A mixed variational formulation in 2-D magnetostatics is presented and discussed, The method treats B and H as direct unknowns and relies on the minimization of the error on the constitutive law, taking Maxwell's equations as constraints. The numerical discretization, based on the lowest order Raviart-Thomas-Nedelec element, is reported, Potential advantages of this innovative method for engineering applications - like the fulfilment of continuity equations - are pointed out and a case study is presented, A computer code has been implemented and a number of numerical experiments have been performed to validate the proposed methodology.