Graduate-level physics curricula in many countries around the world, as well as senior-level
undergraduate ones in some major institutions, include classical mechanics courses, mostly based on
Goldstein’s textbook masterpiece. During the discussion of central force motion, however, the Kepler
problem is virtually the only serious application presented. In this paper, we present another
problem that is also soluble, namely the interaction of Schwinger’s dual-charged (dyon) particles.
While the electromagnetic interaction of magnetic monopoles and electric charges was studied in
detail some 40 years ago, we consider that a pedagogical discussion of it from an essentially
classical mechanics point of view is a useful contribution for students. Following a path that
generalizes Kepler’s problem and Rutherford scattering, we show that they exhibit remarkable
properties such as stable non-planar orbits, as well as rainbow and glory scattering, which are not
present in the ordinary scat…