This question is based on highly intuitive picture of the Aharonov-Bohm effect (perhaps a naive one).
From what I have read, the current explanation of the AB effect is that although the electron passing through the two slits does not experience any magnetic field, the phase difference that leads to interference results from the interaction with the potential.
My question is "If the electron is not really at one single position in the area between the slits and the detection screen, why can it not be inside the solenoid, and thus, experience a magnetic field?". My question is based on my understanding that the electron acts like a wave between the slits and the detection screen.
Also, if the answer to my question is "yes, it can be inside the solenoid.", can we generate electricity by cutting power off the solenoid and letting it act like a passive wire through which some of the electron "wave" passes (Induction) ?