As for the webpage title, it could be: What is the Radiation of a Rotating Bar?

[LCSphysicist]

Homework Statement

A bar with magnetization M parallel to its symmetric axis rotates (axis z) about an axis perpendicular to it (let's say, axis x). What is the power radiated? w/c >> l
radius r

Relevant Equations

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Ok. I was writing a big text about it, but i will summarize it.

We know that $$P = \frac{\mu \ddot{m}^2 w^4}{12 \pi c^3}$$

We know, as well, that $$\nabla \times M = 0$$.

Also, $$\vec K = M \times \hat \rho = M \hat \phi$$

Total current, I = $K l = M l$.

Magnetic moment, so, $$M l \pi r^2 $$

So, $$|\ddot{m}|^2 = |M w^2 l \pi r^2|^2$$

Finally, just subtitute it on the first equation...

Is this right??

I am asking because it is, after all, electromagnetism... It is never that easy.

 

[jbsteele]

Yes, your summary is correct. The only thing to note is that you need to use the angular velocity, $\omega$, instead of the linear velocity. So the equation should be: $$P = \frac{\mu \ddot{m}^2 \omega^4}{12 \pi c^3}$$