1.7. Interactive Forces.
Although we have discussed spherical shells of charge, it is generally true that all of the charge increments in any distribution of like-sign charge repel the other increments. If the distribution is to maintain its shape then these electric forces must be mechanically counteracted by some agent (usually implied).
Similarly, the distribution will react against an accelerating agent with a force proportional to –a. As in the case of a spherical shell, the proportionality constant constitutes the distribution’s electromagnetic mass. Note that, given some amount of charge, melecmag will vary from shape to shape. (Typical example: same-charge spherical shells with different radii.)
Finally, regardless of the shape, a distribution will react with a force of (ada/dt) when a is not constant. And the driving agent must counteract this force too if the distribution is to maintain its shape. Whenever da/dt is nonzero there will be radiation.
What is true for any single distribution is also true for two or more distributions separated by space. Each increment of charge interacts not only with every other increment in its own distribution, but also with every increment in the other distribution(s). It is convenient to refer to the net force, that one distribution experiences in the field of other(s), as the interactive force. The net force that a distribution experiences in its own field is then dubbed the self-force.
An external agent must mechanically counteract both the interactive and the self-forces of an overall "shape" if that shape is to remain static. (Special case: two spherical shells of charge at rest in a given inertial frame of reference.) Interestingly enough, if the agent allows the distance between two distributions to vary, then the interactive force does not invariably vary in a simple way with the separation. As will be demonstrated, if the two distributions oscillate in phase then the interactive force of attraction or repulsion may rise and fall in cyclic fashion as the separation is increased. The "wavelength" plays a prominent role regarding what separation produces the maximum interactive force, and this explains in part why certain length rod antennas are more effective radiators than others are.
The configurations (or distributions) and motions that can be imagined are of course practically infinite. But for purposes of computation each distribution can always be approximated as an array of small but finite point charges. And the point charge field solutions, together with the Lorentz force law, can always be used to compute the self-forces and the interactive forces.
In cases of periodic motion it is always found that the net work per cycle expended by the driving agent, to counteract both the self forces and the interactive forces, equals the field energy flux per cycle out through an enclosing surface. The only caveat here is that the net electric and magnetic fields, at points on the enclosing surface, must be computed prior to computing the Poynting vector.