emhw11 - Electromagnetic Theory I Problem Set 11 Due: 14...

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Electromagnetic Theory I Problem Set 11 Due: 14 November 2011 41. In studying a quantum particle in the presence of an electromagnetic Feld we used the lagrangian L = 1 2 m ˙ r 2 + q ˙ r · A ( r ,t ) ( r ,t ) (1) When there is time dependence we showed near the beginning of the course that the relation between Felds and potentials is B ( r ,t ) = ∇ × A ( r ,t ) , E ( r ,t ) = −∇ φ ( r ,t ) A ∂t ( r ,t ) (2) a) Show that Lagrange’s equations of motion with this Lagrangian imply Newton’s equation with the Lorentz force on the right side. F = q E + q v × B (3) b) Derive the hamiltonian for this system. c) Repeat the discussion of parts a) and b) for the relativistic Lagrangian obtained by replacing the nonrelativistic kinetic energy term in L as follows 1 2 m ˙ r 2 mc 2 p 1 r 1 ˙ r 2 c 2 P (4) 42. J, Problem 5.25. 43. J, Problem 5.32
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This note was uploaded on 01/08/2012 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.

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emhw11 - Electromagnetic Theory I Problem Set 11 Due: 14...

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