Relevant bibliographies by topics / Biot Savart's law

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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's law'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "Biot Savart's law"

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Qihou, Z. "Proof of Biot-Savart's law for a discontinuous current-or another example of displacement current." European Journal of Physics 8, no. 2 (April 1, 1987): 128–30. http://dx.doi.org/10.1088/0143-0807/8/2/010.

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Kim, Ki-Chan. "Comparison of Biot-Savart's Law and 3D FEM in the Study of Electromagnetic Forces Acting on End Winding." Journal of Electrical Engineering and Technology 6, no. 3 (May 2, 2011): 369–74. http://dx.doi.org/10.5370/jeet.2011.6.3.369.

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Zhou, Zhen, Z. H. Guan, J. Luo, L. J. Wang, Y. Qin, and G. F. Sun. "Finite Element Analysis of Inductance Sensor Structure in the Measuring System of the Grade of the Iron Concentrate." Key Engineering Materials 458 (December 2010): 155–60. http://dx.doi.org/10.4028/www.scientific.net/kem.458.155.

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According to the Biot-Savart's Law, the principle of the detecting system which measures the grade of the iron concentrate is analysed in this paper. It carries out an analysis of influence of inductance sensor coil structure parameters on the performance of sensor. The finite element model of the air core coil is established and analysis of finite element simulation is done to inductance sensors by using orthogonal method. According to different structural parameters, the relation of magnetic permeability of the iron concentrate and the inductance of the sensor coil can be established. Moreover, the effect of the sensor coil’s parameter on the linearity and the sensitivity of the sensor can also be determined. All the above provide a reference for the design of coil structure parameter of the inductance sensors.
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BARBOSA, DISTERFANO L. M., JERSON R. P. VAZ, SÁVIO W. O. FIGUEIREDO, MARCELO DE OLIVEIRA E. SILVA, ERB F. LINS, and ANDRÉ L. A. MESQUITA. "An Investigation of a Mathematical Model for the Internal Velocity Profile of Conical Diffusers Applied to DAWTs." Anais da Academia Brasileira de Ciências 87, no. 2 (April 28, 2015): 1133–48. http://dx.doi.org/10.1590/0001-3765201520140114.

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The Diffuser Augmented Wind Turbines (DAWTs) have been widely studied, since the diffusers improve the power coefficient of the wind turbine, particularly of small systems. The diffuser is a device which has the function of causing an increase on the flow velocity through the wind rotor plane due to pressure drop downstream, therefore resulting in an increase of the rotor power coefficient. This technology aids the turbine to exceed the Betz limit, which states that the maximum kinetic energy extracted from the flow is 59.26%. Thus, the present study proposes a mathematical model describing the behavior of the internal velocity for three conical diffusers, taking into account the characteristics of flow around them. The proposed model is based on the Biot-Savart's Law, in which the vortex filament induces a velocity field at an arbitrary point on the axis of symmetry of the diffusers. The results are compared with experimental data obtained for the three diffusers, and present good agreement.
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Ganushkina, N. Yu, M. W. Liemohn, and T. I. Pulkkinen. "Storm-time ring current: model-dependent results." Annales Geophysicae 30, no. 1 (January 17, 2012): 177–202. http://dx.doi.org/10.5194/angeo-30-177-2012.

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Abstract. The main point of the paper is to investigate how much the modeled ring current depends on the representations of magnetic and electric fields and boundary conditions used in simulations. Two storm events, one moderate (SymH minimum of −120 nT) on 6–7 November 1997 and one intense (SymH minimum of −230 nT) on 21–22 October 1999, are modeled. A rather simple ring current model is employed, namely, the Inner Magnetosphere Particle Transport and Acceleration model (IMPTAM), in order to make the results most evident. Four different magnetic field and two electric field representations and four boundary conditions are used. We find that different combinations of the magnetic and electric field configurations and boundary conditions result in very different modeled ring current, and, therefore, the physical conclusions based on simulation results can differ significantly. A time-dependent boundary outside of 6.6 RE gives a possibility to take into account the particles in the transition region (between dipole and stretched field lines) forming partial ring current and near-Earth tail current in that region. Calculating the model SymH* by Biot-Savart's law instead of the widely used Dessler-Parker-Sckopke (DPS) relation gives larger and more realistic values, since the currents are calculated in the regions with nondipolar magnetic field. Therefore, the boundary location and the method of SymH* calculation are of key importance for ring current data-model comparisons to be correctly interpreted.
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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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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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Pyati, Vittal P. "Simplified Biot-Savart Law for Planar Circuits." IEEE Transactions on Education E-29, no. 1 (February 1986): 32–33. http://dx.doi.org/10.1109/te.1986.5570681.

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Kabbary, F. M., B. G. Stewart, and M. C. Hately. "Displacement Current and the Biot-Savart Law." International Journal of Electrical Engineering Education 27, no. 4 (October 1990): 344–55. http://dx.doi.org/10.1177/002072099002700412.

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Phillips, Jeffrey A., and Jeff Sanny. "The Biot-Savart Law: From Infinitesimal to Infinite." Physics Teacher 46, no. 1 (January 2008): 44–47. http://dx.doi.org/10.1119/1.2824000.

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Dissertations / Theses on the topic "Biot Savart's law"

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Gärskog, Gustav. "NUMERICAL CALCULATION METHOD FOR MAGNETIC FIELDS IN THE VICINITY OF CURRENT-CARRYING CONDUCTORS." Thesis, Uppsala universitet, Elektricitetslära, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-353338.

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This thesis aims to develop a calculation method to determine themagnetic field magnitudes in the vicinity of power lines, i.e. bothburied cables and overhead lines. This is done through the numericaluse of Biot Savart's law where the conductors are approximated by aseries of straight segment elements that each contribute to the overallfield strength at the field point. The method is compared to two realcases and to the exact integral solution. Also, a review of some of theresearch material regarding electromagnetic fields from power lines andclaims of adverse health effects due to these fields is conducted.Results show that the numerical error is dependent on the segmentationdegree of the conductors and the mathematical model is inaccurate closeto the conductor. The calculations show slightly higher fieldmagnitudes than the previous survey done by WSP (Williams SalePartnership) far away from the source and slightly lower at the centerconductor. This may be due to the excluded induction in the shieldwires and differences in actual conductor coordinates.
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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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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-11-16T09:48:38Z No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)
Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-11-16T09:49:04Z (GMT) No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)
Made available in DSpace on 2017-11-16T09:49:04Z (GMT). No. of bitstreams: 2 Dissertação - Arthur Melo Pereira - 2017.pdf: 8324435 bytes, checksum: a36f9e13810ace212ce9d44a66fc2fb4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-09-26
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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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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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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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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劉家榮. "Interesting Application of Biot-Savart Law and Experiment." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/88867207385818421956.

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Liang, En-Wei, and 梁恩維. "Velocity-Vorticity Formulation for the 2D Stokes Flows by Biot-Savart Law and Boundary Element Method." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/90456421723735909036.

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碩士
國立臺灣大學
土木工程學研究所
88
In this study, velocity-vorticity formulation and Biot-Savart law are used to solve the two-dimensional steady incompressible stokes flow. The boundary element method is chosen to discrete the governing equations. The geometric shapes of the flow field include both the circular and square cavity flows which all exist exact or series solutions. The boundary conditions of vorticity for the vorticity transport equation are determined by the principle of the relationship between circulation and vorticity, namely, the Stokes theorems. To demonstrate the model feasibility, the results of two-dimensional steady incompressible Stokes flows of the square cavity flows are compared with the Fourier series solutions of [Burggraf , 1966] ；and results of the circular cavity flows are also used to compared with exact solution of [Hwu et al. , 1997]。 The present study show that good results are obtained for all the cases simulated except at the singular points of the boundary.
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Alves, Rui Diogo Quesado. "EasyMAG – Toolbox para cálculo de campos magnéticos de baixa frequência." Master's thesis, 2018. http://hdl.handle.net/10316/86420.

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Dissertação de Mestrado Integrado em Engenharia Electrotécnica e de Computadores apresentada à Faculdade de Ciências e Tecnologia
A evolução tecnológica e o elevado desenvolvimento industrial que caracteriza a civilização contemporânea, torna a sociedade fortemente dependente de energia. Devido a esta evolução, houve um aumento do uso de aparelhos elétricos e consequentemente um aumento das redes elétricas, surgindo assim um aumento na intensidade de campos magnéticos originados pela corrente elétrica que percorre as redes e os aparelhos. Este aumento intensidade de campos magnéticos originou uma preocupação na sociedade sobre os efeitos do campo magnético na saúde dos seres humanos. Foi esta a motivação para este trabalho: desenvolver o software ‘EASYMAG’ para calcular a densidade do fluxo magnético originado por correntes elétricas em condutores, utilizando a lei de Biot-Savart.O software desenvolvido tem incorporadas as seguintes funcionalidades: verificação da introdução correta dos dados, alertando o utilizador se um circuito constituído por várias linhas estiver aberto; visualização gráfica do circuito elétrico definido pelo utilizador com cores diferentes consoante o circuito seja unifilar ou bifilar; cálculo da densidade do fluxo magnético nos pontos indicados pelo utilizador, mostrando a localização onde esse valor é máximo e mínimo; visualização gráfica da densidade do fluxo magnético nos pontos definidos pelo utilizador; guardar simulação feita pelo utilizador.O software ‘EASYMAG’ é inovador comparado com os outros softwares existentes, porque utiliza o Excel como método de introdução de dados, conseguindo assim representar o circuito elétrico pretendido pelo utilizador, sem que este tenha que programar em Matlab o circuito, tornando ainda o software ‘EASYMAG’ acessível para todas as pessoas com conhecimento básico de Matlab.Para validar o software foram usados três exemplos teóricos. O software, nestes três exemplos, obteve resultados com um erro muito pequeno, dependendo do número de pontos usados para a representação dos elementos circuitais, curva e solenoide. O software desenvolvido é assim uma ferramenta fiável para o cálculo de casos teóricos e práticos da densidade do fluxo magnético originado por correntes elétricas em condutores, sendo o erro associado próximo de zero.
The technological evolution and the high industrial development that characterizes the contemporary civilization, makes the society strongly dependent on energy. Due to this evolution, there has been an increase of the electrical devices usage and consequently an increase of the electrical networks, arising an increase in the intensity of magnetic fields originated by the electric current that runs through the networks and electrical devices. This increased intensity of magnetic fields has given rise to the concern in the society about the effects of magnetic fields on human health. This was the motivation for this work: to develop the software 'EASYMAG' to calculate the magnetic flux density originated by electric currents in conductors, using the Biot-Savart law. The developed software incorporates the following functionalities: verification of the correct data entry, alerting the user if a circuit consisting of several lines is open; graphical visualization of the electrical circuit defined by the user with different colors depending on whether the circuit is unifilar or bifilar; calculation of the magnetic flux density at the points indicated by the user, showing the location where this value is maximum and minimum; graphical display of magnetic flux density at user-defined points; save simulation done by the user. The software 'EASYMAG' is innovative compared to other existing software, because it uses Excel as a data entry method, representing the desired electrical circuit without having to program the circuit in Matlab, making the software 'EASYMAG' accessible to all people with basic knowledge of Matlab. Three theoretical examples are presented to validate the software. The software, in these three examples, obtained results with a very small error, depending on the number of points used for the representation of the circuit elements, curve and solenoid. The developed software is a reliable tool for the calculation of theoretical and practical cases of the magnetic flux density originated by electric currents in conductors, the associated error being close to zero.
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Books on the topic "Biot Savart's law"

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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's law"

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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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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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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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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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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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"Appendix F: Solution of the Biot–Savart Law for a Straight-Line Segment." In Introduction to Helicopter and Tiltrotor Flight Simulation, 559–72. Reston ,VA: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/5.9781600862083.0559.0572.

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"coils is also presented in Section 2. The simulation produced by the Helmholtz coils, which damages the results about the optimum parameter for Helmholtz uniform magnetic field. Therefore, theoretical coils are presented in Section 3. Finally, conclusion parameters of Helmholtz coils cannot be used and further work are outlined in Section 4. directly in edge detection. By extracting temperature information using COMSOL via the AC/DC module, we can confirm which optimum parameters 2 METHODOLOGY AND EXPERIMENT SETUP of Helmholtz coils can produce most effective Helmholtz coils are a special arrangement of air-excitation for edge detection. cored coils, and they are all used as a means of This simulation is conducted using COMSOL generating magnetic fields that are uniform over a multiphysics FEM simulation software via the volume (Cakir ). According to Biot-Savart AC/DC module. Fig. 1 shows the constitution of law, magnetic flux density at any point on the axis of Helmholtz coils testing, where r is the minor radius Helmholtz coils can be calculated from Equation (1) of Helmholtz coils, r is the major radius of (Bronaugh )： Helmholtz coils, h is the sample height, d is the N Ir N Ir distance between Helmholtz coils edge and sample H  H H   (1) edge, and z is the distance between Helmholtz coils. 2  r a  2  r a  The physical characteristics of the model to be simulated and studied are given in Table 1. The According to the definition of Helmholtz coils, geometry of the sample is 40502 mm ; the r  r  r , N  N 1 and 2a  2a  r . major and minor radii of Helmholtz coils are equal Using Taylor series expansion and calculating the to 10 mm and 2 mm, respectively, and the turns differential of H (0) (when z  0 ), after some equal 1. The excitation module is a small period (0.3 s) of high-frequency current (256 kHz). manipulation, Equation (1) becomes Table 1. Electrical and thermal parameters for steel  144  z   used in the simulation H ( z )  H (0)   1   125  r   (2)     ." In Structural Health Monitoring and Integrity Management, 200–202. CRC Press, 2015. http://dx.doi.org/10.1201/b18510-65.

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Conference papers on the topic "Biot Savart's law"

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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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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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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. "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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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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Xu, Guanpeng, and Lakshmi N. Sankar. "Application of a Viscous Flow Methodology to the NREL Phase VI Rotor." In ASME 2002 Wind Energy Symposium. ASMEDC, 2002. http://dx.doi.org/10.1115/wind2002-30.

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A numerical technique has been developed for efficiently simulating fully three-dimensional viscous fluid flow around horizontal axis wind turbines (HAWT). In this approach, the viscous region surrounding the blades is modeled using 3-D unsteady Navier-Stokes equations. The inviscid region away from the boundary layer and the wake is modeled using potential flow. The concentrated vortices that emanate from the blade tip are treated as piecewise straight line segments that are allowed to deform and convect at the local flow velocity. Biot-Savart law is used to estimate the velocity field associated with these vortices. Calculations are presented under axial wind conditions for a NREL two-bladed rotor, known as the Phase VI rotor, tested at the NASA Ames Research Center. Good agreement with the measurements is found. The computed results are used to develop improved engineering models for the loss of lift at the blade tip, and for the delay in the stall angle at inboard locations. The improved models are incorporated in a blade element-momentum (BEM) analysis to study the post-stall behavior of a three-bladed rotor tested at NREL.
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Kamemoto, Kyoji, and Akira Ojima. "Application of a Vortex Method to Fluid Dynamics in Sports Science." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37066.

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This paper describes a pioneering work of practical application of an advanced vortex method in the field of fluid dynamics in sports science. The vortex method developed by the present authors is one of vortex element methods based on the Biot-Savart law, and it is known that the method provides a Lagrangian simulation of unsteady and vortical flows. In this study, in order to examine the applicability of the vortex method, three-dimensional, complex and unsteady flows around an isolated 100 m runner and a ski-jumper were calculated. Basic equations and mathematical treatment of the method are explained in this paper, and calculation conditions and panel data of deforming configuration of the athletes are described. As results of the present study, vortical and unsteady flow features around a runner and a ski-jumper are understood, and unsteady variation of aerodynamic forces corresponding to deformation of body configuration due to athletic motion are calculated. And, it is confirmed that the advanced vortex element method is a promising way to a grid-free Lagrangian large eddy simulation of unsteady and complex flows around dynamic bodies of athletes.
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Cuadrado, D. G., S. Lavagnoli, and G. Paniagua. "Methodology to Correct the Magnetic Field Effect on Thin Film Measurements." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42715.

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Machined ferrous metal components may carry a magnetic field, which in rotation disturb the output of electrical sensors. To minimize the effect on the electrical instrumentation, the rotating components are usually demagnetized. However, even after the demagnetization process, a residual magnetism unavoidably remains. This paper presents a methodology to predict the effects of a rotating magnetic field induced on thin-film measurements. In addition to the prediction of the magnetic effects, a procedure to correct the spurious variation in the readings of thin film gauges has been developed to enhance the fidelity of the measurements. An analytical model was developed to reproduce the bias on the electrical signal from sensors exposed to rotor airfoils with magnets. The model is based on the Biot-Savart law to generate the magnetic field, and the Faraday’s law to calculate the electromotive force induced along the measurement circuit. The model was assessed by means of controlled experiments varying the rotor tip clearance and rotational speed. The presented methodologies allowed the correction of the magnetic field effects. The raw signal of the thin film sensors, in the absence of any correction, is prone to deliver errors in the heat flux amounting to about 8% of the mean overall value. Thanks to the developed corrective approach, the residual magnetic effect contribution to the heat flux error would be 2% at most.
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Hu, Site, Chao Zhou, Zhenhua Xia, and Shiyi Chen. "LES and CDNS Investigation of T106C Low Pressure Turbine." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56838.

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This paper investigates the aerodynamic performance of a low pressure turbine, namely the T106C, by large eddy simulation (LES) and coarse grid direct numerical simulation (CDNS) at a Reynolds number of 100,000. The existing experimental data is used to validate the results. The effects of sub-grid scale (SGS) models, mesh densities, computational domains and boundary conditions on the result are studied. A separation zone appears downstream 60% S/S0, which is difficult to be predicted precisely. Two SGS models, i.e. Smagorinsky and WALE model are implemented. WALE model produces a better result than Smagorinsky model when the mesh is coarse. For the fine mesh, the difference due to the SGS models becomes smaller. It is surprising to find that CDNS produces very similar results to WALE model, and their results are in better agreement with the experiment than that of Smagorinsky model. The computational domain is also important for the prediction of the flow near the midspan. 3D features of the separated flow have an effect on the downstream flows, especially for the area near the reattachment. Sufficient long spanwise computational domain is important for an accurate prediction. The current study also find that the endwall secondary flow has an effect on the flow separation near the middle span, which was seldom discussed before. By considering the effects of endwall secondary flows, better prediction of the flow separation near the blade midspan can be achieved. The effect of the endwall secondary flow on the blade suction side separation is also explained with the analytical method based on the Biot-Savart Law.
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