ON THE SIMILARITY OF PLANE PULSED MAGNETIC FIELDS CONTINUED FROM DIFFERENT COORDINATE AXES
Purpose. The purpose of this work is formulation of similarity conditions for plane magnetic fields at a sharp skin-effect continued in non-conducting and non-magnetic medium from different axes bounding plane surfaces of conductors. Methodology. Classic formulation of Cauchy problem for magnetic ve...
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| Дата: | 2020 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English Ukrainian |
| Опубліковано: |
National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine”
2020
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| Онлайн доступ: | http://eie.khpi.edu.ua/article/view/2074-272X.2020.5.07 |
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| Назва журналу: | Electrical Engineering & Electromechanics |
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Electrical Engineering & Electromechanics| id |
eiekhpieduua-article-214963 |
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eiekhpieduua-article-2149632020-10-28T18:22:38Z ON THE SIMILARITY OF PLANE PULSED MAGNETIC FIELDS CONTINUED FROM DIFFERENT COORDINATE AXES О ПОДОБИИ ПЛОСКОПАРАЛЛЕЛЬНЫХ ИМПУЛЬСНЫХ МАГНИТНЫХ ПОЛЕЙ, ПРОДОЛЖАЕМЫХ С РАЗЛИЧНЫХ КООРДИНАТНЫХ ОСЕЙ Mikhailov, V. M. плоскопараллельное магнитное поле резкий поверхностный эффект задача Коши для уравнения Лапласа теория подобия 621.3.01 plane magnetic field sharp skin-effect Cauchy problem for Laplace equation similarity theory 621.3.01 Purpose. The purpose of this work is formulation of similarity conditions for plane magnetic fields at a sharp skin-effect continued in non-conducting and non-magnetic medium from different axes bounding plane surfaces of conductors. Methodology. Classic formulation of Cauchy problem for magnetic vector potential Laplace equations, mathematic physics methods and basics similarity theory are used. Two problems are considered: the problem of initial field continuation from one axis and the problem of similar field continuation form other axis on which magnetic flux density or electrical field strength in unknown. Results. Necessary and sufficient similarity conditions of plane pulsed or high-frequency magnetic fields continued from different axes of rectangular coordinates are formulated. For the given odd and even magnetic flux density distributions on axis of initial field corresponding the distributions on axis and solution of continued similar field problem are obtained. Originality. It is proved that for similarity of examined fields the proportion of corresponding vector field projections represented by dimensionless numbers in similar points of axes is necessary and sufficient. Цель. Целью работы является формулировка условий подобия плоскопараллельных магнитных полей при резком поверхностном эффекте, которые продолжаются в непроводящую и немагнитную среду с различных осей прямоугольных координат, ограничивающих плоские поверхности проводников. Методика. Использованы классическая формулировка задачи Коши для уравнения Лапласа относительно векторного потенциала магнитного поля, методы математической физики и основные положения теории подобия. Рассмотрены две соответствующие задачи: задача продолжения исходного поля с одной оси и задача продолжения подобного поля с другой оси, распределение индукции магнитного поля на которой неизвестно. Результаты. Сформулированы необходимые и достаточные условия подобия плоскопараллельных импульсных или высокочастотных магнитных полей, продолжаемых с различных осей прямоугольных координат. Для заданных нечетного и четного распределений индукции на оси исходного магнитного поля определены соответствующие распределения на оси, а также решены задачи продолжения подобного поля. Научная новизна. Доказано, что для подобия рассмотренных полей необходима и достаточна пропорциональность представленных в критериальной форме соответствующих проекций векторов этих полей в сходственных точках осей. National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” 2020-10-26 Article Article application/pdf application/pdf http://eie.khpi.edu.ua/article/view/2074-272X.2020.5.07 10.20998/2074-272X.2020.5.07 Electrical Engineering & Electromechanics; No. 5 (2020); 44-49 Электротехника и Электромеханика; № 5 (2020); 44-49 Електротехніка і Електромеханіка; № 5 (2020); 44-49 2309-3404 2074-272X en uk http://eie.khpi.edu.ua/article/view/2074-272X.2020.5.07/215149 http://eie.khpi.edu.ua/article/view/2074-272X.2020.5.07/215150 Copyright (c) 2020 V. M. Mikhailov https://creativecommons.org/licenses/by-nc/4.0 |
| institution |
Electrical Engineering & Electromechanics |
| collection |
OJS |
| language |
English Ukrainian |
| topic |
плоскопараллельное магнитное поле резкий поверхностный эффект задача Коши для уравнения Лапласа теория подобия 621.3.01 plane magnetic field sharp skin-effect Cauchy problem for Laplace equation similarity theory 621.3.01 |
| spellingShingle |
плоскопараллельное магнитное поле резкий поверхностный эффект задача Коши для уравнения Лапласа теория подобия 621.3.01 plane magnetic field sharp skin-effect Cauchy problem for Laplace equation similarity theory 621.3.01 Mikhailov, V. M. ON THE SIMILARITY OF PLANE PULSED MAGNETIC FIELDS CONTINUED FROM DIFFERENT COORDINATE AXES |
| topic_facet |
плоскопараллельное магнитное поле резкий поверхностный эффект задача Коши для уравнения Лапласа теория подобия 621.3.01 plane magnetic field sharp skin-effect Cauchy problem for Laplace equation similarity theory 621.3.01 |
| format |
Article |
| author |
Mikhailov, V. M. |
| author_facet |
Mikhailov, V. M. |
| author_sort |
Mikhailov, V. M. |
| title |
ON THE SIMILARITY OF PLANE PULSED MAGNETIC FIELDS CONTINUED FROM DIFFERENT COORDINATE AXES |
| title_short |
ON THE SIMILARITY OF PLANE PULSED MAGNETIC FIELDS CONTINUED FROM DIFFERENT COORDINATE AXES |
| title_full |
ON THE SIMILARITY OF PLANE PULSED MAGNETIC FIELDS CONTINUED FROM DIFFERENT COORDINATE AXES |
| title_fullStr |
ON THE SIMILARITY OF PLANE PULSED MAGNETIC FIELDS CONTINUED FROM DIFFERENT COORDINATE AXES |
| title_full_unstemmed |
ON THE SIMILARITY OF PLANE PULSED MAGNETIC FIELDS CONTINUED FROM DIFFERENT COORDINATE AXES |
| title_sort |
on the similarity of plane pulsed magnetic fields continued from different coordinate axes |
| title_alt |
О ПОДОБИИ ПЛОСКОПАРАЛЛЕЛЬНЫХ ИМПУЛЬСНЫХ МАГНИТНЫХ ПОЛЕЙ, ПРОДОЛЖАЕМЫХ С РАЗЛИЧНЫХ КООРДИНАТНЫХ ОСЕЙ |
| description |
Purpose. The purpose of this work is formulation of similarity conditions for plane magnetic fields at a sharp skin-effect continued in non-conducting and non-magnetic medium from different axes bounding plane surfaces of conductors. Methodology. Classic formulation of Cauchy problem for magnetic vector potential Laplace equations, mathematic physics methods and basics similarity theory are used. Two problems are considered: the problem of initial field continuation from one axis and the problem of similar field continuation form other axis on which magnetic flux density or electrical field strength in unknown. Results. Necessary and sufficient similarity conditions of plane pulsed or high-frequency magnetic fields continued from different axes of rectangular coordinates are formulated. For the given odd and even magnetic flux density distributions on axis of initial field corresponding the distributions on axis and solution of continued similar field problem are obtained. Originality. It is proved that for similarity of examined fields the proportion of corresponding vector field projections represented by dimensionless numbers in similar points of axes is necessary and sufficient. |
| publisher |
National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” |
| publishDate |
2020 |
| url |
http://eie.khpi.edu.ua/article/view/2074-272X.2020.5.07 |
| work_keys_str_mv |
AT mikhailovvm onthesimilarityofplanepulsedmagneticfieldscontinuedfromdifferentcoordinateaxes AT mikhailovvm opodobiiploskoparallelʹnyhimpulʹsnyhmagnitnyhpolejprodolžaemyhsrazličnyhkoordinatnyhosej |
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2024-06-01T14:39:41Z |
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2024-06-01T14:39:41Z |
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