Year: 2026
Type: preprint
Abstract: The charge on a conducting cylinder becomes uniformly distributed at large aspect ratios, albeit very slowly and with nonuniformity persisting near the ends. We show that the charge density and field magnitude are enhanced near the ends by a factor scaling as the square-root of the logarithm of the aspect ratio. This scaling is obtained by locally resumming a perturbation-series solution to the integral equation of slender-body theory. The same scaling applies to a broad class of "truncated" slender bodies -- including cylinders and shapes tapered near the ends on the cross-sectional scale -- as well as other physical setups. We validate this scaling through boundary-element simulations for cylinders with flat and hemispherical caps, and demonstrate its applicability to diffusion, plasmonics and Stokes flow.
Source: arXiv (Cornell University)
Authors: Peng, Gunnar, Schnitzer, Ory
Institutions: University College London, Imperial College London
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162404472
Cites:
Cited by:
Related to: