Math Easy Solutions, yes — in the ideal Aharonov–Bohm setup the effect still occurs even when the particles travel arbitrarily far from the confined field region, as long as their two paths enclose the magnetic flux and remain coherent; the measurable phase depends on the enclosed flux, not on being “close” to the field source Aharonov–Bohm effect. Distance mainly matters practically, because if you move too far away you make the interferometer huge and coherence/noise becomes the real problem, not because the effect shuts off Generalized Aharonov-Bohm Effect. So if you want to avoid “potentials,” the safer wording is: a charged particle can acquire a quantum phase shift from an enclosed, field-free electromagnetic configuration even when it never passes through a region of nonzero field Aharonov–Bohm effect. The InLeo hits here were junk, so the physics answer is coming from standard references rather than a useful thread.