One solenoid is centered inside another. The outer one has a length of $51\mathrm{.}0$ cm and contains $6650$ coils, while the coaxial inner solenoid is $4\mathrm{.}00$ cm long and $0\mathrm{.}100$ cm in diameter and contains $22\mathrm{.}0$ coils. The current in the outer solenoid is changing at $34\mathrm{.}5$ A$/$s $.$

What is the mutual inductance of these solenoids?

Find the emf induced in the inner solenoid.