Electrostatics of a Finite Conducting Cylinder: Elliptic-Kernel Integral Equation and Capacitance Asymptotics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917179759263744 |
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| author | de Sousa, J. Ricardo |
| author_facet | de Sousa, J. Ricardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00031 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Electrostatics of a Finite Conducting Cylinder: Elliptic-Kernel Integral Equation and Capacitance Asymptotics de Sousa, J. Ricardo Classical Physics 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. |
| title | Electrostatics of a Finite Conducting Cylinder: Elliptic-Kernel Integral Equation and Capacitance Asymptotics |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2601.00031 |