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The current distribution and input impedance of an electric dipole antenna operating in a cold magnetoplasma at very low frequency (VLF) is determined through numerical simulation. A full wave solution of Maxwell's equations using a finite-difference frequency-domain (FDFD) method is implemented to simulate electromagnetic wave propagation in this highly anisotropic medium. The classical perfectly matched-layer (PML) boundary condition is found to exhibit instabilities in the form of nonphysical wave amplification in this environment. To circumvent these difficulties, a PML is developed that is tailored to the cold plasma environment at VLF frequencies. It is shown that the current distribution for antennas with length <100 m is approximately triangular for magnetospheric conditions found at L = 2 and L = 3 in the geomagnetic equatorial plane. Calculated variations of input impedance as a function of drive frequency are presented for two case studies and compared with predictions of existing analytical work.