  A one-dimensional equation describing the distribution of the effective
vector potential $\bar A(y)$ across a film width, which holds for thin
($d<\lambda$) and thick ($d>\lambda$) films alike, is derived based on the
analysis of a 2D Maxwell-Londons equation for superconducting films in a
perpendicular magnetic field. The validity of this equation for a
finite-thickness film is verified by a numerical analysis. An approximation
dependence $\bar A(y)$, finite (with all of its derivatives) across the entire
film width, is found for films, being in the Meissner state. The flux-entry
field is evaluated for a film of arbitrary thickness. An approximation
expression is obtained for the distribution of the sheet current density in the
mixed state of a pin-free superconducting film with an edge barrier. The latter
approximation allows to estimate magnetic field concentration factor at the
film edge as a function of external magnetic field and geometrical parameters
of the sample.
