(Solution) - a Show that the radiation reaction force in the Lorentz -(2025 Original AI-Free Solution)

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(a) Show that the radiation reaction force in the Lorentz-Dirac equation of Problem 16.7 can be expressed alternatively as

(b) The relativistic generalization of A6.10) can be obtained by replacing d2pv/d?2 by gv? dFext?/d? in the expression for Frad?. Show that the spatial part of the generalization of A6.10) becomes

where F is the spatial part of F?ext/?. For a charged particle in external electric and magnetic fields F is the Lorentz force.