An inverse problem consists in finding from a set of measurements the source of such data. An approach consists in using tools from operator and function theory to solve them. In this talk, we will solve some inverse problems in dimension 2. We will focus on an inverse problem in magnetism that consists in finding the moment of order 0 of the components of the magnetic field of a line segment from the measures of its external magnetic field. This talk is based on joint work with Juliette Leblond.