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Journal articles on the topic 'Biot-Savart'

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Published: 4 June 2021
Last updated: 14 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

Cavalleri, G., G. Spavieri, and G. Spinelli. "The Ampère and Biot - Savart force laws." European Journal of Physics 17, no. 4 (July 1, 1996): 205–7. http://dx.doi.org/10.1088/0143-0807/17/4/010.

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14

Gyimesi, M., D. Lavers, T. Pawlak, and D. Ostergaard. "Biot-Savart integration for bars and arcs." IEEE Transactions on Magnetics 29, no. 6 (November 1993): 2389–91. http://dx.doi.org/10.1109/20.281007.

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15

Afjeh, A. A., and T. G. Keith. "A Vortex Lifting Line Method for the Analysis of Horizontal Axis Wind Turbines." Journal of Solar Energy Engineering 108, no. 4 (November 1, 1986): 303–9. http://dx.doi.org/10.1115/1.3268110.

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The present paper utilizes an earlier analytical wake model, which essentially applies to helicopter load analysis, to determine the performance of horizontal axis wind turbines. The advantage of this method is that it makes use of an integrated version of the Biot-Savart law for each part of the wake and thereby avoids some of the numerical difficulties present in the Biot-Savart law. Numerical computations were performed for a number of two-bladed rotor geometries and operating conditions. Results were compared with experimental data as well as with predictions of a full free wake method. Good overall agreement with both was observed.
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16

Moyssides, P. G., and P. T. Pappas. "Rigorous quantitative test of Biot–Savart–Lorentz forces." Journal of Applied Physics 59, no. 1 (January 1986): 19–27. http://dx.doi.org/10.1063/1.336863.

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17

Enciso, Alberto, M. Ángeles García-Ferrero, and Daniel Peralta-Salas. "The Biot–Savart operator of a bounded domain." Journal de Mathématiques Pures et Appliquées 119 (November 2018): 85–113. http://dx.doi.org/10.1016/j.matpur.2017.11.004.

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18

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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19

Yan, C. C. "Theoretical experimentation with the law of Biot-Savart." Foundations of Physics 24, no. 1 (January 1994): 163–75. http://dx.doi.org/10.1007/bf02053913.

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20

Teyber, Reed, Lucas Brouwer, Ji Qiang, and Soren Prestemon. "Inverse Biot–Savart Optimization for Superconducting Accelerator Magnets." IEEE Transactions on Magnetics 57, no. 9 (September 2021): 1–7. http://dx.doi.org/10.1109/tmag.2021.3092527.

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21

WOOD, D. H., and J. BOERSMA. "On the motion of multiple helical vortices." Journal of Fluid Mechanics 447 (October 30, 2001): 149–71. http://dx.doi.org/10.1017/s002211200100578x.

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The analysis of the self-induced velocity of a single helical vortex (Boersma & Wood 1999) is extended to include equally spaced multiple vortices. This arrangement approximates the tip vortices in the far wake of multi-bladed wind turbines, propellers, or rotors in ascending, descending, or hovering flight. The problem is reduced to finding, from the Biot–Savart law, the additional velocity of a helix due to an identical helix displaced azimuthally. The resulting Biot–Savart integral is further reduced to a Mellin–Barnes integral representation which allows the asymptotic expansions to be determined for small and for large pitch. The Biot–Savart integral is also evaluated numerically for a total of two, three and four vortices over a range of pitch values. The previous finding that the self-induced velocity at small pitch is dominated by a term inversely proportional to the pitch carries over to multiple vortices. It is shown that a far wake dominated by helical tip vortices is consistent with the one-dimensional representation that leads to the Betz limit on the power output of wind turbines. The small-pitch approximation then allows the determination of the blade&s bound vorticity for optimum power extraction. The present analysis is shown to give reasonable estimates for the vortex circulation in experiments using a single hovering rotor and a four-bladed propeller.
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22

Kou, Su-Peng. "Kelvin wave and knot dynamics on entangled vortices." International Journal of Modern Physics B 31, no. 31 (December 10, 2017): 1750241. http://dx.doi.org/10.1142/s0217979217502411.

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In this paper, starting from Biot–Savart mechanics for entangled vortex-membranes, a new theory — knot physics — is developed to explore the underlying physics of quantum mechanics. Owning to the conservation conditions of the volume of knots on vortices in incompressible fluid, the shape of knots will never be changed and the corresponding Kelvin waves cannot evolve smoothly. Instead, the knot can only be split. The knot-pieces evolve following the equation of motion of Biot–Savart equation that becomes Schrödinger equation for probability waves of knots. The classical functions for Kelvin waves become wave-functions for knots. The effective theory of perturbative entangled vortex-membranes becomes a traditional model of relativistic quantum field theory — a massive Dirac model. As a result, this work would help researchers to understand the mystery in quantum mechanics.
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23

Kimura, Y., and H. K. Moffatt. "Scaling properties towards vortex reconnection under Biot–Savart evolution." Fluid Dynamics Research 50, no. 1 (December 6, 2017): 011409. http://dx.doi.org/10.1088/1873-7005/aa710c.

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24

Titov, Viacheslav S., Cooper Downs, Zoran Mikić, Tibor Török, Jon A. Linker, and Ronald M. Caplan. "Regularized Biot–Savart Laws for Modeling Magnetic Flux Ropes." Astrophysical Journal 852, no. 2 (January 5, 2018): L21. http://dx.doi.org/10.3847/2041-8213/aaa3da.

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25

Pelloni, S., A. Ligabue, and P. Lazzeretti. "Ring-Current Models from the Differential Biot-Savart Law." Organic Letters 6, no. 24 (November 2004): 4451–54. http://dx.doi.org/10.1021/ol048332m.

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26

Khosropour, B., and S. K. Moayedi. "Application of Biot–Savart law and generalized uncertainty principle." International Journal of Geometric Methods in Modern Physics 16, no. 04 (April 2019): 1950065. http://dx.doi.org/10.1142/s0219887819500658.

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In the recent decade, many investigations have been done in the framework of generalized uncertainty principle (GUP), but the phenomenology of models in this framework are less studied. In this work, the applications of Biot–Savart law in the presence of a minimal length scale are investigated. We obtain the modified magnetostatic field from an infinitely long, straight wire carrying current [Formula: see text]. Also, the modified magnetostatic field from a circular loop carrying current [Formula: see text] and the modified magnetostatic field of an ideal solenoid are found. It is interesting to note that in the limit [Formula: see text], all of the modified magnetostatic fields become their usual forms.
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27

Szalek, Marek A. "Pauli versus the Maxwell Equations and the Biot‐Savart Law." Physics Essays 10, no. 1 (March 1997): 95–102. http://dx.doi.org/10.4006/1.3028706.

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28

ESİN, Yunus Emre, and Ferda Nur ALPASLAN. "MRI image enhancement using Biot--Savart law at 3 tesla." TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES 25 (2017): 3381–96. http://dx.doi.org/10.3906/elk-1604-348.

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29

Ton, Tran‐Cong. "On the time‐dependent, generalized Coulomb and Biot–Savart laws." American Journal of Physics 59, no. 6 (June 1991): 520–28. http://dx.doi.org/10.1119/1.16812.

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30

Kröger, R., R. Unbehauen, David J. Griffiths, and Mark A. Heald. "Time‐dependent generalizations of the Biot–Savart and Coulomb laws." American Journal of Physics 60, no. 5 (May 1992): 393–94. http://dx.doi.org/10.1119/1.16888.

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31

Griffiths, David J., and Mark A. Heald. "Time‐dependent generalizations of the Biot–Savart and Coulomb laws." American Journal of Physics 59, no. 2 (February 1991): 111–17. http://dx.doi.org/10.1119/1.16589.

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32

Pooley, Benjamin C., and José L. Rodrigo. "Asymptotics for vortex filaments using a modified Biot-Savart kernel." Journal of Mathematical Analysis and Applications 485, no. 1 (May 2020): 123755. http://dx.doi.org/10.1016/j.jmaa.2019.123755.

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33

Kalhor, H. A. "The degree of intelligence of the law of Biot-Savart." IEEE Transactions on Education 33, no. 4 (1990): 365–66. http://dx.doi.org/10.1109/13.61093.

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34

Evans, M. W. "The Biot-Savart-Ampère law and the vacuum fieldB (3)." Foundations of Physics Letters 8, no. 4 (August 1995): 381–88. http://dx.doi.org/10.1007/bf02187818.

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35

Jolly, David C. "Identity of the Ampere and Biot-Savart electromagnetic force laws." Physics Letters A 107, no. 5 (February 1985): 231–34. http://dx.doi.org/10.1016/0375-9601(85)90589-4.

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36

Kondaurova, Luiza, and Sergey K. Nemirovskii. "Full Biot-Savart Numerical Simulation of Vortices in He II." Journal of Low Temperature Physics 138, no. 3-4 (February 2005): 555–60. http://dx.doi.org/10.1007/s10909-005-2260-9.

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37

Kusiak, Dariusz, Tomasz Szczegielniak, and Zygmunt Piątek. "Magnetic field of a ribbon busbar of finite length." ITM Web of Conferences 19 (2018): 01010. http://dx.doi.org/10.1051/itmconf/20181901010.

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Using the analytic method based on the Biot-Savart law for the electromagnetic field, the distribution of the magnetic field of a ribbon busbar of finite length has been determined. The Mathematica program was used to visualize the solutions obtained. This allowed quick field analysis after changes of geometrical or electrical parameters of systems under examination.
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38

Wang, Xu, Yingxu Li, Yuanwen Gao, and Youhe Zhou. "Self-field calculation of CICC with fast direct Biot–Savart integration." Fusion Engineering and Design 89, no. 4 (April 2014): 473–86. http://dx.doi.org/10.1016/j.fusengdes.2014.04.015.

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39

Garretson, Craig M. "A combined form of the laws of Ampere and Biot–Savart." American Journal of Physics 54, no. 3 (March 1986): 253–58. http://dx.doi.org/10.1119/1.14639.

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40

Ruppeiner, George, Michael Grossman, and Ali Tafti. "Test of the Biot–Savart law to distances of 15 m." American Journal of Physics 64, no. 6 (June 1996): 698–705. http://dx.doi.org/10.1119/1.18235.

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41

Hanson, James D., and Steven P. Hirshman. "Compact expressions for the Biot–Savart fields of a filamentary segment." Physics of Plasmas 9, no. 10 (October 2002): 4410–12. http://dx.doi.org/10.1063/1.1507589.

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42

Weber, T. A., and D. J. Macomb. "On the equivalence of the laws of Biot–Savart and Ampere." American Journal of Physics 57, no. 1 (January 1989): 57–59. http://dx.doi.org/10.1119/1.15869.

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43

Kennedy, Daniel T., and Robert A. Van Gorder. "Motion of open vortex-current filaments under the Biot–Savart model." Journal of Fluid Mechanics 836 (December 12, 2017): 532–59. http://dx.doi.org/10.1017/jfm.2017.826.

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Vortex-current filaments have been used to study phenomena such as coronal loops and solar flares as well as tokamaks, and recent experimental work has demonstrated dynamics akin to vortex-current filaments on a table-top plasma focus device. While MHD vortex dynamics and related applications to turbulence have attracted consideration in the literature due to a wide variety of applications, not much analytical progress has been made in this area, and the analysis of such vortex-current filament solutions under various geometries may motivate further experimental efforts. To this end, we consider the motion of open, isolated vortex-current filaments in the presence of magnetohydrodynamic (MHD) as well as the standard hydrodynamic effects. We begin with the vortex-current model of Yatsuyanagi, Hatori & Kato (J. Phys. Soc. Japan, vol. 65, 1996, pp. 745–759) giving the self-induced motion of a vortex-current filament. We give the ‘cutoff’ formulation of the Biot–Savart integrals used in this model, to avoid the singularity at the vortex core. We then study the motion of a variety of vortex-current filaments, including helical, planar and self-similar filament structures. In the case where MHD effects are weak relative to hydrodynamic effects, the filaments behave as expected from the pure hydrodynamic theory. However, when MHD effects are strong enough to dominate, then we observe structural changes to the filaments in all cases considered. The most common finding is reversal of vortex-current filament orientation for strong enough MHD effects. Kelvin waves along a vortex filament (as seen for helical and self-similar structures) will reverse their translational and rotational motion under strong MHD effects. Our findings support the view that vortex-current filaments can be studied in a manner similar to classical hydrodynamic vortex filaments, with the primary role of MHD effects being to change the filament motion, while preserving the overall geometric structure of such filaments.
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44

Christodoulides, C. "Equivalence of the Ampere and Biot-Savart force laws in magnetostatics." Journal of Physics A: Mathematical and General 20, no. 8 (June 1, 1987): 2037–42. http://dx.doi.org/10.1088/0305-4470/20/8/022.

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45

WANG, JIN, GUOFENG LI, KE LIANG, and XIANHU GAO. "THE THEORY OF FIELD PARAMETERS FOR HELMHOLTZ COIL." Modern Physics Letters B 24, no. 02 (January 20, 2010): 201–9. http://dx.doi.org/10.1142/s0217984910022275.

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In this paper, the field parameters for the magnetic field of a Helmholtz coil is defined, as predicted by the theory of magnetic multipolar fields. In accordance with Biot–Savart law, eleven series of field parameters for the Helmholtz coil are calculated and the effect of each parameter thoroughly analyzed. This is then shown to provide a theoretical basis for obtaining a uniform magnetic field.
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46

Neuenschwander, Dwight E., and Brian N. Turner. "Generalization of the Biot–Savart law to Maxwell’s equations using special relativity." American Journal of Physics 60, no. 1 (January 1992): 35–38. http://dx.doi.org/10.1119/1.17039.

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47

Christodoulides, C. "On the equivalence of the Ampere and Biot–Savart magnetostatic force laws." American Journal of Physics 57, no. 8 (August 1989): 680. http://dx.doi.org/10.1119/1.15917.

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48

Shi-De, Feng, Dong Ping, and Zhong Lin-Hao. "A Conceptual Model of Somali Jet Based on the Biot–Savart Law." Chinese Physics Letters 25, no. 12 (December 2008): 4321–24. http://dx.doi.org/10.1088/0256-307x/25/12/038.

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49

Sahihi, Taliya, and Homayoon Eshraghi. "Biot-Savart helicity versus physical helicity: A topological description of ideal flows." Journal of Mathematical Physics 55, no. 8 (August 2014): 083101. http://dx.doi.org/10.1063/1.4889935.

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50

Feng Shi-De and Feng Tao. "Biot-Savart law and the formation mechanism of Somali low-level jet." Acta Physica Sinica 60, no. 2 (2011): 029202. http://dx.doi.org/10.7498/aps.60.029202.

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