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In this paper we study the non-relativistic dynamic of a charged particle inthe electromagnetic field induced by a periodically time dependent current Jalong an infinitely long and infinitely thin straight wire. The motions aredescribed by the Lorentz-Newton equation, in which the electromagnetic field isobtained by solving the Maxwell's equations with the current distribution J asdata. We prove that many features of the integrable time independent case arepreserved. More precisely, introducing cylindrical coordinates, we prove theexistence of (non-resonant) radially periodic motions that are also of twisttype. In particular, these solutions are Lyapunov stable and accumulated bysubharmonic and quasiperiodic motions.

Motions of a charged particle in the electromagnetic field induced by a non-stationary current