A uniformly charged circular disk with an anisotropic Coulomb interaction potential

Ciftja, Orion

doi:10.1016/j.elstat.2020.103472

Cited by 8 publications

(4 citation statements)

References 36 publications

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“…. when it comes to the expression in equation (15). Obviously, the simplest integral, 1 0 dx P l (x) to calculate is the one for l = 0:…”

Section: Resultsmentioning

confidence: 99%

“…These audiences have the opportunity to discover that, sometimes, simple-looking problems are a great source to uncover the beauty of mathematics at work. Knowledge of the electric field or potential is an important pre-requisite to calculate the electrostatic interaction energy of a system of two or more bodies as well as the energy stored in each of them [15][16][17][18][19]. There are some simple results that apply to a hemispherical surface and/or solid hemisphere at special points [20] but there is no general exact analytical result that we are aware of.…”

Section: Introductionmentioning

confidence: 99%

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Interaction energy between two identical hemispherical surfaces with uniform surface charge density

Ciftja¹,

Colbert-Pollack²,

Ciftja³

et al. 2021

Eur. J. Phys.

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Obtaining the interaction energy between two uniformly charged hemispherical surfaces in compact analytical form seems to be an impossible task to achieve under arbitrary conditions. However, we show in this work that one can obtain the interaction energy between two identical hemispherical surfaces with uniform surface charge density for the special condition of them touching each other along the ‘equator’. The mathematical solution method that we apply is remarkable in that the bulk of the treatment is analytic with the only drawback of having to rely on knowledge of certain special functions and their properties.

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“…. when it comes to the expression in equation (15). Obviously, the simplest integral, 1 0 dx P l (x) to calculate is the one for l = 0:…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interaction energy between two identical hemispherical surfaces with uniform surface charge density

Ciftja¹,

Colbert-Pollack²,

Ciftja³

et al. 2021

Eur. J. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Coulomb self-energy of a uniformly charged circular plate, namely, a uniformly charged disk is readily available, in the literature [ 30 , 31 , 32 ] and one way to write it is:

…”

Section: Theory and Modelmentioning

confidence: 99%

Energy Stored and Capacitance of a Circular Parallel Plate Nanocapacitor

Ciftja

2021

Nanomaterials

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Nanocapacitors have received a great deal of attention in recent years due to the promises of high energy storage density as device scaling continues unabated in the nanoscale era. High energy storage capacity is a key ingredient for many nanoelectronic applications in which the significant consumption of energy is required. The electric properties of a nanocapacitor can be strongly modified from the expected bulk properties due to finite-size effects which means that there is an increased need for the accurate characterization of its properties. In this work, we considered a theoretical model for a circular parallel plate nanocapacitor and calculated exactly, in closed analytic form, the electrostatic energy stored in the nanocapacitor as a function of the size of the circular plates and inter-plate separation. The exact expression for the energy is used to derive an analytic formula for the geometric capacitance of this nanocapacitor. The results obtained can be readily amended to incorporate the effects of a dielectric thin film filling the space between the circular plates of the nanocapacitor.

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“…Overall, the focus of our work is not to draw reader's attention to the difficulty of the problem solved. On the contrary, our main goal is to draw reader's attention to the methodology used and to the versatility of the approach that can, in principle, be applied to other charged bodies with a geometry different from that of a solid sphere [13][14][15][16][17]. In addition, use of different methods to solve a given problem, many times leads to interesting insights or prospects to open a new discussion.…”

Section: Introductionmentioning

confidence: 99%

Fourier transform method for the electrostatic self-energy of a solid sphere with uniform volume charge density

Ciftja¹

2021

Eur. J. Phys.

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The problem of a solid sphere with uniform volume charge density is encountered in virtually all undergraduate calculus-based physics textbooks dealing with the topic of electromagnetism. This example illustrates well the use of Gauss’s law and from there one can easily derive all the quantities of interest such as electrostatic field, potential, self-energy, and so on. Undergraduate physics majors are also well aware of the theory of Fourier transforms from having taken mathematics courses. Nevertheless, despite its great utility, the Fourier transform method is rarely mentioned as a powerful tool to solve physics problems at this level. To address this shortcoming, in this work we propose a possible scenario which may allow an instructor to introduce this powerful method to a proper undergraduate audience without any major pedagogical drawback. The case study that we choose is that of a solid sphere with uniform volume charge density. Specifically, we show the calculation of its electrostatic self-energy by using Fourier transform techniques. The main idea of this work is to draw reader’s attention to the versatility of the approach that can, in principle, be applied to other more geometrically complicated bodies where Gauss’s law does not lead to simple solutions. Concurrently, this work also provides instructional approaches that intertwine content-specific and pedagogical viewpoints that can be useful to all undergraduate students and teachers who wish to enhance their command of the subject.

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A uniformly charged circular disk with an anisotropic Coulomb interaction potential

Cited by 8 publications

References 36 publications

Interaction energy between two identical hemispherical surfaces with uniform surface charge density

Interaction energy between two identical hemispherical surfaces with uniform surface charge density

Energy Stored and Capacitance of a Circular Parallel Plate Nanocapacitor

Fourier transform method for the electrostatic self-energy of a solid sphere with uniform volume charge density

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