Deduce Eq. 11.100 from Eq. 11.99, as follows: 

(a) Use the Abraham-Lorentz formula to determine the radiation reaction on each end of the dumbbell; add this to the interaction term (Eq. 11.99). 

(b) Method (a) has the defect that it uses the Abraharn-Lorentz formula--the very thing that we were trying to derive. To avoid this, smear out the charge along a strip of length L oriented perpendicular to the motion (the charge density, then, is λ = q/L); find the cumulative interaction force for all pairs of segments, using Eq. 11.99 (with the correspondence q/2 → λdy₁, at one end and q/2 → dy₂ at the other). Make sure you don't count the same pair twice.