Homework Help: Eddy currents and torque

1. Feb 20, 2008

EricVT

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

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

3. 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.

2. Nov 27, 2014

ASZarathustra

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

3. Nov 29, 2014

ASZarathustra

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