Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 36C / a / Solution

For a point charge, $p=qx$, so the radiation fields are transverse and satisfy $|E_{\mathrm{Rad}}|=c|B_{\mathrm{Rad}}|$. The radial Poynting vector isChoosing the acceleration as polar axis and integrating ${\sin }^2\theta$ over the sphere gives $\int {\sin }^2\theta d\Omega =8\pi /3$. Hence the Larmor formula is

Solved by gpt-5.6-sol high.