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So the Larmor formula tells us the total power radiated by an accelerating point charge that doesn't go too fast with respect to the speed of light is $P=\frac{2}{3}\frac{q^2 a^2}{c^3}$ (written in CGS units).

Now my question is: Is there an intuitive explanation behind this expression as to why the coefficient of $\frac23$ is the way it is except for the argument that it came from integrating over solid angle?

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  • $\begingroup$ Does "intuitive" mean without mathematics? $\endgroup$ Mar 30, 2022 at 16:30
  • $\begingroup$ I kind of was hoping that the quantity $\frac{q^2 a^2}{c^3}$ has some physical interpretation to it in and of itself, in the sense that 2/3 of it corresponds to the power radiated by an accelerating point charge and another 1/3 corresponds to something else, perhaps some quantity I've never heard of before, hence the post on StackExchange. But I suppose it's nonsense. Thank you for your response. $\endgroup$
    – icannotcan
    Mar 31, 2022 at 13:33

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The 2/3 comes from the average value of $\sin^2\theta$ in the angular integration.

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