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

In summary, we discussed the equations $$P = \frac{\mu \ddot{m}^2 w^4}{12 \pi c^3}$$ and $$\nabla \times M = 0$$, as well as the relation $$\vec K = M \times \hat \rho = M \hat \phi$$ and the values for total current, I, and magnetic moment, M. We also saw that $$|\ddot{m}|^2 = |M \omega^2 l \pi r^2|^2$$ and that this can be substituted into the first equation. However, it is important to note that electromagnetism is not always simple.
  • #1
LCSphysicist
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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
.
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.
 
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  • #2
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: $$P = \frac{\mu \ddot{m}^2 \omega^4}{12 \pi c^3}$$
 

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

1. What is the concept of radiation in a rotating bar?

The concept of radiation in a rotating bar refers to the emission of electromagnetic waves from a rotating object. This radiation is caused by the acceleration of charged particles within the bar, which creates an electromagnetic field that propagates outward.

2. How does the rotation speed of the bar affect the radiation?

The rotation speed of the bar directly affects the frequency and intensity of the radiation. As the speed increases, the frequency of the radiation also increases, resulting in a higher energy output. Additionally, the intensity of the radiation is directly proportional to the square of the rotation speed.

3. What is the difference between radiation from a rotating bar and a stationary bar?

A rotating bar emits radiation due to the acceleration of charged particles, while a stationary bar does not. This is because the acceleration of charged particles is necessary to create an electromagnetic field and produce radiation. Therefore, a rotating bar will always emit radiation, while a stationary bar will only emit radiation if it is exposed to external sources of radiation.

4. Can the radiation from a rotating bar be harmful?

In most cases, the radiation from a rotating bar is not harmful as it is typically in the form of low-frequency electromagnetic waves. However, if the rotation speed is extremely high, the radiation can become more intense and potentially harmful. Additionally, if the bar is emitting ionizing radiation, it can be harmful to living organisms.

5. How is the radiation from a rotating bar used in practical applications?

The radiation from a rotating bar has various practical applications, including in radio and television broadcasting, radar technology, and medical imaging. In these applications, the radiation is harnessed and controlled to transmit information or create images. The frequency and intensity of the radiation can be manipulated to suit specific purposes.

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