Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Caderno Brasileiro de Ensino de Física (Online) |
Texto Completo: | https://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2017v34n3p864 |
Resumo: | Nowadays, we use Biot-Savart’s Law and Grassmann’s force to study the magnetic fields effects. We can observe that this force apparently do not always satisfy the principle of action and reaction. In contrast, Ampère’s force always satisfies this principle explicitly and always along the straight line connecting the two currents elements. The present work presents a historic analysis of the development of these two forces, which have been developed based on interpretations of the Ørsted’s experiment. We also compare these two forces in order to verify if both have the same result. We show that the Grassmann’s expression, in fact, does not satisfy to the principle of action and reaction. Ampère’s force not only follows the principle of action and reaction in the strongest way, but it also explains the phenomena based action at a distance, which is easier to be observed and has many other powerful results, not only in the electromagnetism. In order to compare these two approaches, we calculate the force that an infinite rectilinear wire exerts on a loop of conductive material, both with current. |
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Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elementsAnálise da Lei de Biot-Savart em comparação com a força entre elementos de corrente de AmpèreNowadays, we use Biot-Savart’s Law and Grassmann’s force to study the magnetic fields effects. We can observe that this force apparently do not always satisfy the principle of action and reaction. In contrast, Ampère’s force always satisfies this principle explicitly and always along the straight line connecting the two currents elements. The present work presents a historic analysis of the development of these two forces, which have been developed based on interpretations of the Ørsted’s experiment. We also compare these two forces in order to verify if both have the same result. We show that the Grassmann’s expression, in fact, does not satisfy to the principle of action and reaction. Ampère’s force not only follows the principle of action and reaction in the strongest way, but it also explains the phenomena based action at a distance, which is easier to be observed and has many other powerful results, not only in the electromagnetism. In order to compare these two approaches, we calculate the force that an infinite rectilinear wire exerts on a loop of conductive material, both with current.Atualmente, utilizamos a lei de Biot-Savart, e também a força de Grassmann, para estudar os efeitos do campo magnético e observamos que esta força aparentemente não satisfaz ao princípio da ação e reação. Em contrapartida, a força de Ampère sempre satisfaz a este princípio explicitamente e sempre na forma forte. O presente trabalho faz uma análise histórica do desenvolvimento destas duas equações de força, que foram desenvolvidas a partir de interpretações do experimento de Ørsted. Também faz uma análise comparativa entre as duas equações a fim de verificar se ambas fornecem o mesmo resultado e mostrar que a expressão de Grassmann, de fato, não satisfaz ao princípio da ação e reação. A força de Ampère, além de sempre obedecer ao princípio da ação e reação na forma forte, explica os fenômenos a partir da ação a distância, que é mais simples de ser observada e possui muitos outros resultados poderosos, não só no eletromagnetismo. Para realizar a comparação entre as duas abordagens, calculamos a força que um fio retilíneo infinito exerce em uma espira de material condutor, ambos com corrente.Imprensa Universitária - UFSC2017-12-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2017v34n3p86410.5007/2175-7941.2017v34n3p864Caderno Brasileiro de Ensino de Física; v. 34 n. 3 (2017); 864-8792175-79411677-2334reponame:Caderno Brasileiro de Ensino de Física (Online)instname:Universidade Federal de Santa Catarina (UFSC)instacron:UFSCporhttps://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2017v34n3p864/35534Copyright (c) 2017 Caderno Brasileiro de Ensino de Físicainfo:eu-repo/semantics/openAccessTanaka dos Santos, Hugo ShigueoGardelli, Daniel2017-12-11T07:06:12Zoai:periodicos.ufsc.br:article/47555Revistahttp://www.periodicos.ufsc.br/index.php/fisicaPUBhttps://periodicos.ufsc.br/index.php/fisica/oaicbefisica@gmail.com||fscccef@fsc.ufsc.br|| cbefisica@gmail.com2175-79411677-2334opendoar:2017-12-11T07:06:12Caderno Brasileiro de Ensino de Física (Online) - Universidade Federal de Santa Catarina (UFSC)false |
dc.title.none.fl_str_mv |
Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements Análise da Lei de Biot-Savart em comparação com a força entre elementos de corrente de Ampère |
title |
Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements |
spellingShingle |
Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements Tanaka dos Santos, Hugo Shigueo |
title_short |
Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements |
title_full |
Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements |
title_fullStr |
Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements |
title_full_unstemmed |
Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements |
title_sort |
Analysis of Biot-Savart’s law in comparison with Ampère’s force between current elements |
author |
Tanaka dos Santos, Hugo Shigueo |
author_facet |
Tanaka dos Santos, Hugo Shigueo Gardelli, Daniel |
author_role |
author |
author2 |
Gardelli, Daniel |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Tanaka dos Santos, Hugo Shigueo Gardelli, Daniel |
description |
Nowadays, we use Biot-Savart’s Law and Grassmann’s force to study the magnetic fields effects. We can observe that this force apparently do not always satisfy the principle of action and reaction. In contrast, Ampère’s force always satisfies this principle explicitly and always along the straight line connecting the two currents elements. The present work presents a historic analysis of the development of these two forces, which have been developed based on interpretations of the Ørsted’s experiment. We also compare these two forces in order to verify if both have the same result. We show that the Grassmann’s expression, in fact, does not satisfy to the principle of action and reaction. Ampère’s force not only follows the principle of action and reaction in the strongest way, but it also explains the phenomena based action at a distance, which is easier to be observed and has many other powerful results, not only in the electromagnetism. In order to compare these two approaches, we calculate the force that an infinite rectilinear wire exerts on a loop of conductive material, both with current. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-12-08 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2017v34n3p864 10.5007/2175-7941.2017v34n3p864 |
url |
https://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2017v34n3p864 |
identifier_str_mv |
10.5007/2175-7941.2017v34n3p864 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.ufsc.br/index.php/fisica/article/view/2175-7941.2017v34n3p864/35534 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2017 Caderno Brasileiro de Ensino de Física info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2017 Caderno Brasileiro de Ensino de Física |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Imprensa Universitária - UFSC |
publisher.none.fl_str_mv |
Imprensa Universitária - UFSC |
dc.source.none.fl_str_mv |
Caderno Brasileiro de Ensino de Física; v. 34 n. 3 (2017); 864-879 2175-7941 1677-2334 reponame:Caderno Brasileiro de Ensino de Física (Online) instname:Universidade Federal de Santa Catarina (UFSC) instacron:UFSC |
instname_str |
Universidade Federal de Santa Catarina (UFSC) |
instacron_str |
UFSC |
institution |
UFSC |
reponame_str |
Caderno Brasileiro de Ensino de Física (Online) |
collection |
Caderno Brasileiro de Ensino de Física (Online) |
repository.name.fl_str_mv |
Caderno Brasileiro de Ensino de Física (Online) - Universidade Federal de Santa Catarina (UFSC) |
repository.mail.fl_str_mv |
cbefisica@gmail.com||fscccef@fsc.ufsc.br|| cbefisica@gmail.com |
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1799940573833986048 |