We examine some consequences of the duality that a U(1) phase factor added on a wave function describes a whole system motion and also plays the role of a U(1) gauge potential. First, we show that the duality solves a long-standing puzzling problem that the ‘flux rule’ (the Faraday’s induction formula) and the Lorentz force calculation for an emf emerging in an electron system moving in a magnetic field give the same result (Feynman et al. 1963). Next, we examine a U(1) phase factor induced on the wave function for an electron system due to the single-valuedness requirement of the wave function with respect to the electron coordinates, and its consequential appearance of a U(1) instanton. This instanton explains the Meissner effect, supercurrent generation, flux quantization in the units of ${{h} \over {2e}}$ , and the voltage quantization in the units of ${{hf} \over {2e}}$ across the Josephson junction in the presence of a radiation field with frequency f. In the experiment, a radiation field must be present to have a finite voltage across the Josephson junction; but a clear explanation for it has been lacking. The present work provides an explanation for it, and also explains the high precision of the quantized voltage as due to a topological effect.