Relevant bibliographies by topics / Biot-Savart

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Biot-Savart'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Biot-Savart"

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Singh, Vijay A. "Ampére versus Biot-Savart." Resonance 5, no. 8 (August 2000): 84–91. http://dx.doi.org/10.1007/bf02837939.

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Van Gorder, Robert A. "Helical vortex filament motion under the non-local Biot–Savart model." Journal of Fluid Mechanics 762 (December 3, 2014): 141–55. http://dx.doi.org/10.1017/jfm.2014.639.

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AbstractThe thin helical vortex filament is one of the fundamental exact solutions possible under the local induction approximation (LIA). The LIA is itself an approximation to the non-local Biot–Savart dynamics governing the self-induced motion of a vortex filament, and helical filaments have also been considered for the Biot–Savart dynamics, under a variety of configurations and assumptions. We study the motion of such a helical filament in the Cartesian reference frame by determining the curve defining this filament mathematically from the Biot–Savart model. In order to do so, we consider a matched approximation to the Biot–Savart dynamics, with local effects approximated by the LIA in order to avoid the logarithmic singularity inherent in the Biot–Savart formulation. This, in turn, allows us to determine the rotational and translational velocity of the filament in terms of a local contribution (which is exactly that which is found under the LIA) and a non-local contribution, each of which depends on the wavenumber, $k$, and the helix diameter, $A$. Performing our calculations in such a way, we can easily compare our results to those of the LIA. For small $k$, the transverse velocity scales as $k^{2}$, while for large $k$, the transverse velocity scales as $k$. On the other hand, the rotational velocity attains a maximum value at some finite $k$, which corresponds to the wavenumber giving the maximal torsion.
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Whitney, Cynthia Kolb. "On the Ampere/Biot–Savart discussion." American Journal of Physics 56, no. 10 (October 1988): 871. http://dx.doi.org/10.1119/1.15396.

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Hovey, Arthur. "The Biot-Savart Law—Another Approach." Physics Teacher 46, no. 5 (May 2008): 261–62. http://dx.doi.org/10.1119/1.2909737.

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Scorgie, G. C. "A topical application of Biot-Savart." European Journal of Physics 15, no. 4 (July 1, 1994): 217–18. http://dx.doi.org/10.1088/0143-0807/15/4/010.

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Oliveira, Mário H., and José A. Miranda. "Biot-Savart-like law in electrostatics." European Journal of Physics 22, no. 1 (January 1, 2001): 31–38. http://dx.doi.org/10.1088/0143-0807/22/1/304.

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Caparelli, E. C., and D. Tomasi. "An Analytical Calculation of the Magnetic Field Using the Biot Savart Law." Revista Brasileira de Ensino de Física 23, no. 3 (September 2001): 284–88. http://dx.doi.org/10.1590/s1806-11172001000300005.

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This work presents an analytical method to calculate the magnetic field at any point of the space, by solving the Biot Savart equation in the reciprocal space. This is applied to express the magnetic field due to a circular current distributions as a convergent series. The comparison between the proposed method with the standard numerical integration of the Biot Savart law has shown a good agreement.
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Van Gorder, Robert A. "Self-similar vortex filament motion under the non-local Biot–Savart model." Journal of Fluid Mechanics 802 (August 10, 2016): 760–74. http://dx.doi.org/10.1017/jfm.2016.502.

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One type of thin vortex filament structure that has attracted interest in recent years is that which obeys self-similar scaling. Among various applications, these filaments have been used to model the motion of quantized vortex filaments in superfluid helium after reconnection events. While similarity solutions have been described analytically and numerically using the local induction approximation (LIA), they have not been studied (or even shown to exist) under the non-local Biot–Savart model. In this present paper, we show not only that self-similar vortex filament solutions exist for the non-local Biot–Savart model, but that such solutions are qualitatively similar to their LIA counterparts. This suggests that the various LIA solutions found previously should be valid physically (at least in the small amplitude regime), since they agree well with the more accurate Biot–Savart model.
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Prastyaningrum, Ihtiari, and Jeffry Handhika. "Penggunaan Media e-Modul untuk Meningkatkan Kemampuan Analisis Hubungan Kuat Medan Magnetik dengan Trainer Motor Listrik." JUPITER (JURNAL PENDIDIKAN TEKNIK ELEKTRO) 2, no. 2 (October 30, 2017): 29. http://dx.doi.org/10.25273/jupiter.v2i2.1796.

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Media e-Modul berbasis smartphone merupakan salah satu jenis modul yang dapat digunakan sebagai media pembelajaran. Pada penelitian ini telah dikembangkan media e-Modul untuk mata kuliah Teori Medan. Fokus yang diambil adalah materi Hukum Biot-Savart. Hukum Biot-Savart merupakan salah satu dasar untuk mempelajari tentang kuat medan magnetik. Dengan adanya e-Modul ini diharapkan nantinya mahasiswa dapat menghitung secara tepat besar dari medan magnetik dan menghubungkan kuat medan tersebut dengan perangkat elektronika Motor Listrik.
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Coghi, Michele, and Mario Maurelli. "Regularized vortex approximation for 2D Euler equations with transport noise." Stochastics and Dynamics 20, no. 06 (June 5, 2020): 2040002. http://dx.doi.org/10.1142/s021949372040002x.

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We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot–Savart kernel and the same common noise. The approximation happens by sending the number of particles [Formula: see text] to infinity and the regularization [Formula: see text] in the Biot–Savart kernel to [Formula: see text], as a suitable function of [Formula: see text].
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Dissertations / Theses on the topic "Biot-Savart"

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HUNG, SHI-CHANG. "THE UNSTEADY VISCOUS FLOW OVER A GROOVED WALL: A COMPARISON OF TWO NUMERICAL METHODS (BIOT-SAVART, NAVIER-STOKES)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183957.

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Unsteady two-dimensional laminar flow of an incompressible viscous fluid over a periodically grooved wall is investigated by numerical simulation using two independent finite-difference methods. One is the vorticity-stream function method, and the other involves the vorticity-velocity induction law formulation. The fluid motion is initiated impulsively from rest and is assumed to be spatially periodic in the streamwise direction. The flow field, which includes the time development of the shear layer and the recirculating flow in the zone of separation, is examined in detail during the transient phase to the steady-state condition. The analytical and numerical formulations, which include the implementation of the boundary conditions, are derived in detail. The generation of vorticity at the solid surfaces is modelled differently in the two approaches. This vorticity production plays an important role in determining the surface-pressure distribution and the drag coefficient. Characteristics of the transient solution for a moderate Reynolds number in the laminar range are presented. Included with the graphical results are the temporal development of the constant stream function contours, including the dividing contour between the zone of separation and the main flow, and the constant vorticity contours. These latter contours show the interactions of separated vortices. The flow is found to approach a steady-state condition comprising an undisturbed uniform flow, a nonuniform irrotational flow, a shear layer adjacent to the grooved wall, and a recirculating vortex flow in the groove. Results also include the time development of the surface shear stress, surface pressure, drag coefficient and several typical velocity profiles, which characterize the flow in the recirculating region. Comparisons of the results obtained by the two numerical methods are made during the major development of the flow. The results showing the general features of the flow development including the time development of the shear layer, free shear layer and recirculating vortex flow are in good agreement. However, a significant deviation does exist at early times for the distribution of surface pressure, which accordingly has noticeable effect on the drag coefficient. Nevertheless, the gap between the distributions of surface pressure and drag coefficients dies out gradually as time progresses. The form of the stream function and vorticity contours at the steady state agrees well with those obtained from a recent numerical investigation of the steady flow in grooved channels.
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Lima, Marcos de. "Sistema computacional baseado na lei de Biot-Savart (BSMAG) para cálculo de campos magnéticos em detectores de metais." Florianópolis, SC, 2006. http://repositorio.ufsc.br/xmlui/handle/123456789/88709.

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Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Elétrica.
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Neste trabalho é proposto um sistema computacional para o cálculo de campos magnéticos em detectores de metais. Para analisar o campo magnético em um tipo específico de detector de metais, PDM (Portal Detector de Metais), foi necessário fazer um estudo bibliográfico deste equipamento e desenvolver uma ferramenta numérica para o cálculo tridimensional do campo que permitisse calcular o campo no interior da região de detecção de metais. Com a utilização da ferramenta numérica denominada BSmag (sistema computacional baseado na lei de Biot-Savart para cálculo de campos) foi possível calcular o vetor campo magnético nos pontos de interesse assim como mostrar a sua distribuição no interior do PDM. Na concepção do sistema utilizou-se à lei de Biot-Savart que pode ser considerada como uma discretização da lei de Ampère e que pode ser utilizada em uma grande quantidade de problemas práticos. Após medições realizadas em um equipamento PDM foi possível comparar estes resultados com os valores obtidos utilizando o BSmag. Através do desenvolvimento deste sistema pretendeu-se, além de verificar a eficácia do sistema computacional, conhecer as intensidades e distribuição dos campos magnéticos gerados por estes equipamentos o que pode contribuir para a melhoria destes dispositivos.
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Wiznerowicz, Jan [Verfasser]. "Ein Beitrag zur Berechnung der magnetischen Flussdichte in homogenen und inhomogenen Räumen bei Anwendung des Gesetzes von Biot und Savart / Jan Wiznerowicz." Aachen : Shaker, 2004. http://d-nb.info/1172612447/34.

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Blom, Marcus. "Analys av magnetfält kring högspänd luftledning." Thesis, Uppsala universitet, Elektricitetslära, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414399.

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The digitalization of our community, robotization of our industry and electrification of our transports leads to an increasing demand of electric power, which relies on a strong and reliable grid. In order to continuously be able to deliver stable and qualitative electric power all over Sweden the grid needs to be expanded. To safely expand the grid, several laws, regulations and safety precautions needs to be followed and one of them applies to the magnetic field from high voltage power lines. This Master thesis aims to show two different ways of calculating the magnetic field from high voltage power lines. The first way is to take the transmission line catenary in account and the other is to approximate a straight line and show the magnetic field extension. It also aims to show how the field looks close to transmission poles, both straight and with angles, in order to find out if that changes the field outcome. Both ways of calculating the field shows the same magnetic field magnitude below the point where the catenary hangs down the most. With the catenary taken into account, the magnetic field strength is lower than with the approximation with straight line, and shows the real field extension from the powerline. Using the straight line approximation, the magnetic field is higher and constant below the whole power line. As both ways of calculating takes a high amount of time, the one that gives the real field extension is recommended to use for real life application.
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Buzio, Marco. "Structural effects of plasma instabilities on the JET tokamak." Thesis, Imperial College London, 1999. http://hdl.handle.net/10044/1/7574.

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Cavicchioli, Greta. "Su alcune applicazioni del teorema di Stokes." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7692/.

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Nel lavoro si dimostrano il Teorema della Divergenza e il Teorema di Stokes e le sue generalizzazioni a una curva chiusa di ordine k e a una varietà M, n-dimensionale, orientata con bordo. Successivamente si espongono due applicazioni alla fisica: l'elettromagnetismo e la formula del rotore. Nel primo caso si mostra come applicando il Teorema alle leggi di Biot-Savarat e di Faraday si ottengono le equazioni di Maxwell; nel secondo invece si osserva come il rotore rappresenti la densità superficiale di circuitazione.
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Paese, Evandro. "Estampagem eletromagnética de chapas finas : viabilidade técnica." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2010. http://hdl.handle.net/10183/23932.

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Esta dissertação apresenta modelagem matemática e um método de solução numérica para problemas de conformação eletromagnética de chapas metálicas finas circulares utilizando uma bobina em espiral plana. O método foca especificamente o cálculo do campo eletromagnético gerado pela bobina e análise do circuito que modela o sistema de estampagem eletromagnética. A bobina plana é aproximada por círculos concêntricos carregando a corrente de descarga dos capacitores. Os cálculos das correntes induzidas e perfil da força eletromagnética na chapa e acoplamentos magnéticos entre a bobina e chapa metálica são realizados para o instante inicial, antes da deformação plástica da chapa. O método utiliza a lei de Biot-Savart, sendo que a solução das integrais obtidas para indução magnética é realizada através de métodos numéricos, considerando as simetrias do problema. Para verificação da modelagem matemática, da solução numérica e comprovação da viabilidade técnica deste processo, um dispositivo de estampagem eletromagnética foi desenvolvido e diversos experimentos foram realizados com chapas de alumínio. Os parâmetros investigados foram a espessura da chapa a ser deformada e a influência da presença de vácuo na cavidade da ferramenta. Os resultados experimentais demonstram concordância com os resultados da modelagem proposta. A presença de vácuo também demonstrou um incremento na deformação da chapa. A rotina desenvolvida no software Matlab fornece informações importantes para o processo e permite que se faça ajustes no dispositivo.
This dissertation presents a mathematical model and numerical method to solve the problems of electromagnetic forming of thin circular metal sheets by using a flat spiral coil. The method focuses specifically on the calculation of the electromagnetic field generated by the coil flat and circuit analysis modeling system electromagnetic forming. The flat coil is approximated by concentric circles carrying a discharge current of capacitors. The calculations of induced currents and profile of the electromagnetic force on the plate and magnetic coupling between the coil and sheet metal are made to the initial time, before the plastic deformation of the plate. The method uses the law of Biot-Savart, and the solution of the integral obtained for magnetic induction is performed by numerical methods, considering the symmetries of the problem. To verify the mathematical model, the numerical solution and proving the technical feasibility of this process, a electromagnetic forming device was developed and several experiments were made with aluminum plates. The parameters investigated were the thickness of the plate to be deformed and the influence of the vacuum in the cavity of the tool. The experimental results show agreement with the results of the proposed model. The presence of vacuum also showed an increase in the deformation of the plate. A routine developed in software Matlab provide important information for the process and allow to make adjustments on the device.
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Soukup, Lubomír. "Analýza proudění v potrubí kruhového i nekruhového průřezu metodou využívající rozložení hustoty vířivosti po průřezu." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2016. http://www.nusl.cz/ntk/nusl-256580.

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The doctoral thesis deals with the analysis of the flow in the circular and not circular cross-section pipes by methods using the distribution of the vorticity density. This analysis is particularly focused on the derivation of the new velocity profiles formulas using the above mentioned method. In this work is presented a historical overview of the derived velocity profiles. This overview of already derived velocity profiles will be a fundamental benchmark for newly derived velocity profiles. These new velocity profiles are derived for the circular and not circular cross-section pipes and the derivation is based on the analogy of electromagnetic induction by using Biot-Savart law. It is necessary to apply this analogy at first on solitary vortex filament. By taking this step is possible to get the value of the induced velocity from one solitary vortex filament. Subsequently it is possible to obtain the value of the induced velocity from the vorticity wall and afterwards from the vorticity density distribution over the cross section. This work contains also the results of the experimental measurements of the velocity profiles, and of the CFD simulations. Experimentally measured results are used besides other for the selecting of the most suitable CFD computational model. Selected CFD model will be subsequently declared as a reference model and the valid velocity profiles for this model will serve with the experimentally measured data as a benchmark for the newly derived velocity profiles.
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Payen, Gérard. "Contribution à l'étude des régimes d'écoulement à faible nombre de Reynolds au travers d'expansions symétriques par simulations numériques instationnaires basées sur une méthode de Random Vortex hybride." Rouen, 1991. http://www.theses.fr/1991ROUES017.

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Un outil numérique destiné à la simulation instationnaire d'écoulements incompressibles visqueux partiellement confinés dans le cadre d'une approximation bi-dimensionnelle plane est présenté. Basé sur une méthode de Random Vortex hybride, il exploite l'équation de transport de la vorticité par une discrétisation adaptative sur des éléments lagrangiens à supports compacts. Des algorithmes destinés à améliorer la performance de calcul et la flexibilité sont également introduits. Une étude bibliographique raisonnée relative aux écoulements au travers d'expansions symétriques brusques est menée. Les paramètres déterminants sont dégagés. Différents régimes sont distingués : les transitions rencontrées à nombre de Reynolds croissant conduisent d'un écoulement recirculant symétrique stationnaire à des configurations asymétriques puis à l'apparition d'instabilités. Certaines justifications phénoménologiques sont proposées et les mécanismes mal cernés sont soulignés. La méthode numérique décrite est appliquée à la simulation de ces écoulements et les résultats obtenus comparés aux données expérimentales et numériques disponibles. Les prédictions effectuées sont en excellent accord dans le cas du régime symétrique stationnaire. A un nombre de Reynolds plus élevé, les calculs conduisent à des régimes asymétriques dont seule la nature est conforme aux résultats expérimentaux. Le déclenchement d'instabilités apparaît à une valeur de Reynolds plus faible qu'expérimentalement. Le rôle de la méthode numérique dans ces désaccords est suggéré, ainsi que d'éventuels palliatifs
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Pereira, Arthur Melo. "Cálculo de campos elétricos e magnéticos nas proximidades de linhas de transmissão: uma abordagem analítica e numérica." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/7966.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In a society dependent on electric energy for the execution of various daily activities, it is normal that its use is increasingly increasing over time. In order to carry out the transportation of all electric energy, it is essential to use transmission lines, which with increasing energy demand inevitably have tended to multiply throughout the world, and especially in Brazil, given its continental dimensions. Considering the function of the transmission lines for the electrical system, its importance in the context of the electric power supply is remarkable. However, the lines constitute one of the great emitting sources of electric and magnetic fields of low frequency, which has caused concern and has been motivating fact of several studies, like the realized in this work. Therefore, in view of the scenario presented in the previous paragraph, it is necessary to establish ways of calculating the fields more and more precisely. For the calculation of the electric field is used the Image Method, the Maxwell Potential Coefficients Method and the Coulomb Law, and for the magnetic field the Biot-Savart's Law is used. The results obtained for the electric and magnetic fields were for infinite rectilinear geometries, finite rectilinear and for the conductors taking the form of a catenary, the latter geometry being the most real model for the arrangement of the conductors in a line. In all cases treated, an analytical and numerical approach was performed, in order to allow the calculation of the three geometries with accuracy. Taking advantage of the methodology of calculation of the fields, in addition this work proposes a method of support to the monitoring of transmission lines. The method consists of using the Genetic Algorithm associated to the values of the electric and magnetic fields measured to determine the parameters of the line, such as: phase spacing, cable-soil height, equivalent conductor diameter, current and operating voltage. Given the simplicity of implementation when compared to other methods, the achievement of satisfactory results and the need for a single measuring device to monitor the transmission line, the proposed method proves to be viable and promising to carry out the line monitoring process.
Em uma sociedade dependente da energia elétrica para a execução de diversas atividades do cotidiano, é normal que a sua utilização seja cada vez mais crescente no decorrer do tempo. Para realizar o transporte de toda energia elétrica é imprescindível o uso de linhas de transmissão, que com o aumento da demanda de energia inevitavelmente tenderam a se multiplicar pelo mundo e em especial pelo território brasileiro, dadas as suas dimensões continentais. Tendo em vista a função das linhas de transmissão para o sistema elétrico, é notável a sua importância no contexto do fornecimento de energia elétrica. No entanto, as linhas constituem uma das grandes fontes emissoras de campos elétricos e magnéticos de baixa frequência, o que tem causado preocupação e tem sido fato motivador de diversos estudos, como o realizado neste trabalho. Portanto, diante do cenário apresentado no parágrafo anterior, se faz necessário estabelecer formas de calcular os campos de maneira cada vez mais precisa. Para o cálculo do campo elétrico utiliza-se o Método das Imagens, o Método dos Coeficientes de Potencial de Maxwell e a Lei de Coulomb, já para o campo magnético a Lei de Biot-Savart é empregada. Os resultados obtidos para os campos elétricos e magnéticos foram para as geometrias retilíneas infinitas, retilíneas finitas e para os condutores assumindo a forma de uma catenária, sendo que essa última geometria constitui o modelo mais real quanto à disposição dos condutores em uma linha. Em todos os casos tratados foram realizadas uma abordagem analítica e numérica, de maneira a possibilitar o cálculo das três geometrias com exatidão. Aproveitando-se da metodologia de cálculo dos campos, adicionalmente este trabalho propõe um método de apoio ao monitoramento de linhas de transmissão. O método consiste em utilizar o Algoritmo Genético associado aos valores dos campos elétrico e magnético medidos para determinar os parâmetros da linha, como: espaçamento entre fases, altura cabo-solo, diâmetro equivalente dos condutores, corrente e tensão de operação. Dada a simplicidade de implementação quando comparado a outros métodos, a obtenção de resultados satisfatórios e a necessidade de um único aparelho de medição para monitorar a linha de transmissão, o método proposto mostra-se viável e promissor para realizar o processo de monitoramento de linhas.
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Books on the topic "Biot-Savart"

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Steinle, Friedrich. Electromagnetism and Field Physics. Edited by Jed Z. Buchwald and Robert Fox. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199696253.013.19.

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This article examines developments in electromagnetism and field physics during the early nineteenth century, when electricity had become a fully respected area of research. It begins with a discussion of the ‘Volta’s pile’, an apparatus developed by Alessandro Volta, along with mathematical approaches to electricity and Hans-Christian Ørsted’s discovery of electromagnetism. It then reviews the work of André-Marie Ampère and the Biot–Savart law, introduced by Jean Baptiste Biot and Félix Savart; developments in electrodynamics during the period 1821–1826; and Michael Faraday’s research initiative in electromagnetism, and especially electromagnetic induction and the electrotonic state. It also looks at three important developments in electromagnetism during the 1820s: galvanometers, electromagnets, and Arago’s effect. Finally, it describes Lenz’s law, electromagnetic generators, the electromagnetic telegraph, the Faraday effect, diamagnetism, and the question of polarity as well as the role of mathematics in Faraday’s theories.
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Deruelle, Nathalie, and Jean-Philippe Uzan. Constant fields. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0031.

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This chapter reviews the basic ideas of electrostatics (Coulomb’s law) and magnetostatics (the Biot–Savart law). It studies the motion of a charge in a Coulomb field in detail. The chapter shows how the motion of a charge q in the Coulomb field of a charge Q held fixed at the origin of an inertial frame is governed by the Lorentz equation. Moreover, it can be solved like the Kepler problem discussed in the previous Book. Next, the chapter discusses the Rutherford scattering formula which established the ‘planetary’ model of the atom, the Bohr–Sommerfeld quantization which displayed the limits of the theory, and finally the spin coupling explaining the atomic fine structure.
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Book chapters on the topic "Biot-Savart"

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Weik, Martin H. "Biot-Savart law." In Computer Science and Communications Dictionary, 122. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_1573.

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Peratt, Anthony L. "Biot—Savart Law in Cosmic Plasma." In Physics of the Plasma Universe, 93–135. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2780-9_3.

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Peratt, Anthony L. "Biot-Savart Law in Cosmic Plasma." In Physics of the Plasma Universe, 93–137. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-7819-5_3.

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Lee, Yu-Hsun, and Hiroshi Fujiwara. "Multiple-Precision Arithmetic of Biot-Savart Integrals for Reconnections of Vortex Filaments." In Computational Science and Its Applications – ICCSA 2021, 191–201. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86976-2_13.

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Dirickx, M., S. Denis, B. Vanderheyden, L. Dusoulier, and M. Ausloos. "Inversion of the Biot-Savart Law: An Approach Based on Discrete Sine and Cosine Transforms." In Magneto-Optical Imaging, 257–64. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-007-1007-8_33.

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"Interaction of currents, Biot–Savart law, and magnetic field." In Principles of Dielectric Logging Theory, 311–24. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-12-822283-6.00009-x.

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Pesic, Peter. "Electric Sounds." In Music and the Making of Modern Science. The MIT Press, 2014. http://dx.doi.org/10.7551/mitpress/9780262027274.003.0013.

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Those who followed Leonhard Euler’s wave theory of light often re-engaged its relation to sound. The study of electricity and magnetism resonated with ongoing initiatives in light and sound, reflecting also wider philosophical ideas about the unity of nature epitomized by Naturphilosophie. This chapter examines the intertwined study of electricity and acoustics by Georg Christoph Lichtenberg, Johann Ritter, and Ernst Chladni. The search to unify the forces of nature often relied on analogies with sound, which in turn looked to electricity for new tools. Félix Savart studied the vibration patterns of violins; after reviewing this work, Jean-Baptiste Biot joined Savart in working on electromagnetism. In the aftermath of Thomas Young’s work, waves became a newly attractive explanatory approach to the problems of electricity. Building directly on Chladni’s sound figures, Hans Christian Ørsted discovered the synthesis of “electromagnetism” that brought a new unity to these two formerly separate forces, realizing the unitive hopes of Naturphilosophie. Ørsted’s discovery involved realizing the dynamic, transverse action of electromagnetism, qualities he had previously studied in vibrating plates. Throughout the book where various sound examples are referenced, please see http://mitpress.mit.edu/musicandmodernscience (please note that the sound examples should be viewed in Chrome or Safari Web browsers).
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SASLOW, W. "How Electric Currents Make Magnetic FieldThe Biot-Savart Law and Ampère's Law." In Electricity, Magnetism, and Light, 460–504. Elsevier, 2002. http://dx.doi.org/10.1016/b978-012619455-5/50011-5.

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Pierrus, J. "Static magnetic fields in vacuum." In Solved Problems in Classical Electromagnetism. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821915.003.0004.

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Wherever possible, an attempt has been made to structure this chapter along similar lines to Chapter 2 (its electrostatic counterpart). Maxwell’s magnetostatic equations are derived from Ampere’s experimental law of force. These results, along with the Biot–Savart law, are then used to determine the magnetic field B arising from various stationary current distributions. The magnetic vector potential A emerges naturally during our discussion, and it features prominently in questions throughout the remainder of this book. Also mentioned is the magnetic scalar potential. Although of lesser theoretical significance than the vector potential, the magnetic scalar potential can sometimes be an effective problem-solving device. Some examples of this are provided. This chapter concludes by making a multipole expansion of A and introducing the magnetic multipole moments of a bounded distribution of stationary currents. Several applications involving magnetic dipoles and magnetic quadrupoles are given.
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Saslow, Wayne M. "How Electric Currents Make Magnetic Fields: The Biot– Savart Law and Ampère's Law." In Electricity, Magnetism, and Light, 460–504. Elsevier, 2002. http://dx.doi.org/10.1016/b978-012619455-5.50011-5.

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Conference papers on the topic "Biot-Savart"

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Chase, Jay B., and Giles Peterson. "Biot-Savart for bifurcation, BSBIF." In 2012 14th International Conference on Megagauss Magnetic Field Generation and Related Topics (MEGAGAUSS). IEEE, 2012. http://dx.doi.org/10.1109/megagauss.2012.6781449.

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Gyimesi, I., D. Lavers, T. Pawlak, and D. Ostergaard. "Biot-savart Integration For Bars And Arcs." In 1993 Digests of International Magnetics Conference. IEEE, 1993. http://dx.doi.org/10.1109/intmag.1993.642064.

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Li, Chung-Hsin, Meng-Hua Tu, Sung-Mao Wu, and Cheng-Chang Chen. "Novel radiation signal detecting and non-contact probe modeling by Biot-Savart Theorem." In 2015 Asia-Pacific Microwave Conference (APMC). IEEE, 2015. http://dx.doi.org/10.1109/apmc.2015.7411692.

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Volkmar, Chris, Timo Baruth, Jens Simon, Ubbo Ricklefs, and Rainer Thueringer. "Arbitrarily shaped coils' inductance simulation based on a 3-dimensional solution of the Biot-Savart law." In 2013 36th International Spring Seminar on Electronics Technology (ISSE). IEEE, 2013. http://dx.doi.org/10.1109/isse.2013.6648244.

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Ki-Chan Kim and Soo-Jin Hwang. "Comparison study of Biot-Savart law and 3D FEM of electromagnetic forces acting on end windings." In 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2010). IEEE, 2010. http://dx.doi.org/10.1109/cefc.2010.5481680.

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Yoneda, Satoshi, Kenji Hirose, Akihto Kobayashi, Yuichi Sasaki, and Chiharu Miyazaki. "A study for designing an ESL-cancelling circuit for shunt capacitor filters based on the biot-savart law." In 2017 IEEE International Symposium on Electromagnetic Compatibility & Signal/Power Integrity (EMCSI). IEEE, 2017. http://dx.doi.org/10.1109/isemc.2017.8077834.

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Ojima, Akira, and Kyoji Kamemoto. "Virtual Operation of Fluid Machinery by a Vortex Element Method." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45115.

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This paper describes recent works of practical applications of vortex element methods in the field of fluid machinery, carried by the authors’ group, explaining the mathematical basis of the method based on the Biot-Savart law. It is pointed as one of the most attractive features of the vortex method that the numerical simulation using the method is considered to be a new and simple technique of large eddy simulation, because they consist of simple algorithm based on physics of flow and it provides a completely grid-free Lagrangian calculation. As typical results of virtual operation of fluid machinery, the internal flow of a mixed-flow pump stage, unsteady flows through a wind turbine, and behaviors of submerged vortex in a pump sump are explained.
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Straccia, Joseph C., and John A. Farnsworth. "Application of a Biot-Savart Solver to Predict Axis Switching Phenomenon in Finite-Span Vortices Expelled from a Synthetic Jet." In 47th AIAA Fluid Dynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2017. http://dx.doi.org/10.2514/6.2017-3311.

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Saverin, Joseph, David Marten, George Pechlivanoglou, Christian Oliver Paschereit, and Arne van Garrel. "Implementation of the Multi-Level Multi-Integration Cluster Method to the Treatment of Vortex Particle Interactions for Fast Wind Turbine Wake Simulations." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76554.

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A method for the treatment of the evolution of the wake of aerodynamic bodies has been implemented. A vortex particle method approach has been used whereby the flow field is discretized into numerical volumes which possess a given circulation. A lifting line formulation is used to determine the circulation of the trailing and shed vortex elements. Upon their release vortex particles are allowed to freely convect under the action of the blade, the freestream and other particles. Induced velocities are calculated with a regularized form of the Biot-Savart kernel, adapted for vortex particles. Vortex trajectories are integrated in a Lagrangian sense. Provision is made in the model for the rate of change of the circulation vector and for viscous particle interaction; however these features are not exploited in this work. The validity of the model is tested by comparing results of the numerical simulation to the experimental measurements of the Mexico rotor. A range of tip speed ratios are investigated and the blade loading and induced wake velocities are compared to experiment and finite-volume numerical models. The computational expense of this method scales quadratically with the number of released wake particles N. This results in an unacceptable computational expense after a limited simulation time. A recently developed multilevel algorithm has been implemented to overcome this computational expense. This method approximates the Biot-Savart kernel in the far field by using polynomial interpolation onto a structured grid node system. The error of this approximation is seen to be arbitrarily controlled by the polynomial order of the interpolation. It is demonstrated that by using this method the computational expense scales linearly. The model’s ability to quickly produce results of comparable accuracy to finite volume simulations is illustrated and emphasizes the opportunity for industry to move from low fidelity, less accurate blade-element-momentum methods towards higher fidelity free vortex wake models while keeping the advantage of short problem turnaround times.
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Ojima, Akira, and Kyoji Kamemoto. "Applicability of the Vortex Methods for Automotive Flows." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45135.

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This paper describes recent works of practical applications of vortex element methods to study of automotive flows, carried by the authors’ group, explaining the mathematical basis of the method based on the Biot-Savart law. It is pointed as one of the most attractive features of the vortex method that the numerical simulation using the method is considered to be a new and simple technique of large eddy simulation, because they consist of simple algorithm based on physics of flow and it provides a completely grid-free Lagrangian calculation. As typical results of automotive flows, unsteady flows around a simplified vehicle model such as a wedge model, unsteady flows around a heavy vehicle model as a tractor-trailer, and unsteady aerodynamic characteristics of a tractor-trailer with meandering motion are explained.
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