Solenoid/Inductors

1. The problem statement, all variables and given/known data

An 85 mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center. The coil resistance is 8.1 ohms. The mutual inductance of the coil and solenoid is 27 µH. At a given instant, the current in the solenoid is 540 mA, and is decreasing at the rate of 2.5 A/s. At the given instant, the induced emf in the solenoid is closest to:
A) 170 mV
B) 150 mV
C) 210 mV
D) 230 mV
E) 190 mV

2. Relevant equations

emf =-N (ΔΦ/Δt)

3. The attempt at a solution

i’ve tried to think of other equations to use such as ωBA sin θ where it would be 90 degrees because that’s the peak. but that doesn’t work.
so i though i might be able to use the above equation but it seems like i am missing too many variables.
i know the equation for self inductance is ( -L * ΔI/Δt )
but it is in the given instant and not over a range of time..
any small guidance would be much appreciated; i’m not sure where to go from here.

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