In this talk, we will present an immersed boundary method to simulate the motion of magnetized particles in a fluid [4] discretized thanks to a finite element strategy on unfitted meshes, called phi-FEM. This method based on the use of a levet-set function has been successfully carried out for elliptic scalar PDEs with Dirichlet boundary conditions [1] and for Neumann boundary conditions [2]. One of the advantages of the method is the use of standard finite element spaces and classical integration tools. Theoretical challenges [3] have to be dealt like the integration on the whole mesh cells or facets only and the discrete inf-sup stability theory. The last one should been adapted to the case of a non-standard variational formulation posed on the immersed domain.We will focus on particles in a tube containing an unsteady Newtonian fluid and where the magnetic forces are only modeled on the particles. Some numerical illustrations of the optimal convergence in the H1 norm for the velocity and L2 for pressure will be presented.