This paper is an application of the surface charge distribution method to the modeling of the electric antennas installed on board the Polar spacecraft in order to identify the plasma conditions leading to the instability of the sphere-preamplifier-stub-guard system. First we present an analytic approach, which allows us to understand the physical mechanism and to define the conditions of the instability. We then show the results of the numerical modeling for the more common types of instabilities observed in flight. The latter, which we call type-1 oscillations, are observed solely in the low-L plasmasphere region. The modeling predicts that the oscillations can occur in a weakly magnetized Maxwellian plasma in the upper hybrid range (fpt) when the Debye length lies between well-defined limits. The frequency modulation of the oscillations in this range versus the spin angle of the antennas with respect to the Earth's magnetic field is well explained by the model. The type-2 oscillations are observed occasionally and occur always in the exterior cusp, at large L values. They are most likely to be associated with high-density clouds of solar wind streaming plasma entering into that region. Our analytic modeling indeed predicts that the instability conditions can be satisfied when the antennas are crossing a 10 eV electron flow, with a density of ~100 cm-3 and a bulk velocity of the order of 200 km s-1. ¿ 2001 American Geophysical Union