A $460-$V$,50-$kW$,60-$Hz$,$ three$-$phase synchronous motor has a synchronous reactance of Xs $=4\mathrm{.}15$ and an armature$-$to$-$field mutual inductance, Laf $=83$ mH$.$ The motor is supplied with a rated voltage through a feeder of Zf $=0\mathrm{.}084+$j$0\mathrm{.}82.$ Assuming the system $($as measured at the source$)$ to be operating at an input power of $40$ kW$.$ Calculate the magnitude and phase angle of the line$-$to$-$neutral generated voltage Eaf and the field current, If if the motor is operating at

$($a$)0\mathrm{.}85$ power factor lagging, $($b$)$ unity power factor, and $($c$)0\mathrm{.}85$ power factor leading.