Dependence of the Casimir Energy Between Magnetodielectric and Metallic Plates in a Liquid on the Dielectric Permittivity and Magnetic Permeability

We investigate the Casimir energy between a magnetodielectric plate and a metallic plate in a liquid and show that the Casimir repulsion is enhanced compared with that in vacuum when the metal is described by the plasma model. This enhancement occurs because the attractive transverse magnetic (TM) mode contribution depends on the dielectric contrast between the magnetodielectric plate and the liquid. At large enough separations, exact dielectric matching completely suppresses the attractive TM mode, maximizing repulsion. Using an yttrium iron garnet (YIG)–gold system, we analyze the distance dependence and the effect of imperfect dielectric matching to assess the experimental observability of liquid-mediated repulsion. Observation of this repulsive force provides a practical scheme to address the long-standing Drude–plasma controversy.