The electrostatic sheath formation surrounding an electric dipole antenna at very low frequencies (VLF) in a magnetoplasma is examined through numerical simulation. In this paper, a hydrodynamic approach is used to solve for the nonlinear sheath dynamics of antennas located in plasmas similar to that which exists in the plasmasphere between L = 2 and L = 3 in the geomagnetic equatorial plane. The plasma environment at this location is assumed to be fully ionized and collisionless consisting of electrons and protons. Poisson's equation is used to close the system, providing the quasi-electrostatic fields within the sheath region. Sheath characteristics are given as a function of antenna drive frequency and voltage with results that are compared with existing theory. Capacitance and resistance values are given to reflect the sheath's contribution to the input impedance of the antenna. Finally, the importance of ion motion and the nonlinear sheath effects on the current, charge collection and bias voltage for the transmitting antenna are shown. The primary assumptions underlying the closure mechanisms for the infinite set of fluid moments are examined through theoretical observations and simulated comparisons of the truncation schemes. This paper constitutes one of the first works on the subject of high-voltage transmitting dipole antenna in a space plasma using a three-dimensional nonlinear formulation.