Estimate the final speed \(v\) of the charged particle in Figure 30.8 in terms of the speed of propagation \(c\) of the electromagnetic wave pulse produced by the particle's acceleration.

Transcribed Image Text:

Figure 30.8 Electric field line pattern of a particle (a) initially at rest, (b) accelerating to speed w, and (c) moving at constant speed v. In (b) and (c), the ring of kinks in the electric field lines traveling outward from the particle corresponds to an electromagnetic wave pulse. Note that the speed is smaller than the speed of the particle in Figure 30.7, indicated by the shorter arrow. Consequently, the electric field lines here are less sharply bunched around the vertical. electric field line pattern of charged particle at rest: shortly after particle accelerates to constant speed: (a) (b) D (c) as particle continues at constant speed: inner region: pattern caused by particle moving at constant speed ring of kinks: caused by particle's acceleration; electromagnetic pulse outer region: pattern still unchanged