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.

我们研究了一个和两个带电非相对论粒子在强度均匀的磁场存在下在球体上的运动。对于一个粒子，运动始终是圆形的，并且由速度和运动半径之间的简单关系决定。对于通过余切势相互作用的两个相同粒子，我们表明有两个相对平衡族，称为 I 型和 II 型。I 型相对平衡适用于所有磁场强度，而 II 型只有在磁场足够强时才存在。如果粒子质量相等但电荷相反，情况也是如此。我们还确定了两个相对平衡族的稳定性。