Effect of a Magnetic Field

The phase of the electron-pairs can be affected not only by the current density but also quite strongly by an applied magnetic field. In the presence of a magnetic field the momentum, $\boldsymbol{p}$ , of a particle with charge in the presence of a magnetic field becomes $m\boldsymbol{v} + q\boldsymbol{A}$ where $\boldsymbol{A}$ is the magnetic vector potential. For electron-pairs in an applied field their moment $\boldsymbol{P}$ is now equal to $2m\boldsymbol{v} + 2e\boldsymbol{A}$ .[12]

In an applied field the phase difference between points X and Y is now a combination of that due to the supercurrent and that due to the applied field, ie

$\displaystyle (\Delta\phi)_{XY} = [ (\Delta\phi)_{XY} ]_{i} + [ (\Delta\phi)_{XY} ]_{B}$

(3.21)

where

$\displaystyle [ (\Delta\phi)_{XY} ]_{i} = \frac{4\pi m}{hn_{s}e} \int^{Y}_{X} \boldsymbol{J}_{s} \centerdot \mathrm{d}\boldsymbol{l}$

(3.22)

and

$\displaystyle [ (\Delta\phi)_{XY} ]_{B} = \frac{4\pi e}{h} \int^{Y}_{X} \boldsymbol{A} \centerdot \mathrm{d}\boldsymbol{l}$

(3.23)

Dr John Bland, 15/03/2003