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We analytically solve the radiation problem for a spherical magnetic dipole antenna with a material-coated perfectly electrically conducting core. Using the closed-form expressions derived for the internal and external stored energies as well as for the radiation quality factor Q, we determine the optimal geometrical and material parameters of the antenna. We show that the optimal permeability of the coating increases as the coating becomes thinner; as a result, the energy stored in it and the radiation quality factor Q reduce. In the limit of an infinitely thin coating, the optimal permeability tends to infinity, the internal stored energy vanishes, and the Q reaches the Chu lower bound, irrespective of the antenna electrical size ka and permittivity of the coating.