Introduction to Electrodynamics · Problem 11.17

Electrodynamics and Relativity — David J. Griffiths

Physics · radiation-reaction

Problem

(a) A particle of charge

q

moves in a circle of radius

R

at a constant speed

v

. To sustain the motion, you must, of course, provide a centripetal force

mv^2/R

; what additional force (

\mathbf{F}_e

) must you exert, in order to counteract the radiation reaction? [It's easiest to express the answer in terms of the instantaneous velocity

\mathbf{v}

.] What power (

P_e

) does this extra force deliver? Compare

P_e

with the power radiated (use the Larmor formula). (b) Repeat part (a) for a particle in simple harmonic motion with amplitude

A

and angular frequency

\omega

\mathbf{w}(t) = A\cos(\omega t)\,\hat{\mathbf{z}}

. Explain the discrepancy. (c) Consider the case of a particle in free fall (constant acceleration

g

). What is the radiation reaction force? What is the power radiated? Comment on these results.