2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/151634We have exactly solved the eigenequation of a two-dimensional Dirac fermion moving on the surface of a sphere under the influence of a radial magnetic field B, and obtained an exact expression of the collective excitation energy gap for the filling factors $ν=p/(2mp\pm 1)$, m and p are non-zero integers, which is very well agreement with the computing results.Revtex, 11 pages, no figuresMesoscale and Nanoscale Physicstext