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The electrostatics problem of a point charge next to a conducting plane isbest solved by placing an image charge placed on the opposite side. For acharge between two parallel planes this can be solved with image chargesoutside the planes at evenly spaced intervals moving out to infinity. What isthe corresponding image of a point charge is when placed on the axis of acylinder?. The potential of a point charge in a cylinder is well known and mayexpressed in many forms involving integrals or series of Bessel functions, butnone of which elude to an image. In fact the image is complex (in both senses),consisting of infinitely many rings on a disk with some surface chargedistribution. This manuscript attempts to describe the image as accurately aspossible, and in doing so finds simple accurate approximations for thepotential.

The image of a point charge in an infinite conducting cylinder