One solenoid is centered inside another. The outer one has a length of $47\mathrm{.}0$ cmcm and contains $6700$ coils, while the coaxial inner solenoid is $5\mathrm{.}0$ cmcmlong and $0\mathrm{.}200$ cmcm in diameter and contains $18$ coils. The current in the outer solenoid is changing at $38\mathrm{.}0$ A$/$sA$/$s $.$

Part A

What is the mutual inductance of these solenoids?

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Part B

Find the emf induced in the inner solenoid.