Faraday's Disk Dynamo: why is there an emf?

[jpas]

Consider a rotating disk on a uniform magnetic field. Faraday's law states that

$$\epsilon = - \frac{d\phi}{dt}$$

In this situation, $$\vec B$$ is constant and the area of the disk is constant. Hence, the magnetic flux is constant and there should be no emf. What am I missing?

 

[elect_eng]

Consider a rotating disk on a uniform magnetic field. Faraday's law states that

$$\epsilon = - \frac{d\phi}{dt}$$

In this situation, $$\vec B$$ is constant and the area of the disk is constant. Hence, the magnetic flux is constant and there should be no emf. What am I missing?

This question is common and has been discussed in several threads previously.

This is one of those tricky situations that appears paradoxical, but really isn't. This paper provides a good explanation.

Basically, even though the field could be considered constant, the total flux includes area. The area also appears constant at first, but as this paper shows, the conduction path usually chosen is not valid. In reality, the area is changing if a valid conduction path is chosen. And, changing area with constant field gives rise to a flux change.