# emhw17 - Electromagnetic Theory II Problem Set 3 Due 31...

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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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emhw17 - Electromagnetic Theory II Problem Set 3 Due 31...

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