Integral-equation analysis of a finite closed conducting cylinder

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 C ̃ ( α ) = C / ( 2 π ɛ a ) , with α = a / L . In the thin-disk limit α → ∞ , the capacitance approaches the isolated-disk value C ̃ disk = 4 / π from above. The extrapolated data are well described by C ̃ ( α ) ≃ C ̃ disk 1 + π 4 α ln ( 2 α ) + O 1 α . The non-analytic ln ( 2 α ) / 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.