Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non–relativistic two-dimensio-nal charged particle motion. These symmetries comprise a quasi–invariance transformation, a time–dependent rotation, a time–dependent spatial translation and a dilatation. The associated electromagnetic fields satisfy a system of first–order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries.