ABSTRACT
Equation 27.36 is valid for any acceleration of the electron. However, it is convenient to describe Equation 27.36 in two different regimes, namely, for nonrelativistic speeds ( / 1)v c and for relativistic speeds v/ 1c( ). The field emitted by an accelerating charge observed in a reference frame where the velocity is much less than the speed of light: that is, the nonrelativistic regime, is seen from Equation 27.36 to reduce to
E r u u v( , ) ( ) ,t e c R
= ( ) × ×[ ]4 0 2πε (28.1) where E(r, t) is the field vector of the radiated field measured from the origin, e is the charge, c is the speed of light, R is the distance from the charge to the observer, u = R/R is the unit vector directed from the position of the charge to the observation point, and v is the acceleration vector of the charge. The relation between the vectors X and u is shown in Figure 28.1.
