Addition to 12.11(c): The Stanford Linear Collider (SLC) can accelerate polarized electrons and positrons. The particles collide at the end of two semicircular arcs with radius 0.46 km. The energy of each particle is 45 GeV when the SLC operates at the energy of the Z boson. Suppose that the particles were longitudinally polarized when they entered the arcs. How may times would the particle spins have rotated at the collision point? How would this be a problem if you wanted high longitudinal polarization in the collision?

12.5: This problem illustrates the use of the invariants of the electromagnetic field to simplify the calculation of particle motion in perpendicular E and B fields. However, the simple results are not in the original Lorentz frame. Explain carefully how the results in the original frame are to be obtained. A kinematic diagram may be useful. You do not need to obtain explicit expressions for the motion in the original frame.   12.10: How is this problem related to the earth's Van Allen belt? To the aurora? For reference, the equatorial radii of the inner and outer Van Allen belts are roughly 1.6 and 3.7 earth radii. The zone of maximum auroral activity is centered at lattitude 68°.   12.11: Watch your units! Recall that we are using Gaussian cgs units. See the Appendix on units in Jackson, especially the tables. For reference, e = 4.8 × 10-10 esu, c = 3 × 1010 cm/s, 1 eV = 1.9 × 10-12 erg.

Hint for 12.18: Suppose that and are defined by integrals of and on the spacelike surfaces t = constant and t' = constant, respectively, where the 's are connected by a Lorentz transformation with transformation matrix . Show that you can express ' in terms of and change to the new surface to obtain the integral for .

LD 7: Once you find E as a function of position in the wire from the Lorentz force equation, it is simple to obtain the charge density using Gauss' law, .

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© 1997, 1998, 1999 Loyal Durand