  We investigate the motion of one and two charged non-relativistic particles
on a sphere in the presence of a magnetic field of uniform strength. For one
particle, the motion is always circular, and determined by a simple relation
between the velocity and the radius of motion. For two identical particles,
interacting via a cotangent potential, we show there are two families of
relative equilibria, called Type I and Type II. The Type I relative equilibria
exist for all strengths of the magnetic field, while those of Type II exist
only if the field is sufficiently strong. The same is true if the particles are
of equal mass but opposite charge. We also determine the stability of the two
families of relative equilibria.
