Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 9.13

Radiation of Electromagnetic Waves

Physics — Landau & Lifshitz · radiation-reaction

Problem

The Abraham–Lorentz formula for the radiation reaction force is

\mathbf{F}_{\text{rad}} = \frac{\mu_0 q^2}{6\pi c} \dot{\mathbf{a}},

where

\mathbf{a} = \ddot{\mathbf{r}}

is the acceleration. (a) Show that this formula is consistent with energy conservation for a charged harmonic oscillator. (b) Estimate the time scale

\tau = \mu_0 q^2 / (6\pi m c)

for an electron, and comment on its physical significance.