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A novel approach for obtaining left-handed material behavior is presented. In this paper, we study a composite-medium model of insulating magnetic-dielectric spherical particles embedded in a background dielectric matrix. We show that the effective permeability and permittivity of the mixture can be simultaneously negative for wavelengths where the spherical inclusions are resonant, thus forming an effective double negative index material. This material is simpler to construct than structures used in previous work. We indicate how we can tune the material behavior to make it relatively broadband. The use of these non-conducting metamaterials can be used to develop "smart" or controllable surfaces.