How do I calculate the torque of an eddy current brake?

[EricVT]

Homework Statement

An electromagnetic "eddy current" brake consists of a disc of conductivity \sigma and thickness d rotating about an axis passing through its center and normal to the surface of the disc. A uniform B is applied perpendicular to the plane of the disc over a small area a^2 located a distance P from the axis. Show that the torque tending to slow down the disc at the instant its angular speed is W is given approximately by \sigma*W*d*[B*P*a]^2

The Attempt at a Solution

I assume that you need to calculate the force on the disc at the small section a^2 and then from this a torque can be easily found. Can you say:

F=q\cdot(E+v \times B)

And since the electric field is motional make this

F=q\cdot(E+v \times B)=q\cdot(v \times B+v \times B)=q\cdot(2v \times B)

v \times B = BPW

F=2qBPW

If so, how do you find the charge enclosed inside of the little region of volume d*a^2? I don't quite see how the conductivity plays into all of this, or where the second factor of B comes from in the solution.

Any help would be appreciated.

 

[ASZarathustra]

I'm bumping this (I hope there's nothing wrong with me doing so). I'm having the exact same problem as well.

 

[ASZarathustra]

Anyone? This problem is due soon, and I'm having trouble getting beyond that point.