  Equations of motion for an electrically charged string with a current in an
external electromagnetic field with regard to the first correction due to the
self-action are derived. It is shown that the reparametrization invariance of
the free action of the string imposes constraints on the possible form of the
current. The effective equations of motion are obtained for an absolutely
elastic charged string in the form of a ring (circle). Equations for the
external electromagnetic fields that admit stationary states of such a ring are
revealed. Solutions to the effective equations of motion of an absolutely
elastic charged ring in the absence of external fields as well as in an
external uniform magnetic field are obtained. In the latter case, the frequency
at which one can observe radiation emitted by the ring is evaluated. A model of
an absolutely nonstretchable charged string with a current is proposed. The
effective equations of motion are derived within this model, and a class of
solutions to these equations is found.
