A 73-MH Solenoid Inductor Is Wound on a Form That $0.80 \mathrm {~m}$

A 73-mH solenoid inductor is wound on a form that is $0.80 \mathrm {~m}$ long and $0.10 \mathrm {~m}$ in diameter. A coil having a resistance of $7.7 \Omega$ is tightly wound around the solenoid at its center. The mutual inductance of the coil and solenoid is $19 \mu \mathrm { H }$ . At a given instant, the current in the solenoid is $820 \mathrm {~mA}$ and is decreasing at the rate of $2.5 \mathrm {~A} / \mathrm { s }$ . At the given instant, what is the induced current in the coil?

A) $8.6 \mu \mathrm { A }$
B) $9.9 \mu \mathrm { A }$
C) $4.9 \mu \mathrm { A }$
D) $6.2 \mu \mathrm { A }$
E) $7.4 \mu \mathrm { A }$