Calculating Induced Current in a Circular Loop Inside a Solenoid

[pentazoid]

Homework Statement

A long solenoid of radius a , is driven by an alternating current , so that the field inside is sinusoidal: B(t)=B₀cos(omega*t)z-hat. A circular loop of wire, of raduis a/2 and resistance R, is placed inside the solenoid and coaxial with it. Find the current induced in the loop , as a function of time.

Homework Equations

I=$$\epsilon$$/R
$$\Phi$$=$$\int$$B$$\cdot$$ da

$$\epsilon$$=$$\int$$E$$\cdot$$dl=$$\int$$(dB/dt)$$\cdot$$da

The Attempt at a Solution

dB/dt=-omega*B₀sin(omega*t)z-hat
$$\epsilon$$=$$\int$$omega*B₀sin(omega*t) da, since the area of a circle is pi*r², da is just pi*r²

I=omega*B₀*sin(omega*t)*$$\pi$$a²/(R)

episilon is supposed to be the electromotive force BTW.

 

[scienture]

Excuse me, but I think among 'da=pi*r^2', r should be a/2

 

[pentazoid]

Excuse me, but I think among 'da=pi*r^2', r should be a/2

What about my remaining solutions?