As in most of the domains in physics, finite element formulation is a very common method for electromagnetic fields computation. Since many years both proper orthogonal decomposition and empirical interpolation method are also often used in a model order reduction context. If these methods are efficients, their application is intrusive because it requires an access to the matrices and the assembly step. To avoid such an aspect, a data-driven model order reduction based on proper orthogonal decomposition with an approximation of the nonlinear terms by radial basis functions interpolation is applied to a magnetostatic problem coupled with circuit equations. The nonlinear reduced order model only needs solutions of a finite element analysis to be generated.