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We present an exact analytical solution for the radiation impedance of an infinitesimal dipole surrounded by a thin spherical shell of epsilon negative material (ENG). The negative epsilon leads to a non-Foster reactance in the equivalent circuit and a much broader impedance bandwidth than would be expected from the Q of the antenna. When dispersion is considered, the non-Foster reactance disappears and the Q reverts back to the value based on the ratio of stored energy to radiated power. The analysis shows that a thin shell of ENG material provides no significant improvement in the performance of the dipole antenna.