A novel method of solving two-dimensional electrostatic potential problems

Dasgupta, Basab B.

doi:10.1119/1.14014

Cited by 3 publications

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“…Sadly, most students do not usually appreciate the similarities between the two classes of problems 8 due to a limited exposure to practical examples involving the magnetostatic potential. We feel that this ability is useful 9 , particularly because scalar potentials are generally more intuitive and easier to visualize. Besides, a unified treatment could be pedagogically relevant in generalizing the discussion of the multipole expansions [10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

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Analysis of off-axis solenoid fields using the magnetic scalar potential: An application to a Zeeman-slower for cold atoms

Muniz¹,

Bagnato²,

Bhattacharya³

2015

American Journal of Physics

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In a region free of currents, magnetostatics can be described by the Laplace equation of a scalar magnetic potential, and one can apply the same methods commonly used in electrostatics. Here we show how to calculate the general vector field inside a real (finite) solenoid, using only the magnitude of the field along the symmetry axis. Our method does not require integration or knowledge of the current distribution, and is presented through practical examples, including a non-uniform finite solenoid used to produce cold atomic beams via laser cooling. These examples allow educators to discuss the non-trivial calculation of fields off-axis using concepts familiar to most students, while offering the opportunity to introduce important advancements of current modern research.

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Section: Introductionmentioning

confidence: 99%

“…We feel that this ability is useful 9 , particularly because scalar potentials are generally more intuitive and easier to visualize. Besides, a unified treatment could be pedagogically relevant in generalizing the discussion of the multipole expansions [10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

Analysis of off-axis solenoid fields using the magnetic scalar potential: An application to a Zeeman-slower for cold atoms

Muniz¹,

Bagnato²,

Bhattacharya³

2015

American Journal of Physics

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“…Since the field and currents are related by linear equations, this method is sure to work, but the relationship between the desired field and the required coil is only as clear as one's understanding of an integral equation involving a tensor Green function. Surface and bulk current distributions have been described as fictitious magnetization densities [21][22][23][24] which can take an arbitrary form in the limit of infinitesimal dipoles. Various optimiation procedures include variational principles [16,24] and linear programming [15].…”

mentioning

confidence: 99%

“…In problems with either real or fictitious magnetization density, the net pole density plays the role of electric charge in an analogous boundary value problem to that of the electric field [21,[25][26][27]. For real current distributions stream functions specify the resulting discontinuity of the scalar potential [2,28,29], which has also been applied to eddy currents [30] and the analysis of fields [31].…”

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confidence: 99%

The physical meaning of the magnetic scalar potential, and how to use it to design an electromagnet

Crawford

2020

Preprint

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The magnetic scalar potential can be used to design electromagnets accurately and efficiently. I will describe a practical construction algorithm: the prescribed field in a "Target" region (constrained only by Maxwell's equations) specifies boundary conditions which uniquely determine the potential in the surrounding field "Return" region. As required by the physical representation of the magnetic scalar potential, the conducting elements of the resulting coil are directed along equipotentials on the surface of each region, at equal increments of the potential. I give some examples and comments on the limits of precision of the constructed field.

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The physical meaning of the magnetic scalar potential and its use in the design of hermetic electromagnetic coils

Crawford

2021

Review of Scientific Instruments

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The magnetic scalar potential U(r⃗) has an intuitive physical interpretation, representing the electric current I = ΔU, which must be directed between any pair of isocontours along the boundary of a region, differing in potential by ΔU, in order to generate the corresponding magnetic intensity H⃗=−∇⃗U inside the region with no tangential component outside the boundary. This physical significance is exploited to invert the design process of hermetic (fringeless) electromagnetic coils from standard iterative techniques (calculating the magnetic field of refined current distributions) to a procedure for calculating the exact surface currents required to generate a given field configuration. A practical construction algorithm is given to produce the prescribed field in a “Target” region (constrained only by Maxwell’s equations) while confining the fringe field to a specified hermetic “Return” region. Example coils are analyzed along with a discussion of the limits of precision of the constructed field.

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A novel method of solving two-dimensional electrostatic potential problems

Abstract: A novel method of solving a certain class of two-dimensional electrostatic potential problems is developed by exploiting their analogy with magnetostatic problems.

Cited by 3 publications

References 0 publications

Analysis of off-axis solenoid fields using the magnetic scalar potential: An application to a Zeeman-slower for cold atoms

Analysis of off-axis solenoid fields using the magnetic scalar potential: An application to a Zeeman-slower for cold atoms

The physical meaning of the magnetic scalar potential, and how to use it to design an electromagnet

The physical meaning of the magnetic scalar potential and its use in the design of hermetic electromagnetic coils

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