Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 9.4

Radiation of Electromagnetic Waves

Physics — Landau & Lifshitz · radiation-reaction

Problem

Assuming that the radiation reaction force is Frad=μ0q2v¨/(6πc)\mathbf{F}_{\text{rad}} = \mu_0 q^2 \ddot{\mathbf{v}} / (6\pi c), find the equation of motion for a free charged particle (no external force). Show that there exists a runaway solution in which the acceleration grows exponentially. What happens if Frad=0\mathbf{F}_{\text{rad}} = 0 at t=0t = 0?

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