(a) Generalize the circumstances of the collision of Problem 14.5 to nonzero angular momentum (impact parameter) and...
Question:
(a) Generalize the circumstances of the collision of Problem 14.5 to nonzero angular momentum (impact parameter) and show that the total energy radiated is given by
![image](https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2022/11/636a56f09435c_456636a56f083e6a.jpg)
where rmin is the closest distance of approach (root of E ? V ? L2/2mr2), L = mbv0, where b is the impact parameter, and v0 is the incident speed (E = mv20/2).
(b) Specialize to a repulsive Coulomb potential V(r) = zZe2/r. Show that ?W can be written in terms of impact parameter as
![image](https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2022/11/636a56f100ca3_456636a56f0e4973.jpg)
where t = bmv20/zZe2 is the ratio of twice the impact parameter to the distance of closest approach in a head-on collision. Show that in the limit of t going to zero the result of Problem 14.5b is recovered, while for t >> 1 one obtains the approximate result of Problem 14.7a.
(c) Using the relation between the scattering angle 0 and t (= cot ?/2), show that ?W can be expressed as
![image](https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2022/11/636a56f1607bd_457636a56f15033f.jpg)
(d) What changes occur for an attractive Coulomb potential?
Step by Step Answer: