Using the spherical harmonic expansion given by Mead for the magnetic field created by the currents on the surface of the geomagnetic cavity, the nature of the trapping regions has been discussed. It is shown that to a first order of approximation in the expansion coefficients, the allowed regions are still determined by a cubic equation. Numerical determinations have been made for the structure of the allowed regions for particles of different energies both on the sunlit side as well as the dark side of the Earth.