Classical Electrodynamics · Problem 14.8

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · relativistic-bremsstrahlung-straight-line

Problem

A swiftly moving particle of charge

ze

and mass

m

passes a fixed point charge

Ze

in an approximately straight-line path at impact parameter

b

and nearly constant speed

v

. Show that the total energy radiated in the encounter is

\Delta W = \frac{\pi z^4 Z^2 e^6}{4m^2 c^4 \beta}\left(\gamma^2 + \frac{1}{3}\right)\frac{1}{b^3}

This is the relativistic generalization of the result of Problem 14.7.