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According to Larmor, accelerated charges will radiate power (Watts): Larmor

So that means if electrons travel in circle then they will endlessly radiate power because of their constant acceleration.

Suppose we have a current going through a circular coil and connected to itself so the current runs forever. If we want the radiation generated by such an infinite coil then we have:

$$ \nu =\frac{\sqrt{\frac{c}{{{\epsilon }_0} h}} \left| x\right| }{\sqrt{6}\, \sqrt{{\pi} }\, \left| r\right| } $$

Or: Larmor's Frequency vs Current Second

Where:

  • $a = c^2/r$ (assuming electrons travel at c)
  • $q = 1\;\mathrm{C}$ (Coulomb)
  • $h$ = Planck's constant (in Joules seconds)

This seems like a strong radiation for such a small current: EM Spectrum

How is this possible?

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    $\begingroup$ A steady current in coil does not radiate. Where is the graph and equation taken from? $\endgroup$
    – mike stone
    Jun 4 at 11:54

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You're grossly overestimating the speed at which electrons travel in a wire. While the signal may travel near the speed of light, the individual charges move much slower.

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  • $\begingroup$ Maybe but even 0.1 * c doesn't change the order of magnitude by much. $\endgroup$
    – Phil Bouchard
    Jun 4 at 22:22
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    $\begingroup$ That's still orders of magnitude faster than it should be. Refer to the question I linked. $\endgroup$
    – Logan J. Fisher
    Jun 4 at 22:26
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    $\begingroup$ unfortunately (for your estimate) the velocity of the electron is the drift velocity. en.wikipedia.org/wiki/Drift_velocity we are talking of about ~um/s. So your calculation are 0.000[..help yourself...]00001 * c $\endgroup$
    – EarlGrey
    Jun 5 at 11:24

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