One solenoid is centered inside another. The outer one has a length of $48\mathrm{.}0$ cmcm and contains $6800$ coils, while the coaxial inner solenoid is $4\mathrm{.}0$ cmcm long and $0\mathrm{.}200$ cmcm in diameter and contains $24$ coils. The current in the outer solenoid is changing at $36\mathrm{.}5$ A$/$sA$/$s $.$ What is the mutual inductance of these solenoids? Find the emf induced in the inner solenoid.