  We investigate Faraday's law of induction manifested in the quantum state of
Aharonov-Bohm loops. In particular, we propose a flux-switching experiment for
a double-dot AB ring to verify the phase shift induced by Faraday's law. We
show that the induced {\em Faraday phase} is geometric and nontopological. Our
study demonstrates that the relation between the local phases of a ring at
different fluxes is not arbitrary but is instead determined by Faraday's
inductive law, which is in strong contrast to the arbitrary local phase of an
Aharonov-Bohm ring for a given flux.

Mesoscale and Nanoscale Physics;Quantum Physics