Two coils, A and B$,$ have self$-$inductances of $120$H and $300$H respectively. When a current of $3$ A through coil A is reversed, the deflection on a flux meter connected across B is $600$Wb$-$turns. Calculate: $($a$)$ the mutual inductance between the coils; $($b$)$ theaverage e$.$m$.$f$.$ induced in coil B if the flux is reversed in $0\mathrm{.}1$ s; and $($c$)$ the coupling coefficient.