Integral-equation analysis of a finite closed conducting cylinder

2026-06-18

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J. Ricardo de Sousa

DOI：10.1016/j.enganabound.2026.106862

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We study the electrostatic boundary-value problem of a finite closed conducting cylinder of radius a and length L , consisting of a lateral wall and two circular end caps held at a constant potential. The problem is formulated as a coupled axisymmetric first-kind boundary-integral system obtained from a single-layer potential. After azimuthal reduction, the wall–wall, wall–cap, and cap–cap interactions are all expressed in terms of complete elliptic-integral kernels. The resulting equations are solved using a Jacobi-weighted Nyström discretization in which the integrable rim singularities are factored out explicitly. This yields stable surface-charge densities on the lateral wall and end caps, and allows controlled N→∞ extrapolation of the dimensionless capacitance C̃(α)=C/(2πɛa) , with α=a/L . In the thin-disk limit α→∞ , the capacitance approaches the isolated-disk value C̃disk=4/π from above. The extrapolated data are well described by C̃(α)≃C̃disk1+π4αln(2α)+O1α. The non-analytic ln(2α)/α correction reflects charge crowding near the sharp wall–cap junctions and differs from the corresponding smooth oblate-spheroid thin-body correction. The formulation provides an edge-resolved benchmark for the closed finite cylinder and a systematic route for extracting asymptotic amplitudes in sharp-edged electrostatic boundary-value problems.

Integral-equation analysis of a finite closed conducting cylinder

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