The action of an AC magnetic field on a thin liquid metal layer is studied in an experimental and theoretical way. In the first chapter, the experimental bench is described. An experimental study is then undertaken where the difference in behavior between a thick and a thin liquid metal layer is underlined. Indeed, if the inductor and the liquid metal layer unit is axisymetric in absence of a magnetic field, this axisymetric remains when an AC magnetic field is applied. On the other hand, the axisymmetry is broken (aperture of the circular liquid metal) when the liquid metal is thin. At a given magnetic field, the shapes of the liquid metal layer are frozen states for the both thickness of layers.The main aim of this work is to explain those frozen states of the liquid metal layer by relying on a minimum energy method. The first approach of the phenomenon consists in establishing an equivalent electric model which is simple to study. The obtained results allow us to streamline the problem and thus that way to begin to think over an electromagnetic model. The second chapter deals with the electromagnetic model and with the computation of the magnetic energy. The third chapter of this thesis describes the used calculus method for the resolution of our electromagnetic model. Two numerical methods are presented, one is the finite elements method and the other one is the boundary elements method. The last chapter presents the obtained numerical results which are compared to the experimental results.
