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We investigate the quality factor Q for electrically small current distributions and practical antenna designs radiating the TE10 magnetic dipole field. The current distributions and the antenna designs employ electric currents on a spherical surface enclosing a magneto-dielectric material that serves to reduce the internal stored energy. Closed-form expressions for the internal and external stored energies as well as for the quality factor Q are derived. The influence of the sphere radius and the material permeability and permittivity on the quality factor Q is determined and verified numerically. It is found that for a given antenna size and permittivity there is an optimum permeability that ensures the lowest possible Q, and this optimum permeability is inversely proportional to the square of the antenna electrical radius. When the relative permittivity is equal to 1, the optimum permeability yields the quality factor Q that constitutes the lower bound for a magnetic dipole antenna with a magneto-dielectric core. Furthermore, the smaller the antenna the closer its quality factor Q can approach the Chu lower bound. Simulated results for the TE10-mode multiarm spherical helix antenna with a magnetic core reach a Q that is 1.24 times the Chu lower bound for an electrical radius of 0.192.