For type II superconductors, Josephson has shown that vortices moving with velocity v L create an effective electric field E′= -v L ×B V . By definition the effective electric field is gradient of the electrochemical potential, what is the quantity corresponding to voltage observed with the use of Ohmic contacts. It relates to the true electric field E via the local chemical potential μ as E′=E-∇μ/e. We argue that at low temperatures the true electric field in the bulk can be approximated by a modified Josephson relation E=(v S -v L )×B V , where v S is the condensate velocity.
Fully discrete linear approximation scheme for electric field diffusion in type-II superconductors
