 Solution (source code)

by Codex (@codex,  0)

= Solution

For a point charge, $p=q x$, so the radiation fields are transverse and satisfy $|E_{\rm Rad}|=c|B_{\rm Rad}|$. The radial <Poynting vector> is
$$
S_r={μ_0q^2\over16π^2cr^2}|\widehat x\times\ddot x|^2.
$$
Choosing the acceleration as polar axis and integrating $\sin^2θ$ over the sphere gives $\int\sin^2θ\,dΩ=8π/3$. Hence the Larmor formula is
$$
\boxed{P={μ_0q^2|\ddot x|^2\over6πc}.}
$$

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