A Non-Radiating, Accelerating Charge G.R.Dixon, 1/17/04
As specified in a previous article, the relativistically correct equation of motion for a tiny spherical shell of charge is: (1) . Presumably no radiation is emitted when . (2) One obvious solution to Eq. 2 is: , (3a) . (3b) A second solution can be , (4a) , (4b) and by then applying the following algorithm (where dt<<1 sec):
t=0 Do da v a t=t+dt Loop The loop can be terminated when v Figs. 1 and 2 plot the computed v
Figure 1
v Figure 2
a Let us stipulate that m
. (5) Fig. 3 plots the computed F
Figure 3
F It is noteworthy in Fig. 2 that a Interestingly enough, in the case of periodic motions Larmor and Abraham-Lorentz produce the same radiated energy per cycle time. This owes to the fact that sin An experiment might settle this disconnect between Larmor and Abraham-Lorentz. For example, a charge could be inserted through a pinhole in one of the plates of a large, parallel plate capacitor. The charge is subject to a constant force while between the plates, and will certainly accelerate. Yet according to Abraham-Lorentz it should not radiate. However, short pulses of radiation might be expected in the pinhole(s), where the radiation term in Eq. 1 is nonzero. |