The surface charge on coated superconductors carrying transport current

A careful solution of Maxwell's equations for the case of a circuit carrying a forced transport current in zero applied magnetic field shows that the current in the circuit is not divergenceless. A small component of the current diverges into the surface leading to a surface charge. This current along with the surface charge it produces is computed for two parallel strips of coated conductor with one strip acting as the return path for the other. Although the component of current with divergence is too small to be of much importance for the vector potential, it is completely responsible for the surface charge and scalar potential.