Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 9.15

Radiation of Electromagnetic Waves

Physics — Landau & Lifshitz · radiation-fields-moving-charge

Problem

A charged particle moves along the

x

-axis with velocity

v(t)

and acceleration

a(t)

. Using the Liénard–Wiechert fields, show that in the nonrelativistic limit the power radiated into solid angle

d\Omega

at angle

\theta

to the acceleration is

\frac{dP}{d\Omega} = \frac{\mu_0 q^2 a^2}{16\pi^2 c} \sin^2\theta,

and integrate to obtain the Larmor formula

P = \mu_0 q^2 a^2 / (6\pi c)