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Stokes' theorem is investigated in the context of the time-dependentAharonov-Bohm effect -- the two-slit quantum interference experiment with atime varying solenoid between the slits. The time varying solenoid produces anelectric field which leads to an additional phase shift which is found toexactly cancel the time-dependent part of the usual magnetic Aharonov-Bohmphase shift. This electric field arises from a combination of a non-singlevalued scalar potential and/or a 3-vector potential. The gauge transformationwhich leads to the scalar and 3-vector potentials for the electric field isnon-single valued. This feature is connected with the non-simply connectedtopology of the Aharonov-Bohm set-up. The non-single valued nature of the gaugetransformation function has interesting consequences for the 4-dimensionalStokes' theorem for the time-dependent Aharonov-Bohm effect. An experimentaltest of these conclusions is proposed.

Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect