1. Jan 8, 2009

### pentazoid

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

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

3. 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.

2. Jan 9, 2009

### scienture

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

3. Jan 9, 2009