Induced Current problem from review

[Boris_The_Red]

Homework Statement

A 40 turn circular coil of a 4.0 cm radius and a total resistance of 0.20 Ω is placed in a uniform magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies with time as B = 50*sin(10π*t) mT where t is measured in s. What is the induced current in the coil at 0.10 s?

Homework Equations

I believe these are the equations needed:
ε = -N*d(Φ_B)/dt
I = V/R
Φ_B = ∫B*dA

The Attempt at a Solution

The way I did it was start off with I = V/R, then knowing that V is the emf, I plugged in ε = -N*d(Φ_B)/dt.

Then I used the flux equation, but modified it since we were given dB (or what I assume is dB) and I thus get I = (-N* ∫dB*A)/ R.

From there I get I = (-N*50*sin(10π*t)*10^-3 *πr²)/R

I solve this, but I don't get the correct answer (which is known since this is from an older exam that I'm doing as additional practice for my fnal).

Am I missing something key here, or did I improperly set up the mag. field equation?

 

[rude man]

Then I used the flux equation, but modified it since we were given dB (or what I assume is dB) and I thus get I = (-N* ∫dB*A)/ R.

Why did you bring dB into the picture? The problem does not allude to dB in any way.
This problem could have been made really interesting if B = 0 for t < 0. But you don't want to consider that possibility. Just assume the B field has been there for a long time and then when the field is zero and starting to increase (B=0, dB/dt > 0) that defines t=0. Then you want the current 0.1sec. later.