Electric vector potential and the Biot-Savart like law in electrostatics

Salazar, Robert; Bayona-Roa, Camilo; Jaramillo, Diego

doi:10.18257/raccefyn.1671

Cited by 2 publications

(4 citation statements)

References 13 publications

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“…The angular integral in the previous expression can be written in terms of special functions, by following an analogous procedure than the one in equation (1). The angular integral is…”

Section: Discussionmentioning

confidence: 99%

“…The system can be also modeled as two-dimensional plasma where within Ω in , reside N 1 particles with charge q 1 ∈ R, while Ω out holds N 2 particles with charge q 2 ∈ R (see figure 1). The foregoing study draws inspiration from [1], where the gapped SE was characterized by two-conductor flat regions with differing potentials and a distinct gap. Electric field and surface charge density analysis in that system involved resolving Laplace's equation with specified conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In that study, interactions followed an inverse power law potential 1/r, where the coupling parameter Γ has been found inversely proportional to the system's temperature and proportional to q 2 . Furthermore, authors of [1] explored the electric vector potential and the Biot-Savart law analogy in electrostatics. These efforts set the zero stage for the present study, aiming to further analyze the system in question with the statistical mechanics approach.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, authors of Ref. [1] explored the electric vector potential and the Biot-Savart law analogy in electrostatics. These efforts set the zero stage for the present study, aiming to further analyze the system in question with the statistical mechanics approach.…”

Section: Introductionmentioning

confidence: 99%

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Comparative analysis of molecular dynamics and method of moments in two-dimensional concentric circular layers

Salazar,

Cobos,

Jaramillo

et al. 2024

J. Phys.: Condens. Matter

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In this manuscript, we undertake an examination of a classical plasma deployed on two finite co-planar surfaces: a circular region Ω in into an annular region Ω out with a gap in between. It is studied both from the point of view of statistical mechanics and the electrostatics of continua media. We employ a dual perspective: the first one is by using molecular dynamics (MD) simulations to find the system’s positional correlation functions and velocity distributions. That by modeling the system as a classical two-dimensional Coulomb plasma of point-like charged particles q 1 and q 2 on the layers Ω in and Ω out respectively with no background density. The second one corresponds to a finite Surface Electrode (SE) composed of planar metallic layers displayed on the regions Ω in , Ω out at constant voltages V in , V out considering axial symmetry. The surface charge density is calculated by the Method of Moments (MoM) under the electrostatic approximation. Point-like and differential charges elements interact via a 1 / r —electric potential in both cases. The thermodynamic averages of the number density, and electric potential due to the plasma depend on the coupling and the charge ratio ξ = q 1 / q 2 once the geometry of the layers is fixed. On the other hand, the fields due to the SE depend on the layer’s geometry and their voltage. In the document, is defined a protocol to properly compare the systems. We show that there are values of the coupling parameter, where the thermodynamic averages computed via MD agree with the results of MoM for attractive ξ = − 1 and repulsive layers ξ = 1.

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“…The angular integral in the previous expression can be written in terms of special functions, by following an analogous procedure than the one in equation (1). The angular integral is…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparative analysis of molecular dynamics and method of moments in two-dimensional concentric circular layers

Salazar,

Cobos,

Jaramillo

et al. 2024

J. Phys.: Condens. Matter

Self Cite

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Modeling of electromagnetic radiation using a dual four-potential representation: from dipole blade radiators to ribbon loop-like antennas

Salazar,

Bayona-Roa

2024

Phys. Scr.

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In this paper, we explore classical electromagnetic radiation using a dual four-dimensional potential $\Theta^\mu$ approach. Our focus is on the Planar Dipole Blade Antenna (PDBA), a system consisting of two flat perfect conductive regions on the $xy$-plane, separated by a gap $\mathcal{G}$, with alternating potentials applied to the conductors. This method emphasizes the use of the scalar magnetic potential $\Psi(\boldsymbol{r},t)$ and the electric vector potential $\boldsymbol{\Theta}$, which generates the electric field $\boldsymbol{E}(\boldsymbol{r},t)=\nabla\times\boldsymbol{\Theta}(\boldsymbol{r},t)$ in free space. These potentials replace the standard magnetic vector potential $\boldsymbol{A}$ and the scalar electric potential $\boldsymbol{\Phi}$ in our analysis. For harmonic radiation, the electromagnetic field can be expressed in terms of the electric vector potential $\boldsymbol{\Theta}(\boldsymbol{r},t)$. We derive a corresponding retarded vector potential for $\boldsymbol{\Theta}$ in terms of a two-dimensional vector field $\boldsymbol{\mathcal{W}}(\boldsymbol{r},t)$, which flows through the gap region $\mathcal{G}$. This dual analytical approach yields mathematically equivalent expressions for modeling Planar Blade Antennas, analogous to those used for ribbons in the region $\mathcal{G}$, simplifying the mathematical problem. In the gapless limit, this approach reduces the two-dimensional radiator (PDBA) to a one-dimensional wire-loop-like antenna red, significantly simplifying the problem's dimensionality. This leads to a dual version of Jefimenko's equations for the electric field, where $\mathcal{W}$ behaves like a surface current in the gap region and satisfies a continuity condition. To demonstrate the utility of this approach, we provide an analytical solution for a PDBA with a thin annular gap at low frequency.

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Electric vector potential and the Biot-Savart like law in electrostatics

Cited by 2 publications

References 13 publications

Comparative analysis of molecular dynamics and method of moments in two-dimensional concentric circular layers

Comparative analysis of molecular dynamics and method of moments in two-dimensional concentric circular layers

Modeling of electromagnetic radiation using a dual four-potential representation: from dipole blade radiators to ribbon loop-like antennas

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