Representational competence is essential for the acquisition of conceptual understanding in physics. It enables the interpretation of diagrams, graphs, and mathematical equations, and relating these to one another as well as to observations and experimental outcomes. In this study, we present the initial validation of a newly developed cross-contextual assessment of students' competence in representing vector-field plots and field lines, the most common visualization of the concept of vector fields. The Representational Competence of Fields Inventory (RCFI) consists of ten single choice items and two items that each contain three true or false questions. The tool can be easily implemented within an online assessment. It assesses the understanding of the conventions of interpreting field lines and vector-field plots, as well as the translation between these. The intended use of the tool is both to scale students' representational competences in respect to representations of vector fields and to reveal related misconceptions. The tool was administered at three German-speaking universities in Switzerland and Germany to a total of 515 first- and third-semester students from science, technology, engineering, and mathematics subjects. In these first steps of the validation of the RCFI, we evaluated its psychometric quality via classical test theory in combination with Rasch scaling and examined its construct validity by conducting student interviews. The RCFI exhibits a good internal consistency of ?=0.86. The RCFI revealed misunderstandings and shortcomings, such as the confusion of the conventions for representing field lines and vector-field plots. We report on specific erroneous student conceptions and discuss future adaptations of the RCFI.