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Rotating Charge

  1. Dec 1, 2009 #1
    Hi I just read this in an introductory physics book "However, a spinning ball of charge would violate the laws of relativity and other physical laws." It was in a section on electron "spin".

    Is that true? Couldn't I take a metal ball and put some charge on it and spin it up? Would the centripetal acceleration of the ball cause it to slow down because of the emission of EM radiation? Would the ball really stop or just slow down?

    Even if that's the case, what does that have to do with relativity? Or should I be thinking general?

  2. jcsd
  3. Dec 1, 2009 #2
    The emission of radio frequencies from a charged particle happens only when we try to accelerate that charge. If no forces are applied to the charged particle, it will not radiate any EM radiation at all, and will continue on its course unperturbed (in vacuo).
    Relativity is relevant, because the emission of the EM radiation places a limit on how fast we can make these charged particles travel. For example, if we have an electron in the particle accelerator going 98% the speed of light, the more magnetic energy we apply to that charge, the more will get radiated off as radio waves and will not cause the electron to move much faster than it is already.
    Helpful? (Y/N)
  4. Dec 1, 2009 #3
    Assume that the electron is a rotating sphere of radius R. Its angular momentum (spin) around the z-axis is S=Iω, where I is the electron's moment of inertia.
    You already know that S must be equal to hbar/2. Thus hbar/2 = mRu . Now use the classical electron radius R=2.8x10^-15 m and you 'll see that u >> c .
  5. Dec 1, 2009 #4
    You're right! thanks!

    How very strange...it's something I never would of thought of. cool.
  6. Dec 1, 2009 #5


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    What if we think at the sphere as being a single loop coil? I'm pretty sure that we will have an magnetic field generated around the ball. As far as the angular velocity is constant we should only have an constant magnetic field, just as we would have a constant current through the imaginary coil. Some energy will be stored in the magnetic field. If we try to change the rotational speed (increase or decreasing it), the sphere should oppose these variation just as an inductor is opposing to the current variations. So i guess the sphere should behave like having an increased inertia.
    Sure that the charges should emit electromagnetic radiation even when the angular velocity is constant, with a proportional wavelength , and maybe the energy stored as magnetic field will be radiated as EM waves...
    Interesting question! Somebody really should do some serious experiences in this matter...(what edition was the book , 40'? )
    You know :"The only source of knowledge is experience" all the rest are fables..
  7. Dec 2, 2009 #6
    It was a first edition book, a couple of years old. I guess they packed a lot of information into that one sentence!

    So I guess that means that anything with charge that is accelerating at all will act like its motion is being damped since light will carry away all of its energy and angular momentum.
  8. Dec 2, 2009 #7


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    i'm not too familiar with the cyclotron radiation effect, but wouldn't be logical if an electric charge would radiate only when decelerates? Why it would lose its energy while accelerates?

    Earth has a pretty strong electric field (like 200v/m), so that's mean that its motion it is slowed down because of is radiation loss? i just can speculate on this...
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