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A variational formulation is developed for the impedance of a finite strip antenna embedded in a planar dielectric slab which is surrounded by a magnetoionic medium (cold electron plasma) with a static magnetic field impressed in a direction perpendicular to the antenna surface. Closed form expressions are obtained in the limit of low frequencies, and for a short antenna in a uniaxial medium. The impedance becomes large at the plasma frequency, near the upper hybrid resonance frequency, and further resonances are observed near the gyro-frequency if the gyro-frequency exceeds the plasma frequency. The reactance of a short antenna is inductive at low frequencies, but becomes capacitive as the thickness of the insulation around the antenna is increased. For very thin insulating layers the wave number of the variationally approximated current distribution exceeds ( and are the two diagonal elements of the permittivity matrix), where and may have positive or negative real parts. However, this approximation does not apply to current distributions along an insulated antenna. The present calculations are also compared with earlier work on antenna impedances.