Magnetic Field inside Solenoid and EMF

[jderm]

A small loop of area A is placed inside a long solenoid that has n turns per meter and carries a sinusoidally varying current of amplitude i. The central axes of the loop and solenoid coincide. If i = i₀sin ωt, find the emf in the loop.




EMF_induced = - d(\phi_B)/ dt
\phi_B=BA
B_solenoid= \mu₀ni





The product of B and A = A\mu₀ni₀sin (ωt)
So the derivative of \phi_B with respect to time:
=A\mu₀ni₀cos (ωt) ω
so;
EMF_induced = - A\mu₀ni₀cos (ωt) ω

Apparently this is incorrect. I'm sorry about the sloppy formatting, could someone help me out with this?

 

[Illuminitwit]

EMF = nABω sinωt
F(magnetism) = B • i • l
F(mag) = qvB

I don't know if that helps much, but those are a few more equations that might apply, although I think you already had them in various forms. If you had the magnitude of electrical/magnetic force or the length it might be easier. Sorry...