# (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

where r_{min} is the closest distance of approach (root of E ? V ? L^{2}/2mr^{2}), L = mbv_{0}, where b is the impact parameter, and v0 is the incident speed (E = mv^{2}_{0}/2).

(b) Specialize to a repulsive Coulomb potential V(r) = zZe^{2}/r. Show that ?W can be written in terms of impact parameter as

where t = bmv^{2}_{0}/zZe^{2} 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

(d) What changes occur for an attractive Coulomb potential?

## Step by Step Answer:

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