We analyze features of particle behavior in magnetospheric convection using simple analytic forms for the electrostatic potential which have been used in other recent works. We show that analytic approximations for the the shape and position of surfaces delimiting closed and open particle orbits can be derived. These approximations are good for any pitch angle and at most energies. They break down only for the medium-energy protons that are predicted by such models to penetrate far inside the plasmapause. The expression we derive allow rapid tests of a variety of electric field models when analyzing particle data, and we illustrate this by intercomparing field models with several observations.