  The search for Noether point symmetries for non-relativistic charged particle
motion is reduced to the solution for a set of two coupled, linear partial
differential equations for the electromagnetic field. These equations are
completely solved when the magnetic field is produced by a fixed magnetic
monopole. The result is applied to central electric field cases, in particular
to the time-dependent monopole-oscillator problem. As an additional example of
the theory, we found all Noether point symmetries and invariants for a constant
magnetic field and a time-dependent harmonic electric field with a forcing
term.
