HW Chapter 13

HW Chapter 13 - R is directed along the z-axis The density...

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PHYS4102 HOMEWORK CHAPTER 13 Assigned Thursday, March 24; Due Thursday, March 31. Problem 1. A massless spring of length b and spring constant k connects two particles of masses m 1 and m 2 . The system rests on a smooth table and may oscillate and rotate. Determine Hamilton’s equations of motion. Problem 2. Taylor, Problem 13.11 Problem 3. Taylor, Problem 13.17 Problem 4. Taylor, Problem 13.18 Problem 5. Taylor, Problem 13.27 6102 Problem. Discuss the implications of Liouville’s theorem on the fo- cusing of beams of charged particles by considering the following simple case. An electron beam of circular cross section (radius
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Unformatted text preview: R ) is directed along the z-axis. The density of electrons across the beam is constant, but the momen-tum components transverse to the beam ( p x and p y ) are distributed evenly over a circle of radius p in momentum space. If some focusing system re-duces the beam radius from R to R 1 , find the resulting distribution of the transverse momentum components. What is the physical meaning of this result? (Consider the angular divergence of the beam). Relate your results to the “brightness theorem” of optics. 1...
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