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