$2.$ A small laboratory three$-$phase synchronous generator, with two poles and $50$ Hz $,$ has a rotor radius of $5\mathrm{.}71$ cm $,$ a rotor length of $18\mathrm{.}0$ cm $,$ and an air gap length of $0\mathrm{.}25$ mm $.$ The field winding of the rotor consists of $264$ turns with a winding factor of $0\mathrm{.}95.$ The stator winding, connected in Y$,$ consists of $45$ turns per phase with a winding factor of $0\mathrm{.}93.$ Calculate the required field current to obtain an open$-$circuit armature voltage of $380$ V RMS per line at $50$ Hz $.$