Two solenoids A and B$,$ spaced close to each other and sharing the same cylindrical axis, have $420$ and $710$ turns, respectively. A current of $2\mathrm{.}00$ A in solenoid A produces an average flux of $300$Wb through each turn of A and a flux of $90\mathrm{.}0$Wb through each turn of B$.$

$($a$)$ Calculate the mutual inductance of the two solenoids.

mH

$($b$)$ What is the inductance of A$?$

mH

$($c$)$ What is the magnitude of the emf that is induced in B when the current in A changes at the rate of $0\mathrm{.}500$ A$/$s$?$

mV