How Fast Must the Magnetic Field Change to Induce a 3.4 A Current in a Coil?

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Acoil = 7.4506 e^-4
I don't get this. I think you may have made a calculator error. The diameter is 0.038 m, right?
So L = pi*Dwire*102 = 0.18906m
This should be Dcoil instead of Dwire. Dwire tells you nothing of how long the wire is. The diameter of the coil tells you that.

If you fix these two things I think the rest should be OK.
 
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okay so I got an answer or 35.243 T/s and it's still wrong :(
 
actually I forgot to change the L value when I calculated the Resistance so now I am getting 2269.9 T/s which seems extremely large! Is that what you got?