Constant angular speed loop of wire

[darksyesider]

Homework Statement

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?

Homework Equations

$\tau = NIAB\sin\theta$

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?

 

[mfb]

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

 

[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?

 

[mfb]

however, I can't tell which direction they are going in

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

and doesn't it change as the loop rotates?

Sure it does.

 

[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

 

[mfb]

Yeah, I drew a sketch.
How about $F_B = ILB \sin\omega t$?

Looks good.

From my sketch, it seems that all the forces cancel though... hint please

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

 

[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.

 

[mfb]

Looks good.