Abstract
Galilean electromagnetism was discovered thirty years ago by Lévy-Leblond and Le Bellac. However, these authors only explored the consequences for the fields and not for the potentials. Following De Montigny et al., we show that the Coulomb gauge condition is the magnetic limit of the Lorenz gauge condition whereas the Lorenz gauge condition applies in the electric limit of Lévy-Leblond and Le Bellac. Contrary to De Montigny et al., who used Galilean tensor calculus, we use orders of magnitude based on physical motivations in our derivation.