How Does a Rotating Disk Generate Voltage in a Magnetic Field?

[Mannix]

Homework Statement

A little bit of background, my Phys 2 w/Calc class has only covered up to chapter 30(Inductance) in Fundamentals of Physics by Halliday/Resnick. I'm not even sure why this was my homework(turned it in partially completed with written physical reasoning, a picture, and a couple equations). Only after turning it in did I find out the name of the device and the possibility that it may have required more than was covered thus far in class(I just figured that I had missed something). Review of the notes handed out yielded no mention of the Lorentz force.

The question is as follows: A conducting disk of radius r rotates about a perpendicular axis at the center of the disk at angular velocity ω with a magnetic field of magnitude B parallel to the axis covering the disk. What is the voltage difference between the center and the edge of the disk in terms of B, ω, and r?

Homework Equations

$$\varepsilon=-\frac{d\phi_B}{dt}$$
$$d\phi_B=\vec{B}\cdot \vec{A}$$

The Attempt at a Solution

Physically I figured the field would cause electron "drag" with the electrons on the edge being dragged a longer linear distance per unit time. This would result difference in the emf/potential/voltage. Following this line of reasoning the equation would break down to V=Const*B*ω*r. I tried applying the above equations but there was no $${d\phi_B}$$

Am I wrong in thinking this cannot be done with Faraday's law? Does my reasoning hold true at all in reality?

 

[BigJDubs]

In the end I wrote that I could not come up with a closed form equation and left it at that.If you need any clarification feel free to ask.