In this paper, particular attention is paid to the impact of finite_element approximation on uniqueness and to approximations implicit in finite element formulations from the uniqueness requirements standpoint. It is also shown that the flux density is unique without qualifications. The theoretical and numerical uniqueness of the magnetic vector potential in three_dimensional problems is also given. This analysis is restricted to linear, isotropic media with Dirichlet Boundary conditions. As an interesting consequence of this analysis it is shown that, under usual conditions adopted in obtaining three_dimensional finite_element solutions, it is not necessary to specify div _ in order that _ be uniquely defined.