By using an inductive procedure we prove that the Galerkin
finite element approximations of electromagnetic eigenproblems
modelling cavity resonators by elements of any fixed order of
either Nedelec's edge element family on tetrahedral meshes are
convergent and free of spurious solutions. This result is not
new but is proved under weaker hypotheses, which are fulfilled
in most of engineering applications. The method of the proof
is new, instead, and shows how families of spurious-free
elements can be systematically constructed. The tools here
developed are used to define a new family of spurious-free
edge elements which, in some sense, are complementary to
those defined in 1986 by Nedelec.