2025/12/30 by J. Ricardo de Sousa · 1 voice · 2 citations
Physics and Astronomy · #physics.class-ph
We study the electrostatics of a thin, finite-length conducting cylindrical shell held at constant potential V0. Exploiting axial symmetry, we recast the problem as a one-dimensional singular integral equation for the axial surface-charge density, with a kernel written in terms of complete elliptic integrals. A Chebyshev-weighted collocation scheme that incorporates the square-root edge singularity yields rapidly convergent charge profiles and dimensionless capacitances for arbitrary aspect ratios L/a, recovering known long- and short-cylinder limits and providing accurate benchmark values in the intermediate regime. The method offers a compact, numerically robust reference formulation for the electrostatics of finite cylindrical conductors.