PHY532 Problem Set 2. Due February 20, 2001

1.

Jackson problem 9.14. In part c evaluate the long wavelength electric dipole, electric quadrupole and magnetic dipole moments only. Note, work in Gaussian units only.

2.

Jackson problem 9.16. Work in Gaussian units. At the end of the calculation also convert your radiation resistance expression into a numerical value in ohms.

3.

Jackson problem 14.14.

4.

Jackson problem 14.15 part a only. Take the nonrelativistic limit and show that you get the long wavelength electric dipole result.

5.

Jackson problem 15.4. For part b, calculate dI/d$\omega$ assuming the radiation does not affect the kinematics. That is the decay product particles are emitted with equal and opposite velocity so that the total momentum remains zero. Energy conservation requires that

$$\omega \gamma$$ (1)

where $\gamma$ = (1 - $\beta^{2}_{}$)^{- 1/2} and $\mbox{\boldmath$\space {\beta} $}$ = $\mbox{\boldmath$\space {v} $}$/c . Next, use the result of Jackson problem 11.21 to get the maximum photon energy E_max allowed kinematically. Then with $\beta$ fixed at the zero radiation value integrate dI/d$\omega$ from zero to E_max/$\hbar$ . Be sure to give numerical values in MeV for the approximate energy loss to photons.