8. The Effect of Charge Separation.
In this article the effect of varying the separation between two collinear, oscillating charges is investigated. ‘D’ denotes the separation, and ‘W(D)’ denotes the work done per cycle to drive the two charges when their separation is D. At any given separation the charge motions are
, (8_1)
. (8_2)
W(D) is computed over the range
. (8_3)
Each charge is 1 coul, and the amplitude of oscillation is 1 meter. wA, the maximum speed, is .001c at all separations.
Fig. 8_1 plots the computed values of W(D), with D given in wavelength units.
Figure 8_1
W(D), Two Collinear Oscillating Charges
Noteworthy are the facts that (a) the first maximum occurs at a separation of 1.44
l, and (b) the second minimum occurs at 1.96l.The work done per oscillation to drive either charge when it is isolated is
. (8_4)
Twice this amount is displayed as a blue line in Fig. 8_1. The work required to drive the two charges in tandem, over the range of separations specified in Eq. 8_3, oscillates around this reference value. Of course the energy flux per cycle through a surrounding surface equals W(D) at all separations.
The two charges constitute an antenna. When W(D) is greater than 2Wisolated then there is positive gain. And when W(D) is less than 2Wisolated there is negative gain (or positive loss). Of course strictly speaking energy is neither gained nor lost. The driving agent must simply expend more power (to counteract the radiation reaction and interactive forces) at some separations than at others. As usual, the inertial reaction force plays no role in the computation of W(D), since –FInertReactv integrates to zero over any given cycle time.