The interference of two-dimensional superconducting induced current in vector potential A field

J u n e 2 0 1 6 w w w . c i r w o r l d . c o m The interference of two-dimensional superconducting induced current in vector potential A field Yuanjie Li, Wenchuan Jia 1 Huazhong University of Science and Technology, Wuhan, China Corresponding Author: Yuanjie_li@sina.com 2 School of Mechanical Engineering and Automation, Shanghai University, Shanghai, China; Shanghai Key Laboratory of Intelligent Manufacturing and Robotics, Shanghai, China lovvchris@shu.edu.cn ABSTRACT


1.Introduction
Scalar potential is indeterminate in physics, but the difference of potential vectors like gravitational potential difference and electric potential difference is determinate and can be measured. While it seems different for magnetic vector potential. Existing theory holds that for the total description of magnetic field, magnetic induction intensity is not enough, vector potential A is redundant. However vector potential A together with its circulation integral , and AB effect. AB effect is essentially one-dimensional interference effects, and this manuscript will explore new two-dimensional interference effects.
We suppose that a two-dimensional superconducting metal surface is passed through by two infinite straight magnetic flux which are shielded by superconductor separately, and the distance between the two magnetic flux is d, as shown in fig. 1. According to the following test procedure.
At the beginning we have As the torque function of vector potential A, additional angular momentum which lead to additional phase of cooper pairs would be generated. Then, the two-dimensional interference distribution streamlines of superconducting induced current will appear. The interference phenomenon caused by these induced current with same or opposite direction can be verified by experiments. The two-dimensional interference phenomenon is named L-J effect, and it can be considered the two-dimensional AB effect.

The distribution of superconducting induced current without A field
If the effect of vector potential A is not considered, and while the induced current are with the opposite direction, the vector of superconducting induced current of any point (shown in figure 2) in metal surface can be calculated by   Fig. 3. It can be found that the value of the current along the horizontal line that connects the two fluxes is zero.  In contrast, if the induced current are with the same direction, the superposition of induced current can be calculated by The current streamlines are shown in Fig. 4. It can be can found that the value of the current along horizontal line is also equal to zero according to the symmetry.

Interference of superconducting induced current with vector potential A field
After superconducting induced current is produced, to keep 0 const   . Then, according to momentum minimum coupling principle or angular momentum minimum coupling principle, the interference in the superposition of currents would occur because of the phase difference caused by vector potential A or its first moment. The previous formulae should be revised correspondingly as follow.
In which For special cases like two-dimensional surface superconductor is replaced by superconducting coil (as shown in Fig.  5), it has In which

Fig. 6. Interference of superconducting induced current with vector potential A field
The theoretical research demonstrate that the main factor that affect the distribution shape of the interference streamline, is whether the direction of superconducting induced currents are same. The same or opposite direction of vector potential is the physical reason of interference, but not observably affect the distribution shape of the interference streamlines.

Conclusion
As a conclusion, in this manuscript: 1) A two-dimensional AB effect was proposed, which was named L-J effect.
2) If streamline of interference does exist, a new measurement technique and method is provided, especially for the measurement of the difference value between two vector potential A field.
The most important contribution of this manuscript is the new advance in understanding of magnetic vector potential A, and providing a new method to measure the difference value between two vector potential A field.