I read that niobium metal has a Cooper-pair density of about 10^22 per cubic centimeter. However, when a current flows through a superconductor my understanding is that it all flows near the surface, beginning at the London penetration depth, which is a very small distance. So, let's say that you have a 10 cm. long piece of (circular) niobium rod with a cross-sectional area of 1 cm. Once a supercurrent begins flowing would all, or most, of the Cooper-pairs throughout the bulk of the rod migrate to the surface region? And, if so, how deep would this surface region be where the Cooper-pair current flows? Thanks.