ps5 - PHY 504 Problem Set#5 due 1 October 2010 1 A particle...

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Unformatted text preview: PHY 504 Problem Set #5 due 1 October 2010 1. A particle of mass m moves in a uniform magnetic field of magnitude B . (a) Write down a Lagrangian describing this system and the resulting equations of motion. (b) What are the symmetries? What conserved quantities are associated to each? (c) Use Noether’s theorem to obtain expressions for the conserved energy , momentum , and angular momentum in the plane perpendicular to the magnetic field. Write these in both rectangular and polar coordinates. (d) Explain how to solve for the particle’s motion. Obtain the general solution for an orbit in the perpendicular plane of energy E and angular momentum l . 2. For the inverse-square potential ܸ /ݎ ଶ ሺݎሻ ൌ െ݇ V ( r ) = − (a) show that the orbits can have the following forms, depending on the energy E and angular momentum l : ) ( sinh 1 ) ( cosh 1 ) ( cos 1 θ θ β θ θ β θ θ β − = − = − = A r A r A r βθ θ θ ± = − = e r r A r o 1 1 ) ( 1 (b) For what E and l does each of the above types of motion occur? does each of the above types of motion occur?...
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ps5 - PHY 504 Problem Set#5 due 1 October 2010 1 A particle...

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