A $50$ Hz$,$ two$-$pole, $750$ kVA, $2300$ V$,$ three phase synchronous machine has a synchronous reactance of $7\mathrm{.}75$ and achieves rated open$-$circuit terminal voltage at a field current of $120$ A$.$

a$)$ Calculate armature to field mutual inductance.

b$)$ The machine is to be operated as a motor supplying a $600$ kW of load at its rated

rated terminal voltage. Calculate the voltage Eaf and the corresponding field current

if the motor is operating at a unity power factor.