# Constant angular speed loop of wire

1. May 21, 2014

### darksyesider

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

You have a loop of wire (dimensions c and d) which is oriented vertically on the y axis (the y axis splits the rectangle in two equal pieces), and rotates about the y axis at constant angular $\omega$. The magnetic field is in the +i direction.

What would be the torqque needed to have the loop rotate at a constant w?

2. Relevant equations

$\tau = NIAB\sin\theta$

3. The attempt at a solution

$\mathcal{E} = B(cd)\omega \sin( \omega t )$ from Faraday's law.

$I = \dfrac{B(cd)\omega\sin (\omega t)}{R}$

I am not sure how to proceed from here...what do I set the torque, $\tau = NIAB\sin\theta$ equal to?

Last edited: May 21, 2014
2. May 21, 2014

### Staff: Mentor

You have a current flow in a magnetic field. Do you see any forces from this?

3. May 21, 2014

### darksyesider

I see $F_B = ILB\sin\theta$, however, I can't tell which direction they are going in, and doesn't it change as the loop rotates?

4. May 21, 2014

### Staff: Mentor

Did you draw a sketch?
In principle, you don't need that, if you use the cross-product..

Sure it does.

5. May 21, 2014

### darksyesider

Yeah, I drew a sketch.
How about $F_B = ILB \sin\omega t$?
From my sketch, it seems that all the forces cancel though... hint please

6. May 22, 2014

### Staff: Mentor

Looks good.

Then your sketch might be wrong. As I don't have the sketch, I can't say which part.

7. May 22, 2014

### darksyesider

OH wait, would it be:

$\tau = IA\times B = IAB\sin (\omega t)$
$I(cd)B\sin\omega t$

Then plug in I from the equation in the original post ? i am fairly confident on this now.

8. May 22, 2014

Looks good.