# Understanding Aharonov-Bohm Effect: Confusions Explained

• spidey
In summary, the Aharonov-Bohm effect refers to the phenomenon where a charged particle experiences a phase shift as it passes around a long solenoid, despite the magnetic field being zero in the region through which the particle passes. This can also occur with electric fields, where the particle is affected by regions with different electric potentials but zero electric field. The phase shift is dependent on the magnetic vector potential A, rather than the magnetic field B. This effect has been experimentally confirmed and is further explained in section 11.2 of the book "Lorentz force from Klein-Gordon" by Hans.
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"

"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:

## 1. What is the Aharonov-Bohm effect?

The Aharonov-Bohm effect is a quantum mechanical phenomenon in which a charged particle is affected by a magnetic field, even when it does not directly interact with the field. This effect is caused by the presence of a magnetic vector potential, which can influence the phase of the particle's wave function.

## 2. How does the Aharonov-Bohm effect differ from the regular electromagnetic force?

The regular electromagnetic force is a classical force that is mediated by the exchange of virtual photons between charged particles. In contrast, the Aharonov-Bohm effect is a quantum mechanical effect that is caused by the influence of a magnetic vector potential on the phase of a particle's wave function. This means that the Aharonov-Bohm effect cannot be explained by classical electromagnetic theory.

## 3. Can the Aharonov-Bohm effect be observed in experiments?

Yes, the Aharonov-Bohm effect has been observed in various experiments, such as the famous double-slit experiment with electrons. In this experiment, the electrons travel through two slits and interfere with each other, creating a diffraction pattern. However, when a magnetic field is present, the interference pattern is shifted, demonstrating the effect of the magnetic vector potential on the electrons' phase.

## 4. What are the applications of the Aharonov-Bohm effect?

The Aharonov-Bohm effect has important implications in quantum mechanics and has been used in various areas of research, such as quantum computation and quantum information processing. It also plays a role in understanding topological phases of matter and has potential applications in developing new technologies, such as quantum sensors and detectors.

## 5. Are there any misconceptions about the Aharonov-Bohm effect?

Yes, there are some misconceptions about the Aharonov-Bohm effect, such as the idea that it violates the principle of local causality. However, the effect can be explained within the framework of quantum mechanics and does not violate any fundamental laws of physics. Another misconception is that the effect is only present in theory and cannot be observed in experiments, which has been proven false by numerous experiments that have successfully demonstrated the effect.

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