The surface defined by the locus of field minima along field lines for an unterminated Jovian model magnetosphere is found to coincide with the surface of the model current disc which provides a good fit to the data. However, when the model is terminated by means of magnetopause currents, preservation of the fit by modifying the current distribution near the outer edge of the disc causes the minimum ‖B↘‖ surface to bifurcate. Energetic electron flux time profiles that are based upon such a minimum ‖B↘‖ configuration are found to be qualitatively consistent with the inbound Pioneer 10 data.