  We present the complete results for the dynamic experiment on measuring the
gradient of the Casimir force between magnetic (Ni-coated) surfaces of a plate
and a sphere. Special attention is paid to the description of some details of
the setup, its calibration, error analysis and background effects. Computations
are performed in the framework of the Lifshitz theory at nonzero temperature
with account of analytic corrections to the proximity force approximation and
of surface roughness using both the Drude and the plasma model approaches. The
theory of magnetic interaction between a sphere and a plate due to domain
structure of their surfaces is developed for both out-of-plane and in-plane
magnetizations in the absence and in the presence of spontaneous magnetization.
It is shown that in all cases the magnetic contribution to the measured force
gradients is much smaller than the total experimental error. The comparison
between experiment and theory is done using the rigorous statistical method. It
is shown that the theoretical approach taking into account dissipation of free
electrons is excluded by the data at a 95% confidence level. The approach
neglecting dissipation is confirmed by the data at more than 90% confidence
level. We prove that the results of experiments with Ni-Ni, Ni-Au and Au-Au
surfaces taken together cannot be reconciled with the approach including free
electrons dissipation by the introduction of any unaccounted background force,
either attractive or repulsive.
