Understanding Aharonov-Bohm Effect: Confusions Explained

[spidey]

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"

 

[jtbell]

"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.

 

[spidey]

"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?

 

[Hans de Vries]

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