Distribution of charge on a finite cylindrical shell and a conducting needle

The distribution of charge on a finite wire of zero thickness has been discussed in several papers in recent years. Here we compute initially the distribution of charge on a finite cylindrical shell using the moment method, with a Fourier basis. We observe that this solution converges slowly, therefore we suggest a different basis of only two functions, and observe improved convergence. We then take the radius to zero and oberve that the charge density converges to a constant, as predicted also by previous studies.