Abstract:
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.
References