Introduction to Electrodynamics · Problem 11.13

Electrodynamics and Relativity — David J. Griffiths

Physics · radiation-from-point-charges

Problem

A positive charge

q

is fired head-on at a distant positive charge

Q

(which is held stationary), with an initial velocity

v_0

. It comes in, decelerates to

v = 0

, and returns out to infinity. What fraction of its initial energy (

\frac{1}{2}mv_0^2

) is radiated away? Assume

v_0 \ll c

, and that you can safely ignore the effect of radiative losses on the motion of the particle. [Answer:

(16/45)(q/Q)(v_0/c)^3