The radiation properties of spherical electric dipole antennas with electric current excitation and material-coated perfectly electrically conducting (PEC) cores are investigated analytically using vector spherical wave functions. Closed-form expressions for electric and magnetic stored energy as well as the radiation quality factor $Q$ are derived. Using these, it is shown that properly selected magnetic coating and radius of the PEC core vastly reduce the internal stored energy, and thus make the $Q$ of an electric dipole antenna approach the Chu lower bound.