Revolving disc in a magnetic field

[Bolter]

Homework Statement

Calculate the number of revolution being made per minute (rpm) by the fly-wheel

Relevant Equations

See image attached below

I know that there is a known equation to calculate the magnetic field strength of a rotating disc which I have made use of in here

Do you agree that revs per minute of the disc turns out to be 9337 rpm?

Thanks for any help! Much appreciated

 

[etotheipi]

I'm sure someone else can give a more rigorous derivation, though to derive the initial equation I considered a radial slice of the disk and integrated up all of the incremental emfs along that slice.

That is, $\int d\varepsilon = \int Bv dr = \int B\omega r dr$

which gives $\varepsilon = \frac{B\omega r^{2}}{2} = B\pi r^{2}f$

But to answer your question, yes, I agree.

 

[Bolter]

I'm sure someone else can give a more rigorous derivation, though to derive the initial equation I considered a radial slice of the disk and integrated up all of the incremental emfs along that slice.

That is, $\int d\varepsilon = \int Bv dr = \int B\omega r dr$

which gives $\varepsilon = \frac{B\omega r^{2}}{2} = B\pi r^{2}f$

But to answer your question, yes, I agree.

This is a really nice and simply way of looking at it which I hadn't thought of :)