### abstract

- Nonradiating electromagnetic sources are sources whose field is identically zero outside of their volume. They are undetectable unless the observation point is in direct contact with them. They are the basis of the theory of source equivalence, which studies the field invariance with respect to source transformations. In this work, we focus on the equivalent source transformations in a nonuniform medium and the implications in the theory of the electromagnetic vector potentials. We identify three types of nonradiating sources. Subsequently, we define the mathematical transformations of the sources, which preserve the field outside of their support (source invariance). We give complimentary expressions, which preserve the field inside the source support as well. We show that the nonuniqueness of the electromagnetic potentials is due to the nonunique solution to the inverse problem. The well known field gauge invariance follows from its source invariance. Also, the gauge-invariant transformation appears to be just one possibility in an infinite set of field-invariant vector-potential representations all related to the respective equivalent source transformations.