Prefactor of classical electron radius

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SUMMARY

The discussion centers on the derivation of the classical electron radius by equating the energy of the electric field with mec², considering the electron as a sphere of finite extent. It highlights the significance of prefactors (3/5 or 1/2) that arise from different charge distributions, such as constant charge density and constant surface density. The conversation questions the rationale behind ignoring these prefactors while retaining the factor of 4 in the denominator, attributing the latter to physical constants rather than geometric assumptions.

PREREQUISITES
  • Understanding of classical electromagnetism
  • Familiarity with the concept of energy density in electric fields
  • Knowledge of charge distribution models
  • Basic principles of relativistic energy-mass equivalence (E=mc²)
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  • Research the derivation of the classical electron radius in detail
  • Explore the implications of different charge distribution models on physical calculations
  • Study the role of prefactors in physical equations and their significance
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The discussion is beneficial for physicists, particularly those specializing in electromagnetism and theoretical physics, as well as students seeking to deepen their understanding of the classical electron radius and its derivation.

greypilgrim
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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 mec2. 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?
 
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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.
 

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