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Unformatted text preview: Electromagnetic Theory II Problem Set 3 Due: 31 January 2011 10. Because the action for a relativistic particle moving in an electromagnetic field S part = m integraldisplay dτ + q integraldisplay dτU μ A μ (1) depends on the potentials, it is apparently not gauge invariant. a) Evaluate the particle action corresponding to the gauge transformed potentials A μ → A μ + ∂ μ Λ. b) Last semester you showed that applying Hamilton’s principle to S part led to the correct equations of motion, which are gauge invariant (since they involve the electomagnetic fields). Show that the gauge independence of the equations of motion follows immedi ately from the way Λ enters the result of part a). 11. J, Problem 11.24 12. J, Problem 11.26 13. Solving the motion of a particle in uniform electric and magnetic fields is straightforward, but tedious. The equations of motion dU μ dτ = q mc F μν U ν (2) form a set of four coupled first order differential equations with constant coefficients for the...
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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.
 Spring '08
 Staff

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