the Drude model interacting with the ferromagnetic dielectric plate are nearly coinciding with those when Au is described by the plasma model and the magnetic properties of ferromagnetic dielectric are disregarded (see below). The computational results are presented in Fig. 10 for the Casimir free energy (a) and pressure (b). The solid (dashed) lines show the results computed using the plasma model for the Au plate with magnetic properties of the ferromagnetic dielectric plate included (disregarded). Note that if the Drude model is used to describe the dielectric properties of the Au plate, the obtained results nearly coincide with the dashed line within the range of separations considered. The relative deviation between the results obtained using both models is equal to only 0.25% and 0.09% at separations a = 0 . 5 and 2 µ m, respectively, and continues to decrease with the increase of separation. As can be seen in Fig. 10, there is the profound effect of magnetic properties of ferro- magnetic dielectric on the Casimir interaction in this configuration if Au is described by the plasma model. Thus, at separations of 0.5, 2 and 6 µ m the respective values of η p F ,fd − Au are equal to –22%, –82% and –111%. For the Casimir pressure at the same respective separa- tions one has η p P,fd − Au = − 14%, –60% and –110%. What is more important, the Casimir free energy F changes sign and becomes positive (we remind that E$_{0}$ < 0) at separations a > 2 . 9 µ m [see Fig. 10(a)]. According to the proximity force approximation, the Casimir force acting between a sphere of radius R and a plate spaced at separation a ≪ R from each other are approximately equal [5, 14] to 2 πR F ( a, T ). This means that at separations a > 2 . 9 µ m the Casimir force acting between the sphere and the plate is repulsive. A similar situation takes place for the Casimir pressure. From Fig. 10(b) it follows that at separations a > 3 . 8 µ m the Casimir pressure P changes its sign and becomes positive. This means that the Casimir force acting between a ferromagnetic dielectric plate and Au plate described by the plasma model becomes repulsive. We emphasize that the effect of repulsion for the two parallel plates interacting through the vacuum gap found by us is not analogous to the results [28] discussed in Introduction. The point is that the paper [28] used some idealized magnetodielectric materials of the plates with frequency-independent ε and µ . As was shown [29], the values of magnetic permeabilities of real materials at characteristic frequencies contributing to the Casimir force are much less than those required to obtain the effect of repulsion because they quickly vanish with the increase of frequency. In the asymptotic limit of very large separations, where the zero-frequency ε and µ can be used, 19