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Gauss's Law: Spherical Symmetry

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...

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Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions

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Published on: February 17, 2019

Thermal Casimir effect in the plane-sphere geometry.

Antoine Canaguier-Durand¹, Paulo A Maia Neto, Astrid Lambrecht

¹Laboratoire Kastler Brossel, CNRS, ENS, Université Pierre et Marie Curie case 74, Campus Jussieu, F-75252 Paris Cedex 05, France.

Physical Review Letters

|April 7, 2010

Summary

The thermal Casimir force between metallic surfaces is geometry-dependent. Plane-sphere geometry reduces the force ratio between Drude and plasma models to 3/2, impacting experimental interpretations.

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Area of Science:

Condensed Matter Physics
Quantum Field Theory
Nanotechnology

Background:

The thermal Casimir force, a quantum electrodynamic effect, is sensitive to material properties and geometry.
Discrepancies exist between theoretical models (Drude, plasma) for metallic bodies, especially at large separations.

Purpose of the Study:

To investigate the influence of plane-sphere geometry on the thermal Casimir force.
To compare force predictions from different material models in realistic experimental geometries.

Main Methods:

Exact numerical calculations for the plane-sphere geometry.
Large-distance analytical approximations.
Comparison of dissipative Drude and lossless plasma models.

Main Results:

The plane-sphere geometry reduces the force ratio between Drude and plasma models from 2 to 3/2.
A repulsive thermal photon contribution to the Casimir force was identified for perfect reflectors.
Negative entropy values were observed at intermediate distances for perfect reflectors.

Conclusions:

Experimental geometries significantly alter the thermal Casimir force compared to idealized parallel plate models.
The choice of material model and geometric configuration is crucial for accurate force predictions.
Novel repulsive forces and negative entropy phenomena warrant further investigation.