A $50-$Hz$,2-$pole, $825-$kVA, $2300-$V$,3-$phase synchronous machine has a synchronous reactance of $7\mathrm{.}47$ and reaches its rated open$-$circuit voltage with a field current of $147$ A$.$

$($a$)$ Calculate the mutual inductance between the armature and the field winding.

$($b$)$ The machine operates as a motor supplying a load of $700$ kW at rated terminal voltage. When the motor operates at unity power factor, calculate the internal voltage E$\_\{$af$\}$ and the corresponding field current I$\_\{$f$\}.$

This is electric machinery problem.