The electrostatic properties of uniformly charged regular bodies are prominently discussed on
college-level electromagnetism courses. However, one of the most basic problems of electrostatics
that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this
level. In this work we revisit the problem of equilibrium charge distribution on a straight
one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature
deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated
analytically for a Coulomb interaction potential between point charges. Surprisingly, different
models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is
even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach
where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate
limit. Instead,…