# Emf of homopolar generator

1. Nov 12, 2009

### Mannix

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

2. Relevant equations
$$\varepsilon=-\frac{d\phi_B}{dt}$$
$$d\phi_B=\vec{B}\cdot \vec{A}$$
3. 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?

Last edited: Nov 12, 2009