Rotating beam in magnetic field.

[center o bass]

Homework Statement

We have a beam of length L which is rotating with frequency f about one of its endbpoints in a constant magnetic field B, normal to the rotationplane of the beam.

a) How big is the induced electric field in the beam?
b) How big is the induced voltage between the endpoints of the beam?
c) Repeat the calculation if the beam is rotating about it's midpoint with the same frequency.

Homework Equations

$$\oint \vec{E} \cdot \vec{dl} = - \frac{d\phi _B}{dt}$$
Is Faraday's law even applicable here? I don't see how i can form a convenient loop
and I don't see that there will be any flux-change since B is uniform in the plane of rotation.

[tex]F = q(\vec{v} \times \vec{B}[tex]
Lorent'z force equation seems a bit more promising, but I'm not really sure how to apply it properly.

The Attempt at a Solution

I'm really stuck here. I don't see how to use Faraday's law since I don't see any flux-change in the problem.

Lorentz I guess lorentz force law could be used to find the work done on the charges in the beam, but since it is only a beam the charges will not go trough any loop, so the work on the charges would depend on what distance from the end of the beam the charges are located.

Need some help.

 

[Mandeep Deka]

Well, if you want get it through Faraday's law, you can definitely find a loop for it.
Say for example you consider some segment of the beam at a distance 'x' from the point of rotation, then the elementary charge in this segment covers a circular path with radius 'x', which is your Faraday's loop!
Then you get your induced electric field for that elementary segment, and hence can integrate it to find the answer!

 

[center o bass]

But then where is the magnetic fluxchange trough that loop? The way I see it, that elementary charge would act like a current loop with radius x. But I still don't see that we have any change in the Bfield.

so then $$\oint \vec{E}\cdot \vec{dl} = 0$$ anyhow.

I did however forget to mention that the beam was conducting! Does this have any effet on the problem?