Given two spherical shells of charge, q1 and q2 on the x-axis and at separation L, the charges interact. Each charge increment in q1 experiences a force from every charge increment in q2, and vice versa. Some agent must counteract these interactive forces if the radii are to remain constant. And of course the agent must also counteract the self-forces.

If the charges oscillate in phase, then the constraining agent may expend a net amount of work per cycle to counteract the interactive forces. It turns out that, when the charges oscillate, this work per cycle does not attenuate monotonically with increasing separation. Fig. 6_1 shows the actual, computed work per cycle over the range of separations .5l<L<3l. Reference Appendix 6_1. Note that at selected separations the work per cycle is actually negative. At these separations the interactive forces collectively do a net amount of work per cycle on the driving agent! Of course the driving agent always does a positive amount of work per cycle in the course of counteracting the radiation reaction forces.

As might be expected, we can compute the energy flux per cycle time through an enclosing surface, at various values of L. Reference Appendix 6_2. If we subtract out the work per cycle expended to counteract the radiation reaction force, then we should get the same result as the work expended to counteract the interactive forces. Fig. 6_2 plots the computed energy flux per cycle time, minus the radiative force's work per cycle, again over the range .5l<L<3l. Note that the plot is virtually identical to Fig. 6_1. The negative flux at selected values of L indicates that this part of the total energy flux per cycle actually flows in through the surface!