Aharonov-Bohm Effect electricity generation 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) ? 
 A: See this answer about the electric field outside the solenoid. It is correct that outside the solenoid there isn't a magnetic field but outside there is an electric field. The electrons moving through the slits will be influent from this field. And I am with you that there is a common influence between this electrons and the surface of the solenoid. Once more there is a common influence between the moving electrons and the surface of the slits too. To be exact, between the moving electrons and the electrons on the slit barrier.
A: No, the electron cannot be inside the solenoid.
The Aharonov-Bohm effect is intrinsically a topological effect caused by the solenoid effectively removing a line from $\mathbb{R}^3$, making it homotopic to the circle $S^1$. It has nothing to do with the electron "acting like a wave" or "acting like a particle" (which are notions one should not use anyway), and everything to do with the possible paths of the electron being non-contractible. I the electron were allowed inside the solenoid, whatever you would observe would not be the Aharonov-Bohn effect.
