Solenoid Magnetic Field Problem

A solenoid of lenght 45 cm has 340 turns of radius 2.2 cm. A tightly wound coil with 16 turns of radius 4.4 cm is at the center of the solenoid. The axes of the coil and solenoid coincide. Find the emf induced in the coil if the current in the solenoid varies according to I=4.6sin(50∏t)A.

Answer: __________cos(50∏t) mV

Comments:
I can't seem to find the correct answer for the magnetic field of the solenoid.
The formula I use is:
B=0.5μ₀nI(sinθ₂-sinθ₁)
The area to use for all equations is the area of the solenoid since it is the area of magnetic field lines felt by the coil.
The flux, denoted ∅ is: ∅=BAcosσ and σ=0^o, therefore ∅=BA
and the EMF=-N(d∅/dt)=-NA(dB/dt)

I really appreciate any help, thank you!

 

Assuming the solenoid is long an using that formula, my answer is wrong. Is there anything missing to the comments I added for solving this problem?