The Larmor's formula seem too powerful

Question

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:

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?

Answer 1

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.