the repulsive Casimir force was recently found [41] in the configuration of an ideal metal cylinder above a magnetodielectric plate. This result was obtained under the assumption that temperature is equal to zero. The Casimir repulsion was predicted for the magnetic permeability of the plate µ = 100 and dielectric permittivity ε < 33 or µ = 10 and ε < 4. Thus in both cases the materials of the plate are ferromagnetic dielectrics. In contrast to this, we consider a real ferromagnetic dielectric plate interacting with an Au plate at room temperature and take into account the dependence of their magnetic permeability and dielectric permittivity on the frequency. Therefore the effect of repulsion found by us can be used as an experimental test for the influence of magnetic properties on the Casimir force and for the model of dielectric permittivity of a metal plate (see Sec. VII). Now we consider some analytical results that can be obtained in the limiting case of large separations. For two similar plates made of ferromagnetic dielectric one can use the reflection coefficient (11) (as was noted above, this one is the same as for a ferromagnetic metal described by the Drude model) and (32). The resulting Casimir free energy per unit area is given by where ε (0), as defined in Eq. (31), and µ (0) are the dielectric permittivity and magnetic permeability of the ferromagnetic dielectric. If we have two dissimilar plates where one is made of ferromagnetic dielectric and the other one of a nonmagnetic metal described by the Drude model, the Casimir free energy per unit area is determined by the contribution of the TM mode alone, For dissimilar plates where the metal plate is described by the plasma model, with account of Eqs. (10), (11), (28) and (32), one obtains F$_{fd}$ ( a, T ) = − k$_{B}$T 16 πa 2 { Li$_{3}$ [ ( ε (0) − 1 ε (0) + 1 ) 2 ] + Li$_{3}$ [ ( µ (0) − 1 µ (0) + 1 ) 2 ]} , (33) F$_{D}$ ( a, T ) = − k$_{B}$T 16 πa $_{2}$Li$_{3}$ [ ε (0) − 1 ε (0) + 1 ] . (34) F$_{p}$ ( a, T ) = − k$_{B}$T 16 πa 2 { Li$_{3}$ [ ε (0) − 1 ε (0) + 1 ] (36) +Li$_{3}$ [ 1 − µ (0) 1 + µ (0) ]( 1 − 2 δ$_{02}$ a )} , 20 By performing integration with respect to y we arrive at F$_{p}$ ( a, T ) = k$_{B}$T 16 πa 2 { − Li$_{3}$ [ ε (0) − 1 ε (0) + 1 ] (35) + ∫ ∞ 0 ydy ln [ 1 + µ (0) − 1 µ (0) + 1 (1 − 2 α$_{2}$y ) e − y ]} .