This is the published version, also available here: http://dx.doi.org/10.1063/1.1666066.It is shown how a new class of stationary electromagnetic vacuum fields can be generated from solutions of Laplace's equation. These fields are a stationary generalization of the static electromagnetic vacuum fields of Weyl, Majumdar, and Papapetrou, and are plausibly interpreted as exterior fields of static or steadily moving distributions of charged dust having numerically equal charge and mass densities