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Aharonov Bohm effect

  1. Mar 22, 2005 #1
    When we derive the phase difference in the classical experiment of the solenoid as shown below

    http://www.public.asu.edu/~ziyads/Aharonovbohm.pdf [Broken]

    Now what if we change the path from the sorce to screen so it follows a rectangular path like this

    http://www.public.asu.edu/~ziyads/rect.gif [Broken]

    the phase difference i.e equation 10 in the slides above will remain the same cause no matter what the path the the closed loop integral of the curl of A remains the same.

    NOw what if I change it a bit, and apply a parpendicular magnetic field throughout the region and my gauge is A=(-By/2, Bx/2,0)

    How will the phase differnce change of the rectangular path.
    and what about if A=(By,0,0) which should be the same as that of A=(-By/2, Bx/2,0)
    Last edited by a moderator: May 1, 2017
  2. jcsd
  3. Mar 22, 2005 #2
    It seems to me that since, in general, the integration is taken over a different area, then the flux will be different, (eqn. 5); and thus will result in a different amount of phase difference, (eqn 10).

    As to your second question; I'm not exactly sure, but it seems to me if you are going to align the axis of the selonoid along the x axis (and the path remains in the x-y plane) then the vector potential should intersect each path with the same rotation --thus no phase difference. However, I'm assuming here the electrons are not spin polarized similarly; if such is the case then [itex]\delta\phi[/itex] may reappear in accordance with some quantum relation. :wink:

    Creator :cool:

    P. S. Nice explanation of AB effect.
    Last edited: Mar 22, 2005
  4. Mar 22, 2005 #3
    actually for the second case. the structure can be thought of inside the solenoid. cause there is a perpendicular magnetic field. IN the first case the path was outside the solenoid and it didn't had magnetic field only vector potential.

    sso i think the question is how does an actual magnetic field change its phase compared to just vector potential
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