Influence of Induced Charges in the Electric Aharonov-Bohm Effect
  This paper states that the induced charge should not be neglected in the electric Aharonov-Bohm effect. If the induced charge is taken into account, the interference pattern of the moving charge will not change with the potential difference between the two metal tubes. It means that the scale potential itself can not affect the phase of the moving charge, and the true factor affecting the phase of the moving charge is the energy of the system including the moving charge and the induced charge. 
Rui-Feng Wang
quant-ph