes place in the terms of the asymptotic series proportional to the small parameter to the second power and to the second derivative with respect to the vertical coordinate from the external magnetic field intensity at the interface. |
| publisher |
National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine |
| publishDate |
2021 |
| url |
http://eie.khpi.edu.ua/article/view/228890 |
| work_keys_str_mv |
AT vasetskyyum penetrationofnonuniformelectromagneticfieldintoconductingbody AT vasetskyyum proniknovenieneodnorodnogoélektromagnitnogopolâvélektroprovodnoetelo |
| first_indexed |
2025-07-17T11:48:28Z |
| last_indexed |
2025-07-17T11:48:28Z |
| _version_ |
1850411961481691136 |
| spelling |
eiekhpieduua-article-2288902021-04-10T12:41:46Z Penetration of non-uniform electromagnetic field into conducting body Проникновение неоднородного электромагнитного поля в электропроводное тело Vasetsky, Yu. M. трехмерное электромагнитное поле формирование электромагнитного поля точное решение задачи скин-эффект three-dimensional electromagnetic field electromagnetic field formation exact analytical solution skin effect The study is based on the exact analytical solution for the general conjugation problem of three-dimensional quasi-stationary field at a flat interface between dielectric and conducting media. It is determined that non-uniform electromagnetic field always decreases in depth faster than uniform field. The theoretical conclusion is confirmed by comparing the results of analytical and numerical calculations. The concept of strong skin effect is extended to the case when penetration depth is small not only compare to the characteristic body size, but also when the ratio of the penetration depth to the distance from the surface of body to the sources of the external field is small parameter. For strong skin effect in its extended interpretation, the influence of external field non-uniformity to electromagnetic field formation both at the interface between dielectric and conducting media and to the law of decrease field in conducting half-space is analyzed. It is shown, at the interface the expressions for the electric and magnetic intensities in the form of asymptotic series in addition to local field values of external sources contain their derivatives with respect to the coordinate perpendicular to the interface. The found expressions made it possible to generalize the approximate Leontovich impedance boundary condition for diffusion of non-uniform field into conducting half-space. The difference between the penetration law for the non-uniform field and the uniform one takes place in the terms of the asymptotic series proportional to the small parameter to the second power and to the second derivative with respect to the vertical coordinate from the external magnetic field intensity at the interface. Исследование основано на точном аналитическом решении общей задачи сопряжения трехмерного квазистационарного поля на границе раздела диэлектрической и проводящей сред. Установлено, что неоднородное электромагнитное поле всегда убывает по глубине быстрее, чем однородное. Теоретический вывод подтверждается сопоставлением результатов аналитических и численных расчетов. Понятие сильного скин-эффекта распространяется на случай, когда глубина проникновения мала по сравнению не только с характерными размерами тела, но также когда отношение глубины проникновения к расстоянию от поверхности тела до источников внешнего поля является малым параметром. Для сильного скин-эффекта в его расширенной интерпретации проанализировано влияние неоднородности внешнего поля на формирование электромагнитного поля на границе и на закон убывания поля в проводящем полупространстве. Показано, что на границе выражения в виде асимптотических рядов для напряженностей полей помимо локальных значений поля внешних источников содержат их производные по координате, перпендикулярной граничной поверхности. Полученные выражения позволили обобщить приближенное импедансное граничное условие Леонтовича для диффузии неоднородного поля в проводящее полупространство. Отличие законов проникновения для неоднородного и однородного полей имеет место в членах асимптотического ряда, пропорциональных малому параметру во второй степени и второй производной по вертикальной координате от напряженности внешнего магнитного поля у граничной поверхности. National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine 2021-04-10 Article Article application/pdf application/pdf http://eie.khpi.edu.ua/article/view/228890 10.20998/2074-272X.2021.2.07 Electrical Engineering & Electromechanics; No. 2 (2021); 43-53 Электротехника и Электромеханика; № 2 (2021); 43-53 Електротехніка і Електромеханіка; № 2 (2021); 43-53 2309-3404 2074-272X en uk http://eie.khpi.edu.ua/article/view/228890/227903 http://eie.khpi.edu.ua/article/view/228890/227904 Copyright (c) 2021 Yu. M. Vasetsky http://creativecommons.org/licenses/by-nc/4.0 |