# 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) ?

• What?! ... Tell me what's wrong with my question. Dont just down vote. – user120404 Jul 23 '14 at 15:44

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.