Self-Force for Longitudinal Rotational Motion

Abstract

We consider the dumbbell charge system, consisting of two like charges q _e /2 rotating about a fixed center, in such a way that its axis always lies perpendicular to a radial line from the center of rotation passing through its midpoint, as shown in Fig. 9.1. As in the last chapter, both A and B have constant speeds. Although the velocities of A and B are not always exactly parallel to the axis joining them, we do not have to worry about changing FitzGerald contractions during the motion, as we did in Chap. 7 (where the whole system was changing length all the time), because each of A and B always has the same speed. So we can assume a fixed length for the system, but there is a question about what the fixed length should be, because we expect it to be contracted in some way as compared with its length when stationary relative to some inertial frame. We shall nevertheless denote the length by d for the moment, and return to the question of its value at the end of the calculation.