  We examine the response of a soft ferromagnetic film to an in-plane applied
magnetic field. Our theory, based on asymptotic analysis of the micromagnetic
energy in the thin-film limit, proceeds in two steps: first we determine the
magnetic charge density by solving a convex variational problem; then we
construct an associated magnetization field using a robust numerical method.
Experimental results show good agreement with the theory. Our analysis is
consistent with prior work by van den Berg and by Bryant and Suhl, but it goes
much further; in particular it applies even for large fields which penetrate
the sample.
