The electrostatics problem of a point charge next to a conducting plane
is best solved by placing an image charge placed on the opposite side.
For a charge between two parallel planes this can be solved with image
charges outside the planes at evenly spaced intervals moving out to
infinity. What is the corresponding image of a point charge is when
placed on the axis of a cylinder?. The potential of a point charge in a
cylinder is well known and may expressed in many forms involving
integrals or series of Bessel functions, but none of which elude to an
image. In fact the image consists of infinitely many rings on a disk
with some complicated surface charge distribution. This manuscript
attempts to describe the image as accurately as possible, and in doing
so finds simple accurate approximations for the potential.