Electrodynamics and Relativity — David J. Griffiths
Physics · radiation-reaction
Problem
(a) Repeat Prob. 11.19, but this time let the external force be a Dirac delta function: F(t)=kδ(t) (for some constant k). [Note that the acceleration is now discontinuous at t=0 (though the velocity must still be continuous); use the method of Prob. 11.19(a) to show that Δa=−k/mτ. In this problem there are only two intervals to consider: (i) t<0, and (ii) t>0.]
(b) As in Prob. 11.30, check that energy is conserved in this process.