Prefactor of classical electron radius

[greypilgrim]

Hi,

Assuming the electron is a sphere of finite extent, the classical electron radius is derived by equating the energy of the electric field with m_ec². For the computation of the field energy, we have to assume a charge distribution. Both constant charge density and constant surface density lead to prefactors (3/5 or 1/2) which are somehow just ignored.

Why? If we are only interested in the order of magnitude, why drop these prefactors but keep 1/4?

 

[rumborak]

I think it's just for "vague ballpark" calculation, yeah, since the prefactor depends on rather arbitrary assumptions (charges are on surface, or equally distributed). Regarding the factor 4 in the denominator, that one is likely left in there because it comes from the other physical constants, not the geometrical assumptions.