# Intuitive explanation for coefficient in the Larmor formula

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?

• Does "intuitive" mean without mathematics? Commented Mar 30, 2022 at 16:30
• 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. Commented Mar 31, 2022 at 13:33

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