  The distributions of electrical current and magnetic field in a thin-film
superconductor ring is calculated by solving the London equation. The maximum
amount of flux trapped by the hole, the fluxoid saturation number, is obtained
by limiting the current density by the depairing current. The results are
compare it with similar results derived for the bulk case of a long hollow
cylinder [Nordborg & Vinokur, Phys. Rev. B 62, 12408 (2000)]. In the limit of
small holes our result reduces to the Pearl solution for an isolated vortex in
a thin film. For large hole radius, the ratio between saturation numbers in
bulk and film superconductors is proportional to the square root of the hole
size.
