NOETHER SYMMETRIES FOR TWO-DIMENSIONAL CHARGED PARTICLE MOTION

We present a Lie point symmetry analysis for non-relativistic two-dimensional charged-particle motion. The resulting symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. We also find that the associated electromagnetic fields must satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of compatible electromagnetic fields.