Understanding Aharonov-Bohm Effect: Confusions Explained

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Discussion Overview

The discussion centers on the Aharonov-Bohm effect, particularly the confusion surrounding the concepts of enclosed magnetic fields and electric potentials in regions where the corresponding fields are zero. Participants explore theoretical implications and clarify terminology related to the effect.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion regarding the terminology of "enclosed magnetic field" and the statement that the magnetic field is zero outside the solenoid.
  • Another participant clarifies that "enclosed magnetic field" refers to the field inside the solenoid, while the field outside is indeed zero.
  • It is noted that the electric field is zero when the electric potential is uniform, with examples provided of different electric potentials in separate regions.
  • A participant questions why there is a phase shift if the magnetic field is zero both before and after placing the solenoid.
  • Another participant introduces the concept of the magnetic vector potential A, explaining that the phase shift is dependent on this vector potential rather than the magnetic field B, which is zero.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the definitions of magnetic and electric fields, but there remains disagreement and confusion regarding the implications of these concepts on the phase shift in the Aharonov-Bohm effect.

Contextual Notes

Participants have not fully resolved the implications of the magnetic vector potential and its relationship to the phase shift, leaving some assumptions and interpretations open to further discussion.

spidey
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I am confussed with aharonov bohm effect. i read the wikipedia article.

http://en.wikipedia.org/wiki/Aharonov-Bohm_effect

The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, is when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being zero in the region through which the particle passes.

it says "enclosed magnetic field" but "magnetic field is zero"

An electric Aharonov–Bohm phenomenon was also predicted, in which a charged particle is affected by regions with different electrical potentials but zero electric field, and this has also seen experimental confirmation

It says "different electric potentials" but "electric field is zero"
 
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"enclosed magnetic field" means the field inside the solenoid. The field is zero outside the solenoid.

The electric field is zero when the electric potential is uniform (does not vary with position). In the second case, there are two regions, each with uniform (but different) electric potential. For example, one region might have a uniform potential of 5 volts, and the other one might have a potential of 10 volts. The electric field is zero in both regions.
 
jtbell said:
"enclosed magnetic field" means the field inside the solenoid. The field is zero outside the solenoid.

The electric field is zero when the electric potential is uniform (does not vary with position). In the second case, there are two regions, each with uniform (but different) electric potential. For example, one region might have a uniform potential of 5 volts, and the other one might have a potential of 10 volts. The electric field is zero in both regions.

Even before placing placing the solenoid the magnetic field is zero. After the placing the solenoid also magnetic field is zero.Then, why there is phase shift?
 
spidey said:
Even before placing placing the solenoid the magnetic field is zero. After the placing the solenoid also magnetic field is zero.Then, why there is phase shift?

There is a magnetic vector potential A around the solenoid which goes with 1/r.
The magnetic field B is the curl of this field and happens to be zero. The phase
shift depends on the vector potential A (not the magnetic field B)

http://www.physics-quest.org/Book_Lorentz_force_from_Klein_Gordon.pdf

see section 11.2

Regards, Hans
 
Last edited:

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