The electrostatic potential of a uniformly charged ring

Ciftja, Orion; Babineaux, Arica; Hafeez, Nadia

doi:10.1088/0143-0807/30/3/019

Cited by 32 publications

(20 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such an energy depends only on the separation distance between the respective centers, r c of the two rings. We have succeeded to calculate the electrostatic potential energy between two co-planar uniformly charged rings starting from the expression of the electrostatic potential created by a ring [41] in its 2D plane, (ρ, z = 0) (in polar coordinates).…”

Section: Semi-classical Modelmentioning

confidence: 99%

Semi‐Classical Model of Strongly Correlated Coulomb Systems in Weak Magnetic Field

Ciftja¹

2011

Contrib. Plasma Phys.

View full text Add to dashboard Cite

The integer and fractional quantum Hall effects are two remarkable macroscopic quantum phenomena occurring in two-dimensional strongly correlated electronic systems at high magnetic fields and low temperatures. Quantization of Hall resistivity in the very high magnetic field regime at partial filling of the lowest Landau level indicates the stabilization of an electronic liquid quantum Hall phase of matter. Other interesting phases that differ from the quantum Hall phases take prominence in weaker magnetic fields when many more Landau levels are filled. These states manifest anisotropic magneto-transport properties and, under certain conditions, appear to mimic charge density waves and/or liquid crystalline phases. One way to understand such a behavior has been in terms of effective interaction potentials confined to the highest Landau level partially filled with electrons. In this work we show that, for weak magnetic fields, such a quantum treatment of these strongly correlated Coulomb systems resembles a semi-classical model of rotating electrons in which the time-averaged interaction potential can be expressed solely in terms of guiding center coordinates. We discuss how the features of this semi-classical effective potential may affect the stability of various strongly correlated electronic phases in the weak magnetic field regime.

show abstract

Section: Semi-classical Modelmentioning

confidence: 99%

Semi‐Classical Model of Strongly Correlated Coulomb Systems in Weak Magnetic Field

Ciftja¹

2011

Contrib. Plasma Phys.

View full text Add to dashboard Cite

show abstract

“…Assuming rotationally-symmetric charge distributions, their (phasor) electric scalarpotential at a field point defined by the position-vector r = xux + zuz (where ux and uz are the unit vectors of the Cartesian coordinate system) is given by [21] …”

Section: Integral Equationsmentioning

confidence: 99%

High-accuracy quasistatic numerical model for bodies of revolution tailored for RF measurements of dielectric parameters

et al. 2021

View full text Add to dashboard Cite

We have developed rotationally symmetrical coaxial chambers for measurements of dielectric parameters of disk-shaped samples, in the frequency range from 1 MHz to several hundred MHz. The reflection coefficient of the chamber is measured and the dielectric parameters are hence extracted utilizing a high-accuracy quasistatic numerical model of the chamber and the sample. We present this model, which is based on the method of-moments solution of a set of integral equations for composite metallic and dielectric bodies. The equations are tailored to bodies of revolution. The model is efficient and accurate so that the major contribution of the measurement uncertainty comes from the measurement hardware.

show abstract

“…Note that only for κ = 0 (and along the z axis) can the integral in Eq. (7) be evaluated in terms of known special functions [68]. For the general case, the integral can be numerically computed on a desktop PC within seconds.…”

Section: B Charged Torimentioning

confidence: 99%

Screened Coulomb interactions of general macroions with nonzero particle volume

Everts

2020

Phys. Rev. Research

View full text Add to dashboard Cite

A semianalytical approach is developed to calculate the effective pair potential of rigid arbitrarily shaped macroions with a nonvanishing particle volume, valid within linear screening theory and the mean-field approximation. The essential ingredient for this framework is a mapping of the particle to a singular charge distribution with adjustable effective charge and shape parameters determined by the particle surface electrostatic potential. For charged spheres, this method reproduces the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Further exemplary benchmarks of the method for more complicated cases, like tori, triaxial ellipsoids, and additive torus-sphere mixtures, leads to accurate closed-form integral expressions for all particle separations and orientations. The findings are relevant for determining the phase behavior of macroions with experiments and simulations for various particle shapes.

show abstract

The electrostatic potential of a uniformly charged ring

Cited by 32 publications

References 8 publications

Semi‐Classical Model of Strongly Correlated Coulomb Systems in Weak Magnetic Field

Semi‐Classical Model of Strongly Correlated Coulomb Systems in Weak Magnetic Field

High-accuracy quasistatic numerical model for bodies of revolution tailored for RF measurements of dielectric parameters

Screened Coulomb interactions of general macroions with nonzero particle volume

Contact Info

Product

Resources

About