A generalized average inverse participation ratio, for the one-electron wave functions of a dilute tight-binding model on a d-dimensional hypercubic lattice, is studied at finite magnetic fields. Extended wave functions appear above a quantum threshold bond concentration, pq. This threshold decreases at small magnetic fields, and shows a periodic dependence on the magnetic flux through a basic plaquette, with period φ0=ℏc/e. Extended states appear and disappear periodically even at d=2.