Question

An electron is released from rest at a large distance ro from a fixed nucleus of charge Ze. Assume the electron is a classical point charge with speed v «c and that the radiation reaction force on the electron is negligible. (a) What is the angular distribution of the emitted radiation, dP/dN? Express your answer as a function of i (the magnitude of the electron's acceleration), o (the angle between v and the vector that points from the electron location to the observation point), and constants. (b) How is the emitted radiation polarized? (c) What is the radiated power P when the electron is a distance r from the nucleus? Express your answer as a function of r and constants. (d) In the limit ro + oo, what is the total energy E radiated by the time the electron is a distance r from the nucleus? Express your answer as a function of r and constants.

Answer 1

Answert. Given that . (a). The electric duphe fields are a H= CK2 (xp) ekr (1 ) c= the f Pavelmentet enampil-P]6s - ) And Recon- Ext] in the radration Zone, field will taken limiting formis, : HCR (MXP) e her .. and E= zo txin care inte ha [ (map) on) Here angular distribution has typical dup de pattern the secret po any 321

(b) The emitted radiation is polarised by dipole distributions contributed by dipole oscillating parallel to the z axis (m=0) . and the othe perpendicular.

(c) Radiation power=

1/2 E4

Since the negative electron and positive nucleus constitute a coloumbic interaction, an electric field will set up by the same interaction,

$P=\frac{1}{2}\epsilon _{0}((\frac{1}{4\Pi \epsilon _{0}})(\frac{Ze^{2}}{r^{2}}))^{2}$